Quantitative Ability: (Practice Exercise-III)

QUANTITATIVE
ABILITY
(Practice Exercise-III)
This book is a part of set, not be sold separately.

Contents
Exercise - 1 ... 5 - 10
Exercise - 2 ... 11 - 17
Exercise - 3 ... 18 - 23
Exercise - 4 ... 24 - 28
Exercise - 5 ... 29 - 35
Exercise - 6 ... 36 - 41
Exercise - 7 ... 42 - 48
Exercise - 8 ... 49 - 53
Exercise - 9 ... 54 - 58
Exercise - 10 ... 59 - 64
Answers ... 65 - 67
QUANTITATIVE ABILITY
EXERCISE – 1
No. of Questions : 25 Time : 50 min
1. A knock-out tournament is a tournament where, out of the two teams that play
in any match, the one that loses gets eliminated from the tournament. The
matches are played in different rounds where, in every round, half the teams
get eliminated from the tournament. If there are 511 matches played in a knock-
out tournament, how many rounds in all are played in the tournament?
(1) 9 (2) 10
(3) 23 (4) None of these
2. In the figure below, the diameter AB of a circie, with center O, intersects
another chord PQ of the circle at M. If BMP = 79°, OQ = QM and R is a point
on the circle, which of the following is not a possible value of ORM?
M
A B
O
(1) 18° (2) 15°

(3) 12° (4) 24°
3. A solid right circular cone is cut parallel to its base to form a smaller cone and
a cone frustum whose volumes are in the ratio 8:19 respectively. If the ratio of
the height of the original cone to the diameter of its base is 2:3, what is the ratio
of the total surface area of the original cone to the sum of the total surface
areas of the smaller cone and the frustum?
(1) 6 : 7 (2) 5 : 6
(3) 3 : 4 (4) 2 : 3
5
4. What is the hundreds digit of the number of 5100

(1) 2 (2) 1
(3) 6 (4) 0
5. In the figure below, BD : DC = 1 : 3 and AE : EC = 1 : 1. Find AM : MD
C
B D
(1) 3 : 2 (2) 3 : 1
(3) 2 : 1 (4) 4 : 1
6. The Kolkata Mail leaves Trivandrum everyday at 12:00 noon and reaches
Kolkata exactly three days later. Also, the Trivandrum Mail leaves Kolkata at
12:00 noon everyday and reaches Trivandrum exactly three days later. Not
counting the trains just starting or just leaving the platform when a train
leaves or arrives, how many Kolkata Mails will one cross when traveling by
Trivandrum Mail?
(1) 2 (2) 3
(3) 5 (4) 9
7. Find the value of k so that the area of the triangle formed by the line kx + 3y –
12 = 0 and the coordinate axes is 12 sq. units.
(1) ±3 (2) ±2
(3) ±4 (4) ±5
8. In ABC, AB = 3 cm and AC = 4 cm. If D is a point an BC, such that AD bisects
A and BD > 2.15 cm, which of the following is a possible value for A?
(1) 60° (2) 75°
(3) 90° (4) 120°
6
9. Find the product of all the factors of 432.

(1) 43212 (2) 43220
25
(3) 186624 (4) 43210
10. Thirteen straight lines are drawn in a plane such that no two lines are parallel
to each other and no three lines are concurrent. A circle is drawn in the same
plane such that all the points of intersection of the above lines lie inside the
circle. How many distinct regions are formed in the plane?
(1) 92 (2) 118
(3) 105 (4) 78
11. Kiran had the habit of taking some amount with him to the temple every Sunday
and distributing it among poor people. Being an egalitarian at heart, he always
made it a point on any given Sunday to distribute equal amounts to every poor
person that he helped (the amount per person need not be the same every
week). On the first Sunday of October, he took Rs.340 with him and returned
home with Rs.4 and on the second Sunday he took Rs.650 with him and returned
with Rs.10, having donated to exactly the same number of people as on the
first Sunday. On no day does Kiran return with an amount more than the
amount donated per person on that day. Find the maximum possible number of
people who received the donations on the two Sundays put together.
(1) 32 (2) 8
(3) 16 (4) 61
12 A test contains 100 questions, a student scores 1 mark for a correct answers,
1 1
– for a wrong answers, and – for not attempting a questions. If Ajay gets
4 8
a net score of 70 in this test, the number of questions answered wrongly by
him cannot be more than
(1) 6 (2) 15
(3) 12 (4) 24
13. A straight pole P subtends a right angle at a point X of another pole at a
distance of 30 m from P, the top of P being 60° above the horizontal line joining
the point X to the pole P. Find the length of pole.
40
(1) 40 3 m (2) m
3
(3) 120 m (4) 20 3 m
7
14. Shyam constructs a certain wall, working in a special way, and takes 12 days to
complete it. If Ln is the length of the wall (in metres) that he constructs on the
nth day, then
Ln = 2n, 0  n  4
= 8, for n = 5
= 3n–7, 6  n  12
Find the total length of the wall that he constructs in the first 10 days.
(1) 31 metres (2) 35 metres
(3) 93 metres (4) 113 metres
15. The following algorithm is executed.
Step 1 x = 1, y = 2 z = 1, n = 0, m = 0
Step 2 z=x–y
Step 3 y= x
Step 4 x= z
Step 5 n=n+1
Step 6 If n < 200, then go to step 2.
else,
go to step 7.
Step 7 m = x + y– z
Step 8 : STOP
Find the final value of m

(1) –5 (2) –1
16. A cylindrical drum A and a cylindrical tank B are such that their heights are in
the ratio 3:1 and radii in the ratio 1:3 respectively. Pipe P can fill A in 1 hour and
pipe R can fill B in 3 hours. Both A and B are initially empty and A is placed in
B and their respective filling pipes are opened at 9:00 a.m. If water overflowing
from A falls into B. at what time does water start overflowing from B?
(1) 10:30 a.m (2) 10:50 a.m.
(3) 10:40 a.m (4) 11:10 a.m
8
17. If 10k = 12m + 10, where m and k are integers, what is 4(k–1)m ?
(1) 4 (2) 16
(3) 1 (4) Cannot be determined
18. Find the approximate sum of the first ten terms of the series—
2 16 78 320 1210
+ 2 + 3 + 4 + 5 + .......
31 3 3 3 3
217 213
(1) (2)
4 4
209 225
(3) (4)
4 4
19. If a + b = c, b + c = d and c + d= a, where a, b, c and d are integers and b is
positive, then what is the maximum value of a-2b + 3c - 4d?
(1) -5 (2) -6
(3) -7 (4) -9
20. There are seven boxes numbered from 1 to 7 and 30 identical balls. In how
many ways can these 30 balls be distributed among these seven boxes such
that each box contains at least one ball and no two boxes contain the same
number of balls?
(1) 5040 (2) 10080
(3) 15120 (4) 20160
21. PQ is the diameter of the circle with centre O. If QOS = 15°, POT = 85°, then
find the measure of TRP.
E
D
85º
15º
A
O B C
(1) 20° (2) 25°

(3) 35° (4) 45°
9
22. N marbles can be distributed equally among P people, where N > P. What is the
number of values that N can assume such that P > 1 and 2 < N + P < 100?
(1) 71 (2) 72
(3) 73 (4) 74
23. A teacher wrote the numbers 1 to 31 on the black board in their binary form.
Find the total number of 1’s that are there on the black board.
(1) 80 (2) 32
(3) 40 (4) 31
24. Coffee beans of two different qualities are mixed and sold at 20% profit. If the
higher quality beans are sold at the above price, then the loss is 4%. If the ratio
of lower quality and the higher quality beans in the mixture is 5:2, then what is
the percentage profit when the lower quality beans are sold at the same price?
3 2
(1) 29 % (2) 29 %
5 5
(3) 30% (4) None of these
25. If x is real, then the maximum value of y = 2(2 – x)(x + x 2 + 9 ) is
(1) 9 (2) 13
(3) 17 (4) 11
Score Table
Total Questions Total Attempts Correct Attempts Wrong Attempts Score
+1 –1/3
25
10
EXERCISE – 2
1. Robin, the cook, can cut either 120 carrots or 72 potatoes or 60 beetroots in t
minutes. One day, during the first K minutes, he spent an equal amount of time
cutting each of the three types of vegetables. However, in the next K minutes,
he cut exactly n carrots, n beetroots and n potatoes. If he cut a total of 282
vegetables during the first 2K minutes on that day, what is the value of «?
(1) 225 (2) 75
(3) 45 (4) 135
2. Digits of a 3 digit number in base 11 get reversed, when expressed in base 9.
Which of the following lists all such numbers expressed in base 11?
(1) 243, 467 (2) 302, 604
(3) 203, 406 (4) 203, 406, 609
3. What is the tan of the acute angle between the lines 6x – 2y + 4 = 0 and
6x – 3y – 15 = 0?
1 1
(1) (2)
7 3
1
(3) (4) 1
2
4. If the average height of all ten girls in a class is 5.5 feet, and the average height
of all five boys is 5.8 feet, then the average height of all the students will be:
(1) 5.3 feet (2) 5.65 feet
(3) 5.6 feet (4) 5.7 feet
11
DIRECTIONS for questions 5 and 6: Answer the questions on the basis of the
information given below.
Let S = {a1, a2, a3, a4,....a967}, where ai = 1 for all i(1  967). Now the following
algorithm is performed upon the elements of S.
Step 1: START
Step2: k = 1
Step 3: i = l
i
Step 4: If remainder of  0
k
then ai = ai (–1)
Step 5: i = i + !,
Step 6: If i 967, go to step4
Step 7: k = k + 1
Step 8: If k 967, go to step 3
Step 9: STOP
5. Find the value of a671.
(1)276 (2)1638
(3)1 (4) None of these
6. Find the value of a1+ a2 + a3....a967.
(1) – 905 (2) –1012
(3) –1012 (4) –905
7. From PaschimGhat and PoorabGhat, which are on the same bank of a straight
stretch river Jamna, Baiju and Gauri start rowing their boats towards each
other. Gauri starts from PaschimGhat at 1:10 am and Baiju starts from PoorabGhat
at 1:00 am. They reach DakkhinGhat, which is on the same bank, simul-
taneously at 1:35 am. It is known that in still water, Gauri rows the boat at only
one-third the speed at which Baiju rows. If Gauri had to row only half the
distance that Baiju had to row, then find the ratio of Gauri’s rowing speed (in
still water) to the speed of the flow of the river.
(1) 3:11 (2) 17:11
(3) 51:11 (4) Either (1) or (2)
12
8. The prices of an apple, a mango and a custard apple are Rs.5, Rs.6 and Rs.4
respectively. If Manas spent Rs.P, Rs.2P and Rs.3P on the three kinds of fruits
respectively, what is the minimum possible total amount he could have spent
in purchasing the three varieties of fruits?
(1) Rs. 180 (2) Rs. 60
(3) Rs. 240 (4) Rs. 360
9. There were 150 questions in CAT 2003, where 1 mark was awarded for every
correct answer and 1/3rd mark was deducted for every wrong answer. A certain
number of students, whose total number of attempts were all different, got the
same mark of 50. Find the maximum number of such students possible.
(1) 26 (2) 24
(3) 35 (4) 25
10. What is the value of ‘x’ so that the number “6952x368” is exactly divisible by
11? (x denotes a singie, digit)
(1) 5 (2) 3
(3) 2 (4) 6
11. There are M positive numbers and the average of each possible pair of these
numbers is found. If the average of all these averages is N, what is the average
of the M numbers?
M+N
(1) N (2)
2
M
(3) M+N (4)
N
12. The area of the trapezium given below is:
25m
S T
o
o 45
45 20m
V U
X Y
(1) 550 sq. m (2) 650 sq. m
(3) 900 sq. m (4) 950 sq. m
13
13. In the given figure x° =?
V 53º
T
(1) 37° (2) 143°

