Algebra

1. Which number has four significant figures?

A. 0.0025
B. 0.02525
C. 0.252
D. 1.2520

2. The LCM of 2x2 3x 2, 3x2 4x 4, x2 4x +4 is

A. (x - )2(2x + 1)
B. (x 2)(2x + 1)(3x + 1)
C. (x 2)2(2x + 1)(3x + 2)
D. (x 2)(2x + 1)

3. What is the lowest common factor of 10 and 32?

A. 320
B. 2
C. 180
D. 90

4. The LCD of the fractions , 2/3, 3/2, 5/9 and 7/36 is

A. 180
B. 36
C. 90
D. 4860

5. The number 0.231231231231. is

A. Irrational
B. Rational
C. Surd
D. Transcendental

6. What is the 2001th digit in the decimal equivalent to 12345/99999 starting from decimal point?
A. 4
B. 3
C. 2
D. 1

7. Solve for y; sq. rt of y + cu. rt of y = 36

A. 27
B. 36
C. 1080
D. 729

devilbat Page 1
 Algebra

8. Solve for x; 5x + 2 3(5x + 1) + 4(5x) + 25(5x 2) = 375

A. 4
B. 2
C. 3
D. -3

9. If 3x = 9y and 27y = 81x then z/x is equal to

A. 3/7
B. 3/5
C.
D. 3/8

10. Solve the inequality x 3 > 2

A. x < -5
B. x > -5
C. x > 5
D. x < 5

11. Solve for x; x2 + 4x > 12

A. -6 > x >3
B. -5 > x > 2
C. -6 > x > 2
D. -4 > x > 2

12. If f(x) = x3 + 3x2 + x +1 and g(z) = z3 + z, then f[g(2)] is equal to:

A. 1311
B. 1310
C. 1309
D. 1308

13. If sq. rt (x 4) = -5, then x is equal to

A. 29
B. -29
C. 0
D. No solution

14. Which of the following quadratic trinomial is factorable?

A. 6y2 5y + 4
B. 6y2 + 7y 34
C. 6y2 -61y + 143
D. 6y2 72y +150

devilbat Page 2
 Algebra

15. What is the value of k so that 2x2 + kx -15 = 0 has one root = 3:
A. -2
B. -1
C. 1
D. 2

16. Find a quadratic equation whose roots are the reciprocals of 3x2 5x 2 = 0.
A. 2x2 + 5x -3 = 0
B. 3x2 5x + 2 = 0
C. 3x2 + 2x -5 = 0
D. 2x2 + 5x -3 = 0

17. Find a and b so that x3 + ax2 + 11x + 6 and x3 + bx2 + 14x + 8 may have common factor of the
form x2 + px + q
A. a = 6, b = 7
B. a = 7, b = 6
C. a = b = 6
D. a = b = 7

18. What is the sum of the coefficients of the expansion of (x + y)20

A. 1,084,576
B. 32
C. 32,768
D. 3,500,000

19. What is the sum of the coefficients of the expansion of (2x 1)20
A. 0
B. 1
C. 2
D. 3

20. What is the sum of the coefficients in the expansion of (2x + y z)10
A. 1062
B. 1024
C. 1232
D. 32

devilbat Page 3
 Algebra

21. What is the sum of the exponents of the expansion (x + 3z)8?

A. 72
B. 60
C. 32
D. 92

22. What is the sum of the exponents of the expansion (x2 y)5?
A. (x + 2y)4
B. (x 2y)6
C. (x + y)8
D. (x y)5

23. Which of the following has no middle term?

A. (x + 2y)4
B. (x 2y)6
C. (x + y)8
D. (x y)5

24. Without expanding, find the term that is free of the variables in the expansion of (2x/y 3y/x)4
A. 4,320
B. -4,320
C. 620
D. -620

25. The sum of three numbers in AP is 15, and the sum of their squares is 83. Find the three
numbers.
A. 3, 5, 7
B. 1, 3, 5
C. 5, 7, 9
D. 1, 7, 8

26. Find the sum of all even integers from 12 to 864, inclusive
A. 372,045
B. 374,052
C. 187,026
D. 93,513

devilbat Page 4
 Algebra

27. If a clock strikes the appropriate number of times on each hour, how many times will it strike in
one week?
A. 3822
B. 84
C. 546
D. 1092

28. Determine the sum of the progression if there are 7 arithmetic means between 3 and 35.
A. 171
B. 182
C. 232
D. 216

29. A besieged fortress is held by 5,700 men who have provisions for 66 days. If the garrison loses
20 men each day, for how many days can the provisions hold out?
A. 495
B. 76
C. 571
D. 36

