30 Quant Data Sufficiency Questions

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Quant Data Sufficiency Practice Questions 2021

1. The question consists of two statements numbered “I and II” given below it. You have to decide
whether the data provided in the statements are sufficient to answer the question.
If x/7 and y/5 are integers and 50 < x < y < 100, then find the value of 5x – 3y.
Statement I: 3x > 210 while 2y < 170.
Statement II: y – x = 3
A. The data either in statement I alone or in statement II alone are sufficient to answer the question.
B. The data in statement II alone are sufficient to answer the question, while the data in statement I alone
are not sufficient to answer the question.
C. The data in statement I alone are sufficient to answer the question, while the data in statement II alone
D. The data given in both statements I and II together are not sufficient to answer the question.
E. The data in both statements I and II together are necessary to answer the question.
Correct Answers : A. The data either in statement I alone or in statement II alone are sufficient to answer
the question.
Explanation : For x/7 to be an integer, values of ‘x’ can be 56, 63, 70, 77, 84 and 91.
For y/5 to be an integer, values of ‘y’ can be 60, 65, 70, 75, 80, 85, 90 and 95.
Statement I:
3x > 210 i.e. x > 70 while 2y < 170 = y< 85
Also x < y, so the given conditions satisfies only for ‘x’ = 77 and y = 80.
So the value of ‘5x – 3y’ = 5 × 77 – 3 × 80 = 145
So, data in statement I alone is sufficient to answer the question.
Statement II:
y – x satisfies only for ‘x’ = 77 and y = 80.
So the value of ‘5x – 3y’ = 5 × 77 – 3 × 80 = 145
So, data in statement II alone is sufficient to answer the question.

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2. The question consists of two statements numbered “I and II” given below it. You have to decide whether
the data provided in the statements are sufficient to answer the question.
A shopkeeper sold two items: A and B. Find the cost price of item A.
Statement I: The overall cost price of the two items is Rs. 1,000. He sold item A at a profit of 20% and item
B at a loss of 10%. In the whole transaction the shopkeeper had a profit of Rs. 80.
Statement II: The selling price of both the items is Rs. 1,080. Selling price of item A is Rs. 720 and the loss
incurred on selling item B is 10%.
A. The data in both statements I and II together are necessary to answer the question.
B. The data given in both statements I and II together are not sufficient to answer the question.
C. The data in statement I alone are sufficient to answer the question, while the data in statement II alone
D. The data in statement II alone are sufficient to answer the question, while the data in statement I alone
E. The data either in statement I alone or in statement II alone are sufficient to answer the question.
Correct Answers : C. The data in statement I alone are sufficient to answer the question, while the data
in statement II alone are not sufficient to answer the question.
Explanation : Statement I: Let the cost price of item A = Rs. x
So the cost price of item B = Rs. 1000 – x
Selling price of item A = Rs. 1.2x
Selling price of item B = 0.90 × (1000 – x) = Rs. 900 – 0.9x
According to question: 1.2x + 900 – 0.9x = 1000 + 80
0.3x = 180
x = 600
So the cost price of item A = Rs. 600
Statement II:
Selling price of item B = 1080 – 720 = Rs. 360

Cost price of item B = 360/0.90 = Rs. 400
Cost price of item A can’t be determined.
So, data in statement II alone is not sufficient to answer the question.
Rahul invested certain amount of money partially in scheme A offering 10% compound interest
compounded annually and rest in scheme B offering 13% simple interest. Find the total amount invested by
Rahul.
Statement I: Total interest earned by Rahul after three years is Rs. 5,827.
Statement II: Total interest earned by Rahul after two years is Rs. 3,810
A. The data in statement I alone are sufficient to answer the question, while the data in statement II alone
B. The data in statement II alone are sufficient to answer the question, while the data in statement I alone
C. The data in both statements I and II together are necessary to answer the question.
D. The data either in statement I alone or in statement II alone are sufficient to answer the question.
E. The data given in both statements I and II together are not sufficient to answer the question.
Correct Answers : C. The data in both statements I and II together are necessary to answer the question.
Explanation : Statement I:
Let the amounts invested by Rahul in schemes A and B are Rs. x and Rs. y respectively.
Interest earned by Rahul from scheme A after three years = x × {(1 + 0.10)3 – 1} = Rs. 0.331x
Interest earned by Rahul from scheme B after three years = y × 0.13 × 3 = Rs. 0.39y
So according to question: 0.331x + 0.39y = 5827 …… (i)
Amount invested by Rahul can‘t be determined
So data in statement I alone is not sufficient to answer the question.
Statement II:
Let the amounts invested by Rahul in schemes A and B are Rs. x and Rs. y respectively.