(3) 127° (4) 135°
14. Consider the following two curves in the x – y plane: y = x2 + 1 and x = y2 + 1
Which of the following statements is true?
(1) The two curves intersect once. (2) The two curves intersect twice.
(3) The two curves intersect thrice. (4) The two curves never intersect.
DIRECTIONS: for Questions 15 and 16: Answer the questions based on the
following information. An air hostess had some candies in her basket. She started
distributing the candies to the children in the following manner. To the first kid, she
gave half the number of candies that she possessed plus half a candy. To the
second kid, she gave half the number of candies she was left with plus half a candy
and so on. Just before she could go to the 7th kid, she found that her basket was
completely empty.
15. How many candies did the air hostess give to the 4th kid?
(1) 3.5 (2) 4
(3) 4.5 (4) Cannot be determined
16. How many candies did the air hostess start with?
(1) 64 (2) 128
14
17. What does the following graph represents?
e
1
-1
-e
(1) |y| = ex (2) y = e |x|

(3) y = |ex| (4) y = e – x
18. The sides of a regular polygon (Number of sides > 4) are extended to form a
star. If the measure of the internal angle at each point of the star is 90°, find the
number of sides of the polygon.
(1) 5 (2) 6
(3) 7 (4) 8
19. The difference between a mother’s age and her daughter’s age is 24 years.
Four years ago, the mother’s age was six more than twice the age of the
daughter 2 years ago. What is the age of the daughter?
(1) 20 years (2) 16 years
20. There are altogether eleven fruits to be bought, from which some re apples and
some are bananas. The price of an apple is Rs.5 and that of a banana is Rs.4. If
I can spend a total of Rs.50, then the number of apples and bananas bought
are:
(1) 5 apples, 6 bananas (2) 7 apple 4 bananas
(3) 8 apples, 3 bananas (4) 6 apples, 5 bananas
15
21. The sum of the digits of a two-digit number is 15. If the number is reversed, the
difference between the number so formed and the original number is 27. What
is the original number?
(1) 57 (2) 69
(3) 78 (4) 84
DIRECTIONS for questions 22 to 24: Read the following information carefully and
answer the questions that follow.
The values of a, b and c are 20, 15 and 20. If a is decreased by 2.5%, b is decreased
by 4% and c is decreased by 2% then:
22. a + b + c is decreased by:
(1) 1.4% (2) 2%
(3) 4.2% (4) 2.7%
23. abc will decrease by:
(1) 8.27% (2) 2.7%
(3) 4.8% (4) 7.2%
24. If the values of a, b and c are changed to 200, 150, and 400 respectively instead
( a  b)
of the ones given above, then after the respective decrements as
c
mentioned above will be:
(1) 75 (2) 71.63
(3) 70.52 (4) 70
3
25. How many times does the graph x = y – 7y – 6 intersect the y-axis?
(1) Once (2) Twice
(3) Thrice (4) None of these
Score Table
+1 –1/3
25
16
EXERCISE – 3
1. Find the remainder when [(6!)7! ]13333 is divided by 13

(1) 1 (2) 5
2. Sandeep turns the pages of his history book and randomly chooses a page,
which has a three-digit number on it. He notices that the sum of the first two
digits is equal to four times the third digit. In addition, the sum of the second
digit and twice the third digit is equal to the first digit. Which of the following
could be the third digit of the number on that page?
(1) 4 (2) 3
(3) 7 (4) 5
3. In a town, 60% of the adult population is male. a% of the adult males and b%
adult females are educated. The total number of educated adult males and
uneducated adult females is equal in number to the total number of uneducated
adult males and educated adult females. If a and b are both integers, which of
the following could be the set of values (a, b)
(1) (20, 30) (2) (20, 10)
(3) (30, 15) (4) (30, 20)
DIRECTIONS for questions 4 to 11: Answer the questions independently of each
other.
4. Calculate the number of zeros at the end of P = 55 × 1010 × l515 × ..……………….
× 125125
(1) 1200 (2) 2000
(3) 2125 (4) 1520
5. Find the circumference of the circle circumscribing the triangle formed by the
x-axis, the y-axis and the line 3x + 4y – 12 = 0.
(1) 3  units (2) 6.25  unite
(3) 5  units (4) None of these
17
6.
A
X
S
B
T
In the adjoining diagram, TB and TC are tangent and secant respectively to

the same circle with radius r. If AB is the diameter, TCB = 30° and CBS = 60°,
find the length of TX.
(1) 2r (2) r  
2 1
 3r 
(3) r (4)  2   1
 