30. A man A set out from a certain point and traveled at the rate of 6 km/hr. After A had gone two
hours, another man B set out to overtake him and went 4 km, the first hour, 5 km, the second
hour, 6 km, the third hour and so on, gaining 1 km every hour. After how many hours were they
together?
A. 3
B. 4
C. 7
D. 8

31. A car coasting down a plane at certain angle travels 3 meters during the first second. In any
second after the first, it slides 6 meters than it did in previous second. How far does it travel in
the 8th second?
A. 192
B. 211
C. 42
D. 45

devilbat Page 5
 Algebra

32. Insert two arithmetic means between -22 and -4

A. -28,-32
B. 16, 32
C. -16, -10
D. 4, 6

33. Two numbers differ by 40, and their arithmetic mean exceeds their positive geometric mean by
2. Find the numbers.
A. 81, 121
B. 80, 120
C. 75, 115
D. 60, 100

34. If 2, 2, 5, and 14 are added respectively to the terms of an arithmetic progression, the result is a
geometric progression. Find the arithmetic progression.
A. 1, 2, 3, 4,
B. 1, -2, -5, -8,
C. 1, 4, 7, 10, ..
D. 4, 7, 8, 10,

35. Find the 10th term of an arithmetic progression whose first term is 3 and whose 1 st, 4th, and 13th
terms form a geometric progression.
A. 3
B. 21
C. 24
D. 6

36. In a geometric progression 18, -12, 8, , which term is 512/729?

A. 12
B. 14
C. 9
D. 20

37. The population of a certain town is 15,000. If it increases 5% every year, what will the
approximate population be at the end of 8 years?
A. 15,245
B. 16,243
C. 22.162
D. 16,543

devilbat Page 6
 Algebra

38. A rich man called his seven sons. He had with him a number of pebbles, each pebble
representing a gold bar. To his first son, he gave half of the pebbles he initially had and one
pebble more. To his second son, he gave half of the remaining pebbles and one pebble more.
He did the same to each of his five sons and then found out that he had one pebble left. How
many pebbles were there initially?
A. 381
B. 382
C. 383
D. 384

39. An equilateral triangle is inscribed within a circle whose diameter is 12 cm. In this triangle, a
circle is inscribed; and in this circle, another equilateral triangle is inscribed; and so on
indefinitely. Find the sum of perimeters of all of the triangles.
A. 36 sq. rt 2 cm
B. 36 sq. rt of 5 cm
C. 36 sq. rt 3 cm
D. 36 sq. rt of 7 com

40. Find the sum of the given infinite geometric progression 1, 0.1, 0.01, 0.001, .
A. 9/10
B. 10/3
C. 10/9
D. 12

41. The third term of a harmonic progression is 15 and the 9th term is 6. Find the 11th term.
A. 4
B. 5
C. 6
D. 7

42. John is 3 times as old as his brother James. In 3 years, he will be 2 years more than twice the
age of his brother will be then. What are their ages?
A. 5, 15
B. 10, 30
C. 6, 18
D. 3, 9

devilbat Page 7
 Algebra

43. I was twice as old as you were when I was as old as you are now. When you get to be as old as I
am now, together our ages will be 63. How old are we now?
A. 27, 18
B. 36, 12
C. 30, 10
D. 24, 8

44. The sum of the ages of two boys is four times the sum of the ages of a certain number of girls.
Four years ago, the sum of the ages of the girls was one eleventh of the sum of the ages of the
boys and eight years hence, the sum of the ages of the girls will be one-half that of the boys.
How many girls are there?
A. 8
B. 6
C. 4
D. 2

45. Find the number which is 7/4 times the excess of the number over 3.
A. 5
B. 7
C. -7
D. -5

46. The sum of two numbers is 11; the sum of their reciprocals is 11/28. Find the numbers.
A. 7, 5
B. 6, 5
C. 7, 4
D. 5, 3

47. The quotient of a two digit number, divided by the sum of its digits, is 4. If the number be
subtracted from the sum of the squares of its digit, the difference is 9. Find the number.
A. 64
B. 32
C. 27
D. 36

48. The sum of a three digit number is 6. The middle digit is equal to the sum of the two other digits
and the number shall be increased by 99 if the digits are reversed. Find the number.
A. 231
B. 401
C. 132
D. 321

devilbat Page 8
 Algebra

49. A can do a piece of work in 2 days less time than B. If both can do the work in 2 2/5 days, how
many days will it take each to do the work?
A. 3 and 5
B. 6 and 8
C. 2 and 4
D. 4 and 6

50. A and B can do a piece of work in 42 days, B and C in 31 days and C and A in 20 days. In how
many days can all of them do the work together.
A. 19
B. 17
C. 15
D. 13

devilbat Page 9