Interest earned by Rahul from scheme A after two years = x × {(1 + 0.10)2 – 1} = Rs. 0.21x
Interest earned by Rahul from scheme B after two years = y × 0.13 × 2 = Rs. 0.26y
So according to question: 0.21x + 0.26y = 3810 ……. (ii)
Amount invested by Rahul can‘t be determined
So data in statement II alone is not sufficient to answer the question.
Combining statement I and II:
Solving equations (i) and (ii) we get x = 7000 and y = 9000
So the total amount invested by Rahul = 7000 + 9000 = Rs. 16,000
So data in statement I and statement II together are necessary to answer the question.
Present average age of Deepak, Harish and Suresh is 30 years.Find the present age of Deepak.
Statement I: Sum of the present ages of Deepak and Harish is 70 years while the present average age of
Deepak and Suresh is 31 years.
Statement II: Present ages of Deepak and Harish are in the ratio 3:2 respectively. Present age of Harish is
40% more than the present age of Suresh.
A. The data in both statements I and II together are necessary to answer the question.
B. The data given in both statements I and II together are not sufficient to answer the question.
C. The data in statement II alone are sufficient to answer the question, while the data in statement I alone
D. The data in statement I alone are sufficient to answer the question, while the data in statement II alone
E. The data either in statement I alone or in statement II alone are sufficient to answer the question.
Correct Answers : E. The data either in statement I alone or in statement II alone are sufficient to answer
the question.
Explanation : Statement I:
Sum of the present ages of Deepak and Suresh = 31 × 2 = 62 years

Sum of the present ages of Deepak, Harish and Suresh = 30 × 3 = 90 years
So the present age of Deepak = 70 + 62 – 90 = 42 years
Statement II:
Let the present age of Suresh be ‘x’ years
So the present age of Harish = 1.4x years
Present age of Deepak = 1.4x × 3/2 = 2.1x years
According to question: x + 1.4x + 2.1x = 3 × 30
4.5x = 90
x = 20
So the present age of Deepak = 2.1 × 20 = 42 years
5. A trader sells a homogenous mixture of a and b at the rate of Rs 32 per kg. what is the profit
percentage of the trader?
(I) He bought b at the rate of Rs 29 per kg
(I) He bought a at Rs 8 higher than the rate of b per kg 1
(III) He bought a at the rate of Rs 34 per kg
A. Either (I) or (II)
B. Any two of these
C. Only I and II
D. Only I and III
E. I, II and III together are not sufficient
Correct Answers : E. I, II and III together are not sufficient
Explanation : The quantity of each gradient a $ b in the mixture is not known, so, the cost price of the
mixture cannot be found out from the available statements. Hence profit percentage cannot be known.

Directions (6-10) : Each of the question below consists of one question and some statements given below
it. Read all the statements carefully and find out which of the statement is/are sufficient to answer the
given question.
6. In how many days Rony and Rudra together can complete work?
A. Per day efficiency of Rony, Rudra and Rohan is in the ratio 3 : 2 : 4
B. Rony and Rudra together can complete the work in 7.2 days
C. Time taken by Rony, Rudra and Rohan alone to complete the work is in the ratio 4 : 6 : 3.
A. Either B alone or A and C together
B. Any two of them
C. Either A and B or B and C
D. Only A and B together
E. All statements are required
Correct Answers : C. Either A and B or B and C
Explanation :
From A per day efficiency = 3 : 2 : 4
⇒ ratio of time taken by Rony, Rudra and Rohan alone to complete work = 4 : 6 : 3 same as (C)
From B) time taken by Rony and Rudra together = 7.2 days
Either B and A or B and C questions can be solved
7. What is the length of the platform?
A. Train L cross train S coming from the opposite side in 12 seconds, speed of train S is 18 m/sec and length
of train S is half of train L.
B. Train L takes 12 seconds to cross a pole.
C. Train L takes 18 seconds to cross a platform.
A. Either B alone or A and C together
B. Any two of them
C. Only A and C together

Correct Answers : E. All statements are required
Explanation :
Length of platform = z
Speed of train L = x
Let the length of train L = y
From statement A,
y+y218+x=12y+y218+x=12
⇒24x−3y=−432⇒24x−3y=−432
Here, two values are unknown so, we can't find the length of the platform from alone statement A.
From statement B,
= yx=12yx=12
⇒y=12x⇒y=12x
So, we can't find the length of the platform from alone statement B.
And from statement A and B,
after solving both equations, we get
x=36m/sec.x=36m/sec.
Here, we can't find the length of the platform from both statements A and B.
From statement C,
z+yx=18z+yx=18
Here, we can't find the length of the platform from alone statement C.
So, with the help of statement A, B, and C we get,
z=18x−yz=18x−y
After put the value of x and y.