7. If WX = WZ and XY = ZY, then the quadrilateral WXYZ is called a kite. If WX

< XY, then W is called the head and Y the tail, while X and Z are called lateral
vertices. In the kite WXYZ, if XYW = XZY, then which of the following is
NOT correct?
(1) XYZ is congruent to XWZ.
(2) Diagonals WY and XZ bisect each other.
(3) The quadrilateral WXYZ cannot be a cyclic quadrilateral.
(4) Diagonals WY and XZ intersect to form 4 right angles.
8. A matrix of 25 dots is arranged such that two adjacent dots in a row or a column
are equally spaced, and the whole arrangement of dots forms a square. A circle
is drawn such that it passes through the maximum possible number of dots.
How many dots does that circle pass through?
(1) 5 (2) 6
(3) 8 (4) More than 8
18
9. The four vertices of a parallelogram PQRS are P(3,5); Q(7,9); R(a,4); S(0,b).
What is the value of a and b
(1) a = 2, b = 2 (2) a = –4, b = 8
(3) a = 4, b = 0 (4) Either (2) or (3)
10. I went to “Eat’ n joy Bakers” and found that there were three things to my
liking - soft drinks costing Rs. 11 each, veg rolls costing Rs. 7 each and veg
cutlets costing Rs. 8 each. I could have spent any amount between Rs. 45 and
Rs. 50 (both values inclusive), in how many ways could I have purchased the
items, if I wanted to purchase at least one of each of the items?
(1) 4 (2) 5
(3) 6 (4) 7
11. Raman has a square cardboard of area 4 sq.ft, from which he clips away a
smaller square of area 1 sq.ft, from one of the corners. Now, if he wants to cut
up the remaining piece of cardboard into exactly four identical smaller pieces,
what is the perimeter of each of the smaller piece?
(1) 4 ft (2) 3.75ft
(3) 3.5 ft (4) 3.25 ft
A dealer purchases three varieties of precious stones - diamonds, rubies and
emeralds - spending a total amount of Rs.2,00,000. He has purchased not less than
10 stones of each variety. The cost of a diamond, a ruby and an emerald is Rs. 2,000,
Rs. 4,000 and Rs. 3,500 respectively.
12. If he has purchased exactly two varieties of stones in equal number, then in
how many ways could he have bought the stones?
(1) 2 (2) 6
(3) 7 (4) 9
13. If he has bought 10 rubies, then the total number of diamonds and emeralds
bought by the dealer could be
(1) 50 (2) 60
(3) 61 (4)-64
19
A, B, and C play a card game with a pack of 52 cards. They play the game with each
player picking one card in each round. They initially have 60 points each. If in a
round a person picks a card less than or equal to 7, he loses the points equal to the
face value of the card and his two opponents gain twice that many points each. If he
picks a card whose face value is greater than 7, then he gets that many points. His
opponents gain or lose nothing. Ace has a face value of one and Jack, Queen and
King have a face value of 10 each.
14. At the end of Round I where all three persons picked a card each, it was found
that A, B and C had 69 points each. Then how many of the following statements
could be true?
I. Each picked a card of face value 9.
II. A picked a card of face value 3 followed by B with 6 and C with 3.
III. Each picked a card of face value 3.
(1) 0 (2) 1
(3) 2 (4) 3
15. Let f(x) + f(2x) + f(1 + x) + f(2 – x) = x for all x, Then f(0) =
1 1
(1) – (2) –
2 4
DIRECTIONS for question 16 to 18: Answer the questions independently of each
other.
16. If ABCD is a parallelogram and E, F are the centroids of triangle ABD and BCD
respectively, then EF can never be equal to
(1) AE (2) CE
(3) BE (4) DE
17. A drum contains 9 litres of water. Two buckets with respective capacities of
3 litres and 4 litres are provided. Neither the drum nor any of the two buckets
is calibrated. Any of the following activities qualifies as an operation,
(i) Drawing water from the drum with a bucket.
(ii) Pouring water from either bucket into the drum
20
(iii) Pouring water out from one bucket into the other bucket.
If it is required to have exactly 3 litres in each bucket, the minimum number of
operations to be performed is
(1) 3 (2) 4
(3) 5 (4) 6
18. How many three-digit numbers with distinct digits can be formed such that the
product of the digits is the cube of a positive integer?
(1) 36 (2) 18
(3) 24 (4) 30
A permutation is an ordered arrangement of two or more objects. The interchange of
any two adjacent objects in a permutation is called a transposition. Thus for three
objects a, b and c, the permutation acb can be obtained from the permutation abc
using one transposition.
19. How many transpositions are needed to completely reverse the permutation
abcdef, to get the permutation fedcba?
(1) 6 (2) 21
(3) 15 (4) 18
20. Consider n, (n > 5) such that permutations of n objects as well as permutations
of (n + 1) objects can always be reversed with an even number of transpositions.
The remainder when n is divided by 4 is
(1) 0 (2) 1
(3) 2 (4) 3
21. If p, q and r are three distinct prime numbers, such that two numbers a and b
have their L.C.M. as pp qq rr, then the number of possible ordered pairs of (a,
b) are
(1) (p + 1) (q + l) (r + l) (2) p2 q2 r2
(3) (2p + 1) (2q + 1) (2r + 1) (4) None of these
21
22. A survey was conducted on the eating habits of a group of 1000 people.
Results show that 92% of the people surveyed eat south Indian food, 91% eat
North Indian food, 82% eat American food, 78% eat Chinese food, 79% eat
Italian food and 80% eat Continental food. What must be the minimum number
of people who eat all the 6 types of food, if 7 people do not eat any of the six
types of food?
(1) 0 (2) 13
(3) 27 (4) 55
23. The age of a person k years ago was half of what his age would be k years from
now. The age of the same person p years from now would be thrice of what his
age was p years ago. What is the value of the ratio k : p?
(1) 3 : 2 (2) 2 : 3
(3) 1 : 4 (4) 4 : 1
24. A piece of string is 50 cm. long. It is cut into three pieces such that the longest
piece is three times as long as the shortest piece and the third piece is 20 cm.
shorter than the longest piece. If the pieces are joined to form a triangular
region, find the area of region formed sush is imposible
(1) 100 cm (2) 200 cm
(3) 150 cm (4) Data insuffient
25. Three people A, B and C start moving around a circular track of 100 m
simultaneously with speeds of 2 m/s, x m/s and y m/s respectively in clock
wise direction. They meet for the first time after t seconds and they meet for
the first time at their common starting point after 3t seconds. Which of the
following can never be the value of x ?
(1) 2 (2) 3
(3) 5 (4) 8
Score Table
+1 –1/3
25
22
EXERCISE – 4
1. 400 loaves of bread are to be distributed to 400 people. Each man gets 3 loaves
of bread, each women gets two loaves and each child gets half a loaf. Which
of the following could be the number of children in the group?
(1) 125 (2) 200
(3) 250 (4) 300
1
1 1 1 1
  2
 1  26.99 3 + 624.98 4 +16.012 - 729.02 6  
2.  3 of  1 1
 = ?
  195.99 2 + 2197.033  
1 1
(1) (2)
3 9
1
(3) (4) None of these
27
3. A farmer has a circular grass field of radius 14m. He tethered a goat to the
centre of the field with a rope of length ‘L’ meters. If the goat is able to graze an
area, which is equal to half the area of the field, then find L.
(1) 7 m. (2) 7 2 m.
7
(3) rn. (4) 14 m.
2
4. A certain clock marks every hour by striking a number of times equal to the
hour, and the time required for a stroke is exactly equal to the time interval
between the two strokes. At 6:00 the time lapse between the beginning of the
first stroke and the end of the last stroke is 22 seconds. At 12:00, how many
seconds elapse is there between the beginning of the first stroke and the end
of the last stroke?
(1) 72 sec (2) 50 sec
(3) 48 sec (4) 46 sec
23
5. The average score of 12 students is 64. Three students scored same as the
average. The average score of four other students is 65 and the score of three
other students is 62, 78 and 80. If the remaining two students had an equal
score, then the score of each of the two is:
(1) 48 (2) 56
(3) 62 (4) 64
6. The number of sweets eaten by each of the 9 contestants in a competition are
in arithmetic progression. What will be the effect on the average of the number
of sweets eaten, if we eliminate the number of sweets eaten by the winner and
the person who stood last?
(1) Average increases (2) Average decreases
(3) Remains same (4) Cannot be determined
7. There will be a 66.67% increase in the gain if a watch is sold for Rs.1000 rather
than profit of Rs.120. What is the cost price of the watch?
(1) Rs. 820 (2) Rs. 750
(3) Rs. 800 (4) None of these
[ 3 1331.04 × 4 26.98 × 3.01 + (27.01)1/3 ]1/2 × 93

8. 2
 3
729 
(1) 18 (2) 36
1 1.08 1 1
9. of + 1.99 × ÷ =?
3 2
2 10.8 26.99 400.01
(1) 10 (2) 11
1/ 25
 (5.01)2 – (3.98) 2 + (2.99)2 – (2.01) 2 + (0.99) 2 + 1 
10.   =?
 (728.97)1/3 – (625.01)1/4 
(1) 2 (2) 4
24
11. The ratio of two positive numbers is 5:7. The product of the two numbers is
7875. Find their difference.
(1) 25 (2) 30
(3) 35 (4) 40
12. A rectangle can be divided into two squares by a 6 cm partition. Find the
perimeter of the rectangle.
(1) 36 cm (2) 18 cm
(3) 72 cm (4) 32 cm
13. The age of mother and father, when Mitesh was born, were in the ratio 5:6.
Today, he is 6 years old and the ratio of the age of his mother and father is 6:7.
Find the present age of his mother.
14. Muneer has 7 children; they want to go on a bike tour. Muneer gave them
money such that the youngest gets maximum and oldest child gets minimum,
and each child gets double the amount that his immediate elder one gets.
Muneer distributed a total of Rs.44450. If his eldest child requires Rs.25 per
day, after how many days the eldest son will have to come back home for more
money?
(1) 7 days (2) 14 days
(3) 12 days (4) 350 days
DIRECTIONS for questions 15 to 25: Find the next number in the sequence.
15. 2, 9, 3, 10, 4, __________.
(1) 5 (2) 4
(3) 11 (4) 10
16. 4, 25, 64, 121, 196, __________.
(1) 225 (2) 256
(3) 144 (4) 289
17. 9, 8, 7, 5, 2, –3, –11, –24, __________.
(1) 48 (2) –45
(3) 46 (4) –34
25
18. 1, 5, 27, 121, 503, __________.

(1) 1014 (2) 2037
(3) 382 (4) 624
4 12 24 40 60
19. , , , ,
3 5 7 9 11
101 88
(1) (2)
15 13
74 84
(3) (4)
13 13
20. 110, 109, 99, 98, 88, 87, 77, __________.

(1) 69 (2) 67
(3) 76 (4) 79
1 1 1 1 1 1 1 1
21. What is the value of        ?
6 12 20 30 42 56 72 90
3 4
(1) (2)
5 5
2 1
(3) (4)
5 5
22. Few newly wed couples plan to go to Mauritius for their honeymoon. The
price of the group package (consisting of return trip to Mauritius including 3
days and 3 nights stay at a five star hotel) lies in the range of Rs. 46,200 and Rs.
47,000. But for some reasons, one couple could not go, due to which each of
the remaining couple had to shell out Rs. 3888 extra because the price of the
group package did not change. If the cost of the package was equally shared
among the couples, then find the exact price of the package.
(1) Rs. 46,656 (2) Rs. 46,665
(3) Rs. 46,500 (4) Rs. 46,750
26
23. Pipe X pours a mixture of acid and water, and pipe Y pours pure water into a
bucket. After 1 hour, the bucket got filled and the concentration of acid in the
bucket was noted to be 8%. If pipe Y was closed after 30 minutes and pipe X
continued to pour the mixture, concentration of acid in the bucket after 1 hour
would have been 10%. What is the ratio of acid to water in the mixture coming
out of pipe X?
(1) 2 : 13 (2) 2 : 15
(3) 3 : 20 (4) 1 : 5
24. If –8  x  –7 and –6  y  6, where x and y are non-zero integers, then which of
the following must be true?
(1) –13  (x + y)  2 (2) –2  xy  48
X
(3) –14  (x – y)  –2 (4) –8  8
Y
25. Average salary of a worker in an automobile company is Rs. 5000 and the
average salary of manager is Rs. 20,000. If the average salary of an employee in
the company is Rs. 6000 and there are 15 managers, then find the total numbers
of workers in the company.
(1) 400 (2) 320
(3) 210 (4) 225
Score Table
+1 –1/3
25
27
EXERCISE – 5
1. A racing-track for motorcars is 2000 metres in circuit. When two cars are racing,
the first is observed to pass a certain spot at 51 minutes 15½ seconds past 3
o’clock, and the second at 51 minutes 57 seconds past 3; the next time round
they pass the same spot at 52 minutes 9 seconds, and 52 minutes 48½ seconds
past 3, respectively. The difference of their speeds in kilometres per hour is
(1) 6.35 (2) 5.22
(3) 4.17 (4) Data insufficient
2. A is a working partner and B is the sleeping partner in a business. A’s capital
is Rs. 12000 and B’s capital is Rs.12000. A receives 10% of the profits for
managing the business and the rest of the profit is shared between them in
proportion to their investments. Of a total profit of Rs.8000, B will get
(1) Rs. 2700 (2) Rs. 5300
(3) Rs. 3500 (4) Rs. 4500
3. Ashok, Dravid, Jassi and Triptender were plucking mangoes in a grove to earn
some pocket money during the summer holidays. Their earnings were directly
related to the number of mangoes plucked and had the following relationship.
Jassi got less money than Triptender. Jassi and Triptender together got the
same amount as Ashok and Dravid together. Ashok and Triptender together
got less than Dravid & Jassi taken together. Who got the most? Who plucked
the least mangoes?
(1) Dravid, Jassi (2) Dravid, Ashok
(3) Jassi, Triptender (4) Jassi, Ashok
4. An icecream company makes a popular brand of icecream in a rectangular
shaped bar 6 cm long, 5 cm wide & 2 cm thick. To cut costs, the company has
decided to reduce the volume of the bar by 20%. The thickness will remain the
same, but the length and width will be decrease by the same proportion. The
new length L will satisfy
(1) 5.5 < L < 6 (2) 5 < L < 5.5
(3) 4.5 < L < 5 (4) 4 < L < 4.5
28
5. A barrel contains 36 litres of beer; it has two taps, and from one tap jug,
holding a1/8th of a litre, is filled every 4 minutes, while from the other tap a jug,
holding a1/4th a litre, is filled every 6 minutes; if the filling of the jugs for the
first time begins at 12 o’clock, how much beer will be left in the barrel at 10
minutes past 8 pm?
1
(1) litres (2) 2
2
13
(3) litres (4) None of the above
48
6. A man decides to travel 160 km in 36 hrs partly by foot and partly on a bicycle,
his speed on foot being 4 kmph and that on bicycle being 8 kmph. What
distance would he travel on his bicycle?
(1) 32 km (2) 48 km
(3) 50 km (4) 76 km
7. A, B and C are three workers. A takes 12 days to complete a work. Now A and
4
B together take 4 days to complete the same work and B and C together
5
1
take 5 days to complete the same work. Now A and C and then C and B work
3
alternately for 4 days. Then in how many days will the work be completed?
1 2
(1) 4 days (2) 6 days
3 9
4
(3) 5 days (4) 8 days
9
29
8. A rectangular window with dimensions 2 meters by 3 meters is to be enlarged

by cutting out a semicircular region in the wall as shown below. What is the
area, in square meters, of this semicircular region?
π π
(1) (2)
4 2
(3)  (4) 2
9. A letter lock contains 3 rings each marked with 10 different digits from 0 to 9. A
man forgot his code and remembered only that the difference between the
digits of the second and the third ring was 1. What is the probability that he
opens it?
999 179
(1) (2)
1000 180
1 1
(3) (4)
180 1000
5 10 7 9
10. Find the LCM of , , ,
8 2 8 20
(1) 305 (2) 310
30
11. 5 men and 10 women can do a pieces of work in 12 days, 7 men and 13 women
can do it in 9 days. In how many days will 25 men and 50 women do a work
2 times as big as the first?
(1) 4.8 days (2) 4 days
(3) 6 days (4) 5 days
12. Find the square root of 17774656
(1) 4516 (2) 4216
(3) 4716 (4) 4126
13. We have to form a rectangle from a 30 cm long wire such that length of the
rectangle is one less than thrice its breadth. Find the area of this rectangle.
(1) 11 cm2 (2) 40 cm2
(3) 44 cm2 (4) 30 cm2
1 1
14. Find the LCM of 1 , 7 and 9.09%.
4 2
(1) 11 (2) 15
1515
(3) (4) 99
2
15. If a, b ,c are in G. P., then which of the following are in G. P.?

A. a2 + b2, ab + bc, b2 + c2
B. a2 + b2, b2 + c2, c2 + a2
C. a2, b2, c2
D. ka3, kb3, kc3
(1) A, B and D (2) A, C and D
(3) A, B and D (4) A and D
31
16. There are two balls in a box, whose colours are not known except that both
may be red or both white or one red and one white. One more ball of the same
size is added to the lot, whose colour is white. If now one ball is drawn at
random from the box, what is the probability that it is white?
1
(1) 1 (2)
5
2
(3) (4) Indeterminate
3
17. ABC is a triangle in which the medians AD & CF intersect at right angles at G.
If BC = 3 cm and AB = 4 cm, the length of AC will be
A
F
G
C
B D
(1) 5 cm (2) 3.5 cm
(3) 12 cm (4) 7 cm
18. Two trains leave a junction simultaneously, one travelling North and the other
travelling West. One of them runs at a speed of 12 kmph more than the other.
If after two hours from start, they are 120 km apart, then the speed of the slower
train is
(1) 24 kmph (2) 36 kmph
(3) 48 kmph (4) 40 kmph
19. The owner of a video-game parlour has fixed the rate of 2 rupees per game for
any machine. However, if a person continuously plays a particular game 6
times, he gets 1 game free. There are 5 different games available. Mr. Audio
enters the parlour and plays a total of 10, 15,7, 13 and 22 games respectively on
the different machines. The minimum amount that he could have paid is (Rs.)
(1) 116 (2) 140
(3) 122 (4) 128
32
20. The special laddus prepared for Puja on a festive occasion are mass-produced
at the rate of 250 per shift. Each shift lasts for 20 minutes and involves an
expenditure of Rs.700. 10% of laddus produced in each shift are stolen and
10%are not good enough. If the manager executes 10 shifts, then the total
profit made at the end by selling all remaining laddus @ Rs.4.2 per laddoo is
(1) Rs.700 (2) Rs.1400
(3) Rs.860 (4) Rs.1200
21. If the perimeters of a number of squares are in G.P., then their sides will be in
(1) A.P. (2) H.P.
(3) G.P. (4) Both A.P. and G.P.
1
22. f(x) = 2x – 1; g(x) = Find f[f{g(x)}] – f[g(x)]
2x
1–x 1 – 2x
(1) (2)
x x
1 – 3x
(3) (4) Cannot be determined
x
23. For the figure given below, the longer diagonal is the diameter and is 10 units.
The shortest side of the polygon is 5 units and the shorter diagonal divides
the longer diagonal in the ratio of 2 : 3. Find the area of the shaded region.
D B
E
(1) 44 sq. units (2) 54 sq, units

(3) 64 sq. units (4) 74 sq. units
33
24. If log4 = 0.6020 and log6 = 0.7782
2
 216  3
Find log (0.64) × log  ÷ log 24.
 100 
(1) –0.0527 (2) 0.0527

(3) –0.0627 (4) 0.0627
25. The total distance between two cities is 270 kms and the journey between the
two is divided into 27 equal stages. A man takes 56 hrs to walk down the 1st
7 stages. He covers the next 9 stages with a cycle at 3 times the speed with
which he walked and the remaining stages 10 using a motor cycle and he
1
takes th of the time he took to cover the 9 stages using a cycle. How much
12
time will the man take to travel the same distance at an average of all the three
speeds?
(1) 11.5 hrs. (2) 12.5 hrs.
(3) 13.5 hrs. (4) 14.5 hrs.
Score Table
+1 –1/3
25
34
EXERCISE – 6
1. All the boys and girls of standard X of St. Joseph convent go to a fast food
joint. If each pastry carries a price tag of Rs.S and each sandwich carries a
price tag of Rs. P, then the complete group will spend a rupee less if every boy
buys a pastry & every girl a sandwich, than when every boy buys a sandwich
& every girl a pastry. If it is known that boys out number girls, then the
difference of the number of boys & girls in X is
1 1
(1) (2)
SP PS
1
(3) (4) None of the above
PS
2. Given BC × BD = 144 and OA = 9, find OB.
A
B
O C
D
(1) 12 (2) 15
(3) 9 (4) 8
3. If a, b, c are all positive and in H.P., then the roots of ax2+ 2bx + c = 0 are
(1) imaginary (2) equal
(3) rational (4) real
4. A contractor agrees to plough a field in 36 days. He employs 6 pairs of bullocks
which work 10 hours daily, but after 20 days only 3/5 of it is ploughed. If a
tractor is used for ploughing the remainder, how many hours a day must the
tractor work to finish the ploughing in the given time, supposing the tractor
can do the work of 8 pairs of bullocks?
1
(1) 6 hours (2) 7 hours
2
1
4
35
5. A certain integer n is a multiple of both 5 and 9. Which of the following must

be true?
I. n is an odd integer.
II. n is equal to 45.
III. n is a multiple of 15.
(1) III only (2) I and II
(3) I and III only (4) II and III only
6. Anil and Sunil invest Rs. 12000 and Rs. 9000 for six months respectively; then
for next six months, Sunil and Kapil invest Rs. 13000 and Rs. 19000 respectively.
They had a 25% profit in that year. Find the profit share of Sunil.
(1) Rs.132000 (2) Rs.3300
(3) Rs.13000 (4) Rs.33000
7. Sonu and Monu bought an item having the same cost price. After selling that
item, they calculated the profit percentage, both had a profit of 331/3%. But
after checking their profit earned, they realised that Monu had calculated his
profit percentage on selling price instead of cost price. If the cost price of the
item was Rs.1000, then find the profit earned by Monu.
(1) Rs.333 (2) Rs.666
(3) Rs.500 (4) Cannot be determined
8. What is the least integer which when added to both terms of the ratio 3 : 7 will
make a ratio greater than 11 : 13?
(1) 15 (2) 25
 15 – 5 
9. Find the value of  
 2 80 – 3 45 + 5 3 – 2 12 
(1) 3 (2) 5
(3) 45 (4) 15
36
126 132 198

10. Find the HCF of , ,
21x y 27x 2 y 2 .
2 3 3 2
25x y
1 3
(1) (2)
4725x 3 y3 2575x 3 y3
2 2
(3) (4)
1575x 3 y3 525x 3 y 3
11. How many ordered triplets (a, b, c) exist such that LCM(a, b)= 1000; LCM
(b, c)= 2000 and LCM (c, a) = 2000? (where LCM (x, y) = least common multiple
of two natural numbers x and y)
(1) 32 (2) 28
(3) 24 (4) 20
12. An atom is excited by an energy source due to which it starts vibrating with a
certain amplitude. The amplitude of vibration decreases in geometric
progression. The initial amplitude of vibration is 39 microns. The amplitude at
the fifth vibration is 0.4815 microns and at the sixth vibration is 0.1605 microns.
Find the amplitude at the seventh vibration.
(1) 0.635 microns (2) 0.0535 microns
(3) 0.0635 microns (4) 0.535 microns
13. In  ABC,  A = 60°,  B = 15°, C= 105°. The external bisector of  A meets
BC extended at D. Find the ratio BC : CD
A
0
60º 0
15º 105º
B C D
(1) 1 – tan15° (2) cot15°

(3) 1 – cot15° (4) tan15°
37
14. Sushil’s age one year hence will be thrice Sona’s present age. Sheela’s age one
year ago was twice Sonu’s present age. If the sum of the present ages of all the
members is 172 years, what are the ages of Sona and Sonu respectively, if
difference in the present ages of Sona and Sonu is 6 years?
(1) 15, 21 (2) 21, 15
(3) 27, 21 (4) 14, 20
DIRECTIONS: Refer to the following information to answer the questions that
follow.
A kite, perched on the top of an upright tree, 52 feet high, on the bank of the river,
pounces upon a fish floating on the surface of the water, at a point in the straight
line through the bottom of the tree at right angles to the bank, and carries it in its
claws to the top of a second upright tree 60 feet high at a diametrically opposite
point on the other bank. If the point where the kite catches the fish, is nearer to the
second bank by 14 feet than it is to the first bank and if the kite flying at a uniform
rate, takes as much time in falling on the fish as it does in carrying it to the second
treetop. (Given 1 metre = 10/3 feet)
15. The breadth of the river will be (in metres)
(1) 19.2 (2) 64
(3) 9.8 (4) 17
16. The total distance traversed by the kite will be (in metres)
1
(1) 33 (2) 39
3
(3) 37 (4) 130
17. two vessels contain mixtures of milk and water in the ralio of 8 : 1 and 1 : 5
respectively. The contents of both of these are mixed in a specific ratio into a
third vessel. How much mixture must be drawn from the second vessel to fill
the third vessel (capacity 26 gallons) completely in order that the resulting
mixture may be half milk and half water?
(1) 14 gallons (2) 12 gallons
(3) 10 gallons (4) 13 gallons
38
18. The sum of four numbers is l00. The average of the first, second and fourth is
24. Difference of the third and first is 10 and fourth number exceeds the second
by 4. One of the numbers is
(1) 25 (2) 21
(3) 31 (4) 26
19. A sports goods manufacturing company has two machines, A & B, both of
which can be operated to make footballs and volleyballs. To make a football, A
must work for 2 minutes and B, for 3 minutes. To make volleyball, A must work
for 4 minutes and B for 2 minutes. Neither machine should work for more than
120 minutes per day. On each football, the company makes a profit of Rs.8, and
on each volleyball it makes a profit of Rs.4. What is the maximum profit that the
company can make per day manufacturing both the items?
(1) Rs.300 (2) Rs.280
(3) Rs.320 (4) Rs.240
20. In a nationwide poll, N people were interviewed. If 1/4 of them answered,
“yes” to question 1, and of those, 1/3 answered, “yes” to question 2, which of
the following expressions represents the number of people interviewed who
did not answer, “yes” to both questions?
(1) N/7 (2) 6N/7
(3) 5N/12 (4) 11N/12
21. At 9.00 a.m. train T left the station and two hours later, train S left the same
station on a parallel track. If Train T averaged 60 kilometers per hour and train
S averaged 75 kilometers per hour until S passed T, at what time did S pass T?
(1) 2.00 pm. (2) 5.00 pm.
(3) 6.00 pm. (4) 7.00 pm.
22. For the given figure, find the shaded area if length AB = length AC = 5 units
and Z. A = 60°.
A
M O N
B C
P
(1) 3.32 sq.units (2) 4.32 sq.units
(3) 5.32 sq.units (4) 6.32 sq.units
39
23. If x2y2 – 6xy = –9 then which of the following statement is true?
1
(1) x < y (2) x < y
(3) x2 < y2 (4) xy = 3

24. A train normally takes 4 hrs to run between the stations A and B. One day, the
train started from station A but after 1 hr its speed went down to half of its
normal speed, due to heavy rain. Having travelled 100 kms in the heavy rain,
the train’s driver could not see the railway track due to water flowing on it, so
he decided to further slow down the speed by 50%. After that, the train reached
at station B in another 4 hrs. Which of the following is the time taken by the
train to reach at station B from station A on that particular day?
(1) 5 hrs (2) 7 hrs
(3) 9 hrs (4) Cannot be determined
25. The manufacturing cost for a certain automobile is n dollars. The manufacturer
sells the car to a retailer at 5 percent more than cost. If the retailer sells the car
to a consumer for 10 percent more than he paid for it, how many dollars does
the car cost to the consumer?
(1) $1.050n (2) $1.150n
(3) $1.155n (4) $1.515n
Score Table
+1 –1/3
25
40
EXERCISE – 7
1. Three friends Lai, Bal and Pal invest in a business in the ratio 3 : 5 : 7. If Lai’s
share in the profit earned by them in a year was Rs.3420, then find profit share
of Bal.
(1) Rs.5700 (2) Rs.7980
(3) Rs.3420 (4) Rs.6300
2. Three concentric triangles are as shown in the diagram. The outermost triangle
is O, The middle one is M, and the inner on is I. When M is inverted its vertices
touch the midpoints of the sides of O, and also the vertices of I touch the mid
points of the sides of M. If the triangles O is equilateral of side = 6, What is the
ratio of the areas O: M: I?
(1) 16: 4: 1 (2) 28: 14: 7

(3) 10: 5: 1 (4) 36: 6: 2
3. Two workers A and B can do a certain work in 12 days. If A worked twice as
1
efficiently as he could work and B worked as efficiently as he could, then
2
they together completed the work in 9 days. In how many days can A complete
the same work?
4 3
(1) 20 days (2) 25 days
7 7
3
(3) 21 days (4) Cannot be determined
5
41
1 1
 a –2 b3  5  a 4 b –1  3
4. Solve:  3 –2  ÷  –2 2 
a b  a b 
b2 1
(1) (2)
a3 a
b 1
(3) (4)
a b
5. A shopkeeper sold an item to A who sold it to B. If the shopkeeper had a profit

of Rs.35 and A had a profit percent equal to the cost price of that item to him,
find the original cost price of the item if cost price to B is Rs.75.
(1) Rs. 65 (2) Rs. 45
(3) Rs. 15 (4) Rs. 50
6. Products A & B are both made from the same raw material X. 20 kg of X is
required to produce 1 unit of A, while only 12.5 kg of X is required to produce
1 unit of B. Total availability of X is restricted to a maximum of 115 kg per week.
Moreover, 4 man-hours are required to pack every unit of A produced, while
the same process for a single unit of B takes 62/3 man-hours. Total man-hours
available per week = 48 (maximum). If the company has the ability to produce
both products under the above constraints, how many units of A & B
respectively must they produce to maximise profits? (Assume that profit per
unit is the same for both A & B)
(1) 5 units of A, 0 units of B (2) 0 units of A, 6 units of B
(3) 2 units of A, 6 units of B (4) 2 units of A, 8 units of B
7. An isosceles right angled triangle with length of its equal sides being 30 cm, is
rotated 180° about its centroid to form a new triangle. Find the area of the
region common to the original and the new triangle.
(1) 275 sq. cm (2) 300 sq. cm
(3) 375 sq. cm (4) 350 sq. cm
42
8. Consider a function ‘f’ on natural numbers such that f(1) + f(3) + f(5) + ...
infinite terms = b and f(n) = a {f(n + 2) + f (n + 4 ) + .................... infinite terms}.
Find the value of f(3).
a ab
(1) (2)
1+a 1+a
ab a
(3) 1 + a 2 (4) 1 + a 2
   
9. Let x, y, z and t be the positive numbers which satisfy the following conditions:
I. If x > y, then z > t and
II. If x > z, then y < t
Then, which of the following is neccessarily true?
(1) If x < y, then z < t (2) If x > z then x – y < z + t
(3) If x > y + z, then z > y (4) None of these
10. In a rectangular field 336 sugarcanes are planted in rows parallel to the breadth
of the field, the distance between any two consecutive sugarcanes and that
between any two consecutive rows being 2 feet throughout. If they had been
planted in the same manner at a distance of 2½ feet instead of 2 feet, their
number would have fallen short of the number of sugar canes in the first case
by 115. The perimeter of the field is
(1) 120 feet (2) 140 feet
(3) 160 feet (4) 180 feet
11. In the adjoining figure, the ratio of area of triangle PCB and quadrilateral
ABCD is (Given DP and AC are parallel)
P
2x
D C
X
A B
(1) 3 : 8 (2) 1 : 2
(3) 1 : 4 (4) 2 : 3
43
1
12 Find the 2nd term of a G.P. whose 4th and 10th terms are and 243 respectively..
3
1
(1) 9 (2)
3
1 1
(3) (4)
27 9
13 A circular park has a pool in the form of a trapezoid. The larger side of the
trapezoidal pool is a chord of the circular park and measures 20m and the
median of the trapezoidal pool is 18m in length and passes through the centre
of the park. If the distance between the median and larger side of the trapezoidal
park is 5m, find the area of the park excluding the pool area.
(1) 103 m2 (2) 113 m2
(3) 213 m2 (4) 123 m2
14. In the figure, if the area of the inscribed rectangular region is 32 sq. units, then
the circumference of the circle is
D 2x C
X
A B
(1) 20 units (2) 4 3  units
(3) 2 units (4) 4 5  units

15. Nx is a family of numbers for different natural numbered values of x. They
share a common property of having 24 factors in each of the numbers. All the
elements of N are arranged in ascending order as follows: N1< N2<N3
and so on. Now, digital sum of a number is defined as the sum of all the digits
of number until we get a single digit. What is the digital sum of N1?
(1) 9 (2) 6
(3) 1 (4) 3
44
16. If  and  are roots of the equation 3x2 – 6x + 1 = 0, then find 3 + 3

(1) 2 (2) 4
(3) 6 (4) 8
17. Find the minimum value of |x – p| + |x – 10| + |x – p – 10|, if 0 < p < 10.
(1) p (2) p + 10
18. A six faced solid has two opposite faces as rectangles and other two opposite
faces as parallelograms, such that the larger lengths of rectangles and
parallelograms form the top and base surfaces (which are not rhombus) of the
solid. The rectangle has one of its sides measuring 2 units an another side
measures 1 unit. The larger side of the parallelogram is 2 units. Find the surface
area of the solid if the acute angle of the parallelogram is 30°.
(1) 7 sq.units (2) 14 sq.units
(3) 21 sq.units (4) 28 sq.units
19. How many 2’s and 1’s will be present in the ternary representation of 3100 – 2?
(1) 50 twos and 50 ones (2) 1 two and 99 ones
(3) 100 twos and no ones (4) 99 twos and 1 one
20. Raju, Navin, Kishan and Kamran are four employees working in a team. Raju
takes thrice the time taken by Kishan and Kamran to complete the work together.
Navin takes four times the time taken by Raju and Kishan to complete the work
together. Kishan takes five times the time taken by Raju and Navin to complete
the work. If Raju, Navin and Kishan complete the work in 30 days, then in how
many days would Raju complete the same work?
1 1
(1) 49 (2) 48
2 2
1
2
45
21. A rocket is propelled by seven stages. After every 50 kms of travel, one stage
drops down and subsequently the velocity of the rocket reduces, the reduction
in velocity being in geometric progression. If the velocity when the 3rd stage
drops was 47.59 m/s and when the 4th stage drops was 46.43 m/s, then find the
velocity when the last stage drops out.
(1) 39.05 m/s (2) 49.78 m/s
(3) 43.11 m/s (4) 52.75 m/s
22. To decide whether a number is divisible by 7, we define a process by which its
magnitude is reduced as follows:
Ultimately the resulting number will be less than seven after repeating the
above process a certain number of times. After how many such stages does
the number 203 reduce to 7?
i1, i2i3….inai1, x 3n–1+ inx3n–2 + ........+ in × 3°.
For example 259 = 2 x 32 + 5 x 31 + 9 x 3° = 42
(1) 2 (2) 3
(3) 4 (4) 1
23. Consider the following steps
(a) Put X = l, Y = 2
(b) ReplaeX by XY
(c) Replace Y by Y + 1
(d) If Y = 5, go to step (f) otherwise go to step (e)
(e) Go to step (b)
(f) stop
Then the final value of X is
(1) 1 (2) 24
(3) 120 (4) 720
46
24. In table tennis, the first player to score 21 points wins. Service alternates
between two players every five points. A player can score points both during
his service and his opponents service. Doshi beat Venkat 21-16 in a game. 24
of the 37 points played were won by the player serving. Who served first?
(1) Doshi (2) Venkat
(3) Indeterminate (4) Inconsistent data
25. Mayank bought a notebook containing 96 pages, and numbered them from 1
through 192. Shyam tore out 25 pages of Mayank’s notebook, and added the
50 numbers he found on the pages. Could Shyam have gotten 1990 as sum?
(1) Definitely yes (2) Definitely no
(3) May be (4) Can’t say
Score Table
+1 –1/3
25
47
EXERCISE – 8
1. Find the square root of q6 + 10q5 + 25q4 – 4pq2(q + 5) + 4p2

(1) 2q3 + 5q2 (2) 2p – q3 – 5q2
(3) 2p + q3 – 5q2 (4) 2p – q3 – 5q2
2. There are three numbers, first two of which are perfect cubes and the square
root of the third number is a perfect square. The least common multiple (LCM)
of the three numbers is equal to the product of the first two numbers. LCM of
the first two numbers is 66. How many such values of the third number are
possible if it can be written as the product of two number which are co-prime
to each other in more than one ways?
(1) 3 (2) 4
3
3. If sin(A + B) = cos(A – B) = . What is the value of [tan 2 (A + B) x tan2
2
(A – B)]? (Given that A & B are acute angles)
(1) sin 2A (2) cos 2B
(3) (tan A + tan B) (4) (tan A – tan B)
4. A solid sphere is cut into 16 identical pieces with 5 cuts. What is the percentage
increase in the combined total surface area of all the pieces over that of the
original sphere?
(1) 350% (2) 150%
(3) 200 % (4) 250%
5. A starts a business with Rs.1400. B joins A after 4 months with investment of
Rs.1200. After 4 months from B’s involvement in business C joins in with share
of Rs.1000. They get the profit of Rs.760 at end of year. Find the share of A.
(1) Rs.168 (2) Rs. 420
(3) Rs. 840 (4) Rs. 440
48
6. From a vessel completely filled up with pure wine, 140 litre is removed &
replaced with equal quantity of water. The process is repeated one more time.
In a 98 L sample of the resulting solution 80 L is water. Find the capacity of the
vessel.
(1) 245 L (2) 235 L
(3) 490 L (4) 2450 L
7. (a – 1)! x a! = n and (a + 1)! x a! = n2. Find the number of factors of n.
(1) 4 (2) 2
(3) 12 (4) 6
8. A certain amount is divided into four parts. Ram keeps one of the parts for
himself and the total of remaining parts is then divided into five parts. Shyam
keeps one of those parts for himself and divides the total of the rest into three
parts. One of the that is kept by Kishan and the total of the remaining parts is
kept by Kiran which amounts to Rs.2500. Find percentage of amount with Ram
and Shyam together to the. total amount.
(1) 36% (2) 40%
(3) 64% (4) 25%
9. If  and  are the roots of the equation 2x2 – 5x + 9 = 0, then find the values of
1 1
2
+ 2
α β
81 11
(1) (2)
11 81
11 1
(3) – (4)
81 9
a 4 – a 3 b – ab 3 + b 4
10. Simplify: .
a 4 + a 3 b – ab 3 – b 4
(a – b) 2 a 2 – b2
(1) (2)
a+b a 2 + b2
a–b
a+b
49
11. Every day Neera’s husband meets her at the city railway station at 6 pm and
drives her to their residence by car. One day she left early from the office and
reached the railway station at 5 pm. She started walking towards her home, met
her husband coming from their residence on the way and they reached home
10 minutes earlier than the usual time. For how long did she walk?
(1) 1 hour (2) 50 minutes
(3) 30 minutes (4) 55 minutes
12. Find ‘the sum of the series (5x + 7y) + (8x + 5y) + (11x + 3y) + (14x + y) +... upto
25 terms.
(1) 1230x + 522y (2) 1025x – 425y
(3) 1025x + 425y (4) 1330x – 620y
13. In a MBA entrance test, the number of failures was 0.25 times the number of
those who passed. The passed and failed candidates would have been in a
ratio of 2: 1 if there would have been 35 candidates less and 9 more would have
failed. The total number of candidates was
(1) 155 (2) 255
(3) 125 (4) 200
14. Pradeep borrowed Rs. 4000 at 5% compound interest. After 2 years, he repaid
Rs. 2210 and after two more years, he repaid the balance with interest. The
total interest paid by him was
(1) Rs. 685.50 (2) Rs. 635.50
(3) Rs. 546.50 (4) Rs. 655.50
15 Kiran invests Rs.40000 partly at compound interest rate of 8% per annum and
partly at simple interest rate of 10% per annum for 2 years. If the ratio of
investment is 5 : 3 respectively, then find the total interest earned?
(1) Rs.7115 (2) Rs.7160
(3) Rs.7511 (4) Rs.7515
16. Find the largest possible four digit number which gives a remainder of seven
divided by 12, 15 and 21.
(1) 9660 (2) 9960
(3) 9967 (4) 9667
50
17. x is increased by 15% to get y, y is increased by 20% to get z, by what percent

should we decrease z to get x?
(1) 32.5% (2) 25.2%
(3) 38% (4) 27.5%
18. A starts a business with an investment of Rs.2000. B joins him after two months
with the investment of Rs.1500, C invests the same amount as A but after two
months after B joined. If they get a profit of Rs.2750 at the end of year, what is
the share of C?
(1) Rs.1200 (2) Rs.800
(3) Rs.750 (4) Rs.700
19. A man facing in south direction walks for 15 m. Then he turns towards the west
and walks 31 m, again turns towards the south and walks 16 m. Find the
shortest distance in which he could cover this journey between starting and
terminating points.
(1) (16 3 + 15 2) m (2) 31 2 m
(3) (3 15 + 2 16) m (4) Cannot be determined

DIRECTIONS for questions 20 and 21: Answer the question on the basis of the
There are five friends A, B, C, D and E. A combination of four of these five friends
used to go for swimming on any day. It is known that A went 5 times, which is the
least & E went 8 times, which is the maximum. No other friend went for swimming 5
or 8 times.
20. Which of the following statements regarding B, C, D is true?
(1) Each of them went 6 times
(2) Each of them went 7 times
(3) Two of them went 6 times and one went 7 times.
(4) Two of them went 7 times and one went 6 times.
21. For how many days did A, B, C, D, E go for swimming?
(1) 10 (2) 9
51
DIRECTIONS for questions 22 to 25: Refer to the data given below and answer the
questions that follow.
A and B start running in opposite directions around a circular track of radius 7 feet.
They follow two rules
• Whenever they meet, they reverse their directions.
• Whenever they meet, A starts running at B’s speed and vice versa.
• They start from Mo and A’s speed is three times B’s speed. They
first meet at M1 then M2 and then at M3
22. What is the length, in feet, of the arc joining M1 and M2?
(1) 7 2 (2) 11
(3) 14 (4) 14 2
23. What is the length, in feet, of the arc joining M1 and M3 ?
(1) 14 (2) 7 2
(3) 14 2 (4) 22
24. With which of the following does M0 coincide?
(1) M1 (2) M2
(3) M3 (4) None of the above
25. What is the total distance, in feet, that A has travelled by the time A and B meet
for the third time ?
(1) 7 (2) 22
(3) 44 (4) 77
Score Table
+1 –1/3
25
52
EXERCISE – 9
1. In the figure below, x = ?

A Q
Xº B 35º
P C
(1) 35° (2) 55°
(3) 125° (4) 145°
2. For the equation in the form ax2 + bx + c = 0, if  and are the roots and
1 3
( – ) = – and ( = , then the equation is
2 2
(1) 5x2 + 3x + 2 = 0 (2) 2x2 – 5x + 3 = 0
(3) 3x2 + 2x + 5 = 0 (4) 3x2 + 5x + 2 = 0
3. When integer n is divided by 17, the quotient is x and the remainder is 5. When
n is divided by 23, the quotient is y and remainder is 14. Which of the following
is true?
(1) 2x + 17y = 19 (2) 17x - 23y = 9
(3) 17x + 23y = 19 (4) 5x - 14y = 6
2 2
4. Find roots of the equation  2  x – 15x + 5 2 
2
=0
15 2  225 15  145
(1) (2)
4 4
2  125 15  140
(3) (4)
2 2 2
5. Find k if one of the roots of the equation (2x – k)2 – 4k = 5 is equal to 0.
(1) 0 (2) either 0 or –1
(3) either 5 or 0 (4) either 5 or –1
53
2
6. Solve 3x + 2 <
3
2 –4
(1) x < (2) x >
3 9
4
(3) –x < (4) None of these
9
7. The value of the discriminant of (kx)2 + k(x2 + 2x) + (x + 1) = 0 is
(1) k (2) k2 – 4k
(3) 1 (4) 0
8. Find the value of (0.5) 3 + 3(0.25)(7.5) + 1.2(7.5) 3
(1) 5.12 (2) 512
(3) 51.2 (4) 0.512
9. Sagar covers a distance of 30 km when he walks partly at a speed of 2 kmph
and party at 5 kmph. If he walks at the speed of 5 kmph for the time he walked
for 2 kmph and; 2 kmph for the time he walked at 5 kmph, he covers 3 km more.
Find the total time duration for which he was walking.
10. A person invested Rs. 25000 in a bank for 2 years at a compound interest rate
of 3% p.a. If he wants to earn the same interest as compound interest for 1 year
at a rate of 2.5% p.a., how much money should he invest?
(1) Rs. 30074 (2) Rs. 50750
(3) Rs. 60900 (4) None of these
11. Choose the best option for a consumer assuming some marked price and cost
price of a product. (Marked price > Cost price)
(1) Successive discounts of 15%, 15% and 10%.
54
12. The average weight of a class of 30 students increases by 2 when a student

having the weight equal to the average weight is replaced by a teacher weighing
85 kg. Find the weight of the student that is replaced.
(1) 15 kg (2) 50 kg
(3) 25 kg (4) Cannot be determined
13 There are 7 steps in a flight of stairs (not counting the top and bottom of the
flight). When going down, you jump over some steps, perhaps even over all 7.
How many ways are there to go down the stairs?
(1) 7! (2) 28
(3) 128 (4) 343
14. Ten l’s and ten 2’s are written on a blackboard. In one turn, a player may erase
any two figures. If the two figures erased are identical, they are replaced with
a 2. If they are different, they are replaced with a 1. The first player wins if a 1
is left at the end, and the second player wins if a 2 is left. Now if A and B begin
playing the game, with B playing first, then who will win, if both play
intelligently?
(1) A (2) B
(3) Sometimes A, Sometimes B (4) Data insufficient
15. Thirty students took an exam and got 2, 3, 4, 5 as their marks. The total marks
of the 30 students was 93. The 3’s were more than the 5’s but less than the 4’s.
Also the number getting 4’s was a multiple of 10 and the number of 5’s was
even. How many students scored three marks?
(1) 6 (2) 7
(3) 8 (4) 9
16. 12 men working 10 hrs a day, 8 women working 8 hrs a day, 10 children working
8 hrs a day complete the work in 5 days. Work done by 3 men is same as that
done by 4 women and as done by 5 children. The same work would be completed
by 20 children working 6 hrs a day in how many days?
(1) 20 (2) 15
(3) 10 (4) 25
55
17. P, Q, R, S are four stations in order on a railway; the single fare, third class, is
Rs. 10 a km, but the company issues weekend return tickets between any two
of these stations at the single fare and a third class; the weekend tickets, third
class, between P and R, Q and S, P and S, cost Rs. 3600, Rs. 3200 and Rs. 4800
respectively; how many km is R distant from Q?
(1) 250 (2) 200
(3) 100 (4) 150
18. Ricardo lives 4 kilometers due west of Pat’s house. Ann lives 6 kilometers due
north of Pat’s house and 4 Kilometers due west of David’s house. What is the
straight-line distance, in kilometers, from Ricardo’s house to David’s house?
(1) 4 (2) 5
(3) 8 (4) 10
19. A, B, C invested a total of Rs. 151800 in the ratio 5: 7: 11. ‘A’ invested his
capital for 8 months, ‘B’ invested for 6 months and ‘C invested for 4 months. If
they earn a profit of Rs. 42273, what is the share of ‘C in the profit?
(1) Rs. 14800 (2) Rs. 16688
(3) Rs. 20000 (4) Rs. 22356
20. Raman divides a sum of Rs.100000 in three parts such that if he diminishes
Rs. 8000, Rs. 7500 and Rs. 9500 out of each parts, the remaining amounts
would be in the ratio 3 : 5 : 7. He then invests the 1st part in 3.5% Rs. 100 stocks
at Rs. 75, the 2nd part in SI at 5% p.a. for a year and the 3rd part in CI at 5% p.a.
for a year. Find the ratio of the earnings out of these investments.
(1) 14 : 25 : 735 (2) 14 : 25 : 35
(3) 14 : 735 : 25 (4) 14 : 35 : 25
21. The volume of the sphere is directly proportional to the square of its diameter.
If two spheres of diameters D1 and D2 have their volume V1 and V2 in 1: 4
proportion, then find the proportion between their respective radii.
(1) 2 : 1 (3) 4 : 1
(3) 1 : 2 (4) 2 : 8
22. Beaker A contains 30% HCL, 45% HNO3 and the remaining is water. Beaker B
contains 25% HNO3, 55% HCL and the rest is water. If for a certain experiment,
a mixture is required containing 40% of HCL, then find the amount of HNO3 in
that mixture if 20 litres of the mixture is prepared.
(1) 7.4 litres (2) 7.8 litres
(3) 7.0 litres (4) Cannot be determined
56
23. Ajay and Vijay start a business. Ajay invests Rs.30000 for 8 months and Vijay
invests Rs.25000 for 10 months. They had a profit of Rs. 147000. Ajay saves
60% of his profit share and Vijay spends 40% of his share. Find the ratio of
their expenditure.
(1) 16 : 25 (2) 36 : 25
(3) 24 : 25 (4) 25 : 24
24. A and B play a game of ‘Dingo’ in which each player in his turn has to choose
a positive integer that is less than the previous number but at least half the
previous number. The player who chooses 1, loses and the game ends there. A
starts by choosing 2021 and after that both the players (A & B) continue to
play with the best strategy. Which integer should B choose immediately after
A has chosen 2021, to ensure his own victory?
(1) 1025 (2) 1011
(3) 2049 (4) 1535
25. Find the ratio of the area of the unshaded region to the area of the shaded
region if the angle of each sector is 60° and the radius is 10 units.
X B
A
Y
R
O C
F Z
Q D
E
P
(1) 65 : 72 (2) 65 : 82
(3) 66 : 92 (4) 65 : 92
Score Table
+1 –1/3
25
57
EXERCISE – 10
1. Among 4 numbers, each pair of numbers has the same highest common factor.
Find the highest common factor of all the four numbers the least common
multiple of first two numbers is 310 and that of other two number is 651.
(1) 21 (2) 31
2. There are hundred consecutive odd numbers written in the ascending order. If
the average of the first seventy of them is N, what is the average of all the
hundred numbers?
(1) N + 15 (2) N + 30
(3) N + 29 (4) N + 31
3. Three natural numbers A, B and C are in arithmetic progression. If A, B and C
are prime numbers less than 20, such that A > B > C. How many triplets (A, B,
C) are possible?
(1) 5 (2) 3
(3) 2 (4) 1
4. There are 2n integers [0, 0, 1, 1, 2, 2 ... (n –1), (n – 1)]. From these 2n integers, n
integers are chosen such that their average is an integer. Find the minimum
average of those chosen n integers, given that n = 23.
(1) 4 (2) 5
(3) 6 (4) 7
DIRECTIONS for questions 5 to 25: Answer the questions independently of each
other.
5. ABCD is a square. Another square A1B1C1D1 can be formed by joining the
midpoints of the sides of the square ABCD. Another square can be formed by
joining the midpoints of the sides of the square A1B1C1D1. If the process is
continued infinitely, then the ratio of the area of the square so formed to the
parent square ABCD, after repeating the process 8 times, is
(1) 1 : 27 (2) 1 : 28
(3) 1 : 82 (4) 1 : 26
58
6. If the equation(x – m)2(x – 10) + 4 = 0 has all the roots as integers, then find the
number of distinct integral values that ‘m’ can assume.
(1) 4 (2) 3
(3) 2 (4) 1
7. A,B,C,D,E are 5 points placed randomly on the circumference of a circle. Every
point is joined with the points that are not adjacent to it by straight line
segments. What is the sum of the angles at the vertices of the star so formed?
(1) 120° (2) 360°
(3) 180° (4) 90°
8. Three baskets marked A, B and C contain 83 apples in all. If a dozen apples are
transferred from basket A to B, basket B will have five times the number of
apples in A; if three apples are transferred from B to C, C will have half of what
B contains. How many apples should be transferred from B to C to make the
number of apples in them equal?
(1) 13 (2) 17
(3) 20 (4) 11
9. What is the probability that in a group of five persons, no two of them are born
on the same day of the week?
260 250
(1) (2)
2401 343
223 360
(3) (4)
343 2401
10 In the parallelogram ABCD shown above, E is a point on CD and F is a point on
AB. If the total area of the shaded region is 21 cm2, what is the area (in cm2) of
the parallelogram?
D E C
A F B
(1) 42 (2) 84
59
11. Two points A and B are taken on one of the perpendicular sides of a rightangled
triangle MNO, rightangled at O, such that OA = 4 cm and OB = 6 cm. A circle is
then drawn such that it passes through the points A and B and touches the
other perpendicular side of the triangle. What is the radius of the circle?
(1) 10 cm (2) 5 cm
(3) 6 cm (4) 2 cm
12. In a 100 metre race, A can beat B by 10 m and C by 20 m. In a certain 500 m race,
if A starts from a point 50 m behind the starting line, B starts from the starting
line and C starts from 50 m ahead of the starting line, who finishes the race
first?
(1) A (2) B
(3) C (4) All three finish simultaneously
13. After a severe storm, an electric pole falls and rests against a vertical wall. The
top of the pole is 8 m above the foot of the wall. Subsequently, the bottom of
the pole slides back by 4 m and the pole then lies flat on the ground with its top
touching the wall. What is the length of the pole?
(1) 12m (2) 9m
(3) 10m (4) 8 2m

14. How many five-digit numbers, formed using the digits 0, 1, 2, 4, 6, 9 and 7,
without any repetition, are divisible by 9?
(1) 300 (2) 216
(3) 312 (4) 248
15. Two straight lines are drawn from an external point A to a circle with center O,
each line intersecting the circle at two points. The first line intersects the circle
at points B and C, while the second line intersects the circle at points D and E,
such that AB < AC and AD < AE. If BOD = 120° and COE = 150°, find BAD.
(1) 30° (2) 15°
(3) 60° (4) 45°
60
16. Let A = {1, 2, 3…...20}; P and Q are two subsets of A. What is the probability
that the set P  Q has exactly 4 elements?
 316  316
(1) 20 C4  20  (2)
4  4 20
20
320 20  3
(3) 19 (4) C4  
4  4
17. Three persons A, B and C start running clockwise simultaneously from a point
 105 
on the circular track whose radius is   km. The ratio of speeds of A, B
2π 
and C is 3 : 5 : 7 respectively. What is the difference between the distance
travelled by A and the distance travelled by C when all three persons meet for
the first time at a point on the track?
(1) 105 km (2) 131.25 km
(3) 262.50 km (4) None of these
18. A cube of 35 cm x 35 cm x 35 cm is formed by many small cubical blocks of side
5 cm in which any two cubes are bonded using a glue spread over the surfaces
in contact uniformly. The volume of glue used is less than 40% of the volume
of the bigger cube. Find the minimum possible thickness of the glue used
between any two surfaces.
5
(1) cm (2) 1 cm
6
5
(3) cm (4) None of these
4
61
19. Triangle ABE and parallelogram ABCD have the same area. If AB = 8 cm and
DX = 1 cm, find the ratio of the area of triangle BYC and parallelogram ABCD.
1 cm X Y C
D
A B
8 cm
1 3
(1) (2)
8 8
5 3
(3) (4)
16 16
20. A convex pentagon ABCDE is inscribed in a circle. If the angles subtended by
the sides AB, BC, CD and DE at the centre are 50°, 80°, 60° and 70° respectively,
what is the measure of the smallest interior angle of the pentagon?
(1) 115° (2) 110°
(3) 80° (4) 95°
21. A is the set of the first ten natural numbers. B is a subset of A such that B
consists of exactly 2 numbers, both co-primes to each other. Find the maximum
number of such subsets possible.
(1) 29 (2) 28
(3) 33 (4) 31
22. In a rowing competition, first boat rows over the course at an average speed of
4 yards/second. Second boat rows over the first half of the course at the rate
1
of 3 yards /second & over the remaining half at 4 yards/second reaching the
2
62
winning post 15 seconds later than the first boat. Find the time taken by the
second boat to cover the entire course.
(1) 225 second (2) 210 sec
(3) 180 second (4) 195 sec
23. How many integral solutions (x, y) does the equation x + y = xy have?
(1) 2 (2) 3
(3) 4 (4) More than four
24. In a triangle ABC, rightangled at B, AB is half of BC, If D and E are points on
AC such that ABD = DBE = EBC, what is the ratio of the length of BD to
that of BE?
2 33 3
(1) (2)
3 33 2
32
2 3 1
25. A plot is in the form an equilateral triangle of side 10 km. Houses are built in the
plot such that all the houses are built at a distance of 1 km or more from each
other. If the dimensions of the houses are neglected, what is the maximum
number of houses that can be built in the plot?
(1) 100 (2) 121
(3) 61 (4) 66
Score Table
+1 –1/3
25
63
ANSWERS EXERCISE – 1
1. (2) 2. (4) 3. (3) 4. (3) 5. (4)
6. (2) 7. (2) 8. (4) 9. (4) 10. (2)
11. (1) 12. (4) 13. (1) 14. (4) 15. (1)
16. (1) 17. (3) 18. (1) 19. (3) 20. (2)
21. (3) 22. (1) 23. (1) 24. (2) 25. (2)
1. (1) 2. (3) 3. (4) 4. (3) 5. (3)
6. (4) 7. (1) 8. (2) 9. (1) 10. (1)
11. (1) 12. (3) 13. (3) 14. (4) 15. (2)
16. (4) 17. (1) 18. (4) 19. (3) 20. (4)
21. (2) 22. (4) 23. (1) 24. (2) 25. (3)
1. (1) 2. (2) 3. (4) 4. (1) 5. (3)
6. (3) 7. (3) 8. (3) 9. (3) 10. (3)
11. (1) 12. (4) 13. (1) 14. (3) 15. (4)
16. (2) 17. (1) 18. (4) 19. (3) 20. (1)
21. (1) 22. (3) 23. (1) 24. (4) 25. (2)
1. (4) 2. (1) 3. (2) 4. (4) 5. (1)
6. (3) 7. (3) 8. (4) 9. (3) 10. (3)
11. (2) 12. (1) 13. (2) 14. (2) 15. (3)
16. (4) 17. (2) 18. (2) 19. (4) 20. (3)
21. (3) 22. (1) 23. (1) 24. (4) 25. (3)
64
1. (2) 2. (3) 3. (2) 4. (2) 5. (3)
6. (1) 7. (2) 8. (2) 9. (3) 10. (4)
11. (3) 12. (2) 13. (3) 14. (2) 15. (2)
16. (3) 17. (1) 18. (2) 19. (1) 20. (2)
21. (3) 22. (2) 23. (3) 24. (3) 25. (3)
1. (1) 2. (2) 3. (1) 4. (3) 5. (1)
6. (4) 7. (1) 8. (4) 9. (2) 10. (3)
11. (2) 12. (2) 13. (3) 14. (3) 15. (1)
16. (2) 17. (1) 18. (1) 19. (3) 20. (4)
21. (4) 22. (2) 23. (1) 24. (3) 25. (3)
1. (1) 2. (1) 3. (3) 4. (1) 5. (3)
6. (3) 7. (2) 8. (3) 9. (3) 10. (2)
11. (1) 12. (3) 13. (3) 14. (4) 15. (1)
16. (3) 17. (3) 18. (2) 19. (4) 20. (3)
21. (3) 22. (1) 23. (2) 24. (1) 25. (2)
1. (2) 2. (2) 3. (1) 4. (4) 5. (2)
6. (2) 7. (4) 8. (2) 9. (3) 10. (3)
11. (4) 12. (2) 13. (1) 14. (2) 15. (2)
16. (4) 17. (4) 18. (2) 19. (2) 20. (3)
21. (3) 22. (2) 23. (4) 24. (4) 25. (4)
65
1. (1) 2. (2) 3. (2) 4. (2) 5. (4)
6. (4) 7. (3) 8. (2) 9. (4) 10. (3)
11. (3) 12. (3) 13. (3) 14. (1) 15. (2)
16. (2) 17. (4) 18. (4) 19. (1) 20. (2)
21. (3) 22. (1) 23. (3) 24. (4) 25. (4)
1. (2) 2. (2) 3. (1) 4. (3) 5. (2)
6. (2) 7. (3) 8. (1) 9. (4) 10. (1)
11. (2) 12. (1) 13. (3) 14. (3) 15. (2)
16. (1) 17. (4) 18. (2) 19. (2) 20. (4)
21. (4) 22. (1) 23. (1) 24. (2) 25. (4)
66

Quantitative Ability: (Practice Exercise-III)

Uploaded by

Copyright:

Available Formats

Quantitative Ability: (Practice Exercise-III)

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Quantitative Ability: (Practice Exercise-III)

Uploaded by

Copyright:

Available Formats

QUANTITATIVE

This book is a part of set, not be sold separately.

(1) 18° (2) 15°

4. What is the hundreds digit of the number of 5100

9. Find the product of all the factors of 432.

(3) 120 m (4) 20 3 m

Find the final value of m

(1) 20° (2) 25°

25. If x is real, then the maximum value of y = 2(2 – x)(x + x 2 + 9 ) is

13. In the given figure x° =?

(1) 37° (2) 143°

17. What does the following graph represents?

(1) |y| = ex (2) y = e |x|

1. Find the remainder when [(6!)7! ]13333 is divided by 13

In the adjoining diagram, TB and TC are tangent and secant respectively to

7. If WX = WZ and XY = ZY, then the quadrilateral WXYZ is called a kite. If WX

[ 3 1331.04 × 4 26.98 × 3.01 + (27.01)1/3 ]1/2 × 93

18. 1, 5, 27, 121, 503, __________.

20. 110, 109, 99, 98, 88, 87, 77, __________.

8. A rectangular window with dimensions 2 meters by 3 meters is to be enlarged

15. If a, b ,c are in G. P., then which of the following are in G. P.?

(1) 44 sq. units (2) 54 sq, units

24. If log4 = 0.6020 and log6 = 0.7782

(1) –0.0527 (2) 0.0527

5. A certain integer n is a multiple of both 5 and 9. Which of the following must

126 132 198

(1) 1 – tan15° (2) cot15°

23. If x2y2 – 6xy = –9 then which of the following statement is true?

(3) x2 < y2 (4) xy = 3

(1) 16: 4: 1 (2) 28: 14: 7

5. A shopkeeper sold an item to A who sold it to B. If the shopkeeper had a profit

(1) 20 units (2) 4 3  units

(3) 2 units (4) 4 5  units

16. If  and  are roots of the equation 3x2 – 6x + 1 = 0, then find 3 + 3

1. Find the square root of q6 + 10q5 + 25q4 – 4pq2(q + 5) + 4p2

17. x is increased by 15% to get y, y is increased by 20% to get z, by what percent

(1) (16 3 + 15 2) m (2) 31 2 m

(3) (3 15 + 2 16) m (4) Cannot be determined

1. In the figure below, x = ?

12. The average weight of a class of 30 students increases by 2 when a student

(3) 10m (4) 8 2m

You might also like