We get, z=216mz=216m
So, All three statements are required.
8. What is the base radius of the cylinder?
A. Total surface area of the cylinder is 4158 cm2cm2 .
B. Volume of the given cylinder is 14553 cm3.cm3.
C. Ratio of height and radius of the given cylinder is 1/2.
A. C and either B or A
B. Any two of them
C. Only A and C together
Correct Answers : A. C and either B or A
Explanation :
𝐹𝑟𝑜𝑚 𝐴) 𝑇. 𝑆. 𝐴 = 2𝜋𝑟ℎ + 2𝜋𝑟 2 = 𝑐𝑚2
1323
(𝑟 + ℎ ) =
2
𝐹𝑟𝑜𝑚 𝐵) 𝑉 = 14553 = 𝜋𝑟 2 ℎ
9261
𝑟2ℎ =
2
From C) h : r = 1∶2
So by using C with either B or A answer can be given.
9. What will be the probability of choosing two fresh mangoes simultaneously from box X given that there are only
two boxes i.e. box X and box Y?
A. Box Y contains 30 Mangoes in which fresh and rotten mangoes in the ratio 7 : 3. Ratio of fresh mangoes in Box X
and Box Y is 2 : 3
B. Box X contains 20 Mangoes in total out of which 14 are fresh and rest are rotten.
C. Box Y contains 30 Mangoes and Box X contains 20 Mangoes respectively. Ratio of Rotten mangoes and fresh
mangoes in Box X is 7 : 3

A. ‘A’ alone
B. Any one of them
C. Either ‘B’ or ‘C’
D. Either ‘A’ or ‘B’
Correct Answers : C. Either ‘B’ or ‘C’
Explanation :
From A) Box Y = 30
Rotten mangoes in Box Y = 9 & fresh mangoes in Box Y = 21
Box X, Fresh mangoes = 14
From B) Box X = 20
Fresh mangoes in Box X = 14 Rotten mangoes in Box X = 6
From C)
Box Y = 30 mangoes
Box X = 20 Mangoes
Rotten mangoes in Box Y = 6
Fresh mangoes in Box X = 14
From Either B or C question can be solved.
10. What is the difference between the interest earned by Prashant from scheme I and II?
I. Prashant invested Rs 920 in Scheme II for the period of 3 years.
II. Prashant invested Rs 800 in scheme III which is Rs 200 less than what he invested in scheme I Time
period for both schemes I and III is 2 years
III. The ratio of the rate of Interest offered in scheme I and II is 3: 5.
A. Only II and III
B. Only I and III

C. All I,II and III
D. Any II out of given statements
E. More data is required
Correct Answers : E. More data is required
Explanation :
From Statement I
Principal for scheme II = Rs 920
Time = 3 years
From Statement 2
Principal for scheme III = Rs 800
Principal for scheme I = 800 + 200 = Rs 1000
Time = 2 years
From statement 3
I : II = 3 : 5 (Rate of Interest)
We can’t neither calculate the interest earned nor the difference in them for scheme I and II.
11. The problem consists of a question followed by 2 statements. Decide whether the data in the
statements are sufficient to answer the question. Choose the option accordingly.
Is m/9 + n/20 an integer?
I. m/18 and n/10 are integers respectively
II. m/3 and n/40 are integers respectively
A. Either statement alone is sufficient.
B. Both statements taken together are sufficient to answer the question, but neither statement alone is
sufficient.
C. Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.
D. Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.
E. Both statements together are not sufficient to answer the question.


Correct Answers : B. Both statements taken together are sufficient to answer the question, but neither
statement alone is sufficient.
Explanation :
From statement I:
m/18 is an integer
So, m is divisible by 18
So, m/9 is an integer
n/10 is an integer
n is divisible by 10
But it does not necessarily mean it is divisible by 20
So, m/9 + n/20 may or may not be an integer
From statement II:
n/40 is an integer
So, n is divisible by 40
So, n/20 is an integer
m/3 is an integer
But it does not necessarily mean it is divisible by 9
So, m/9 + n/20 may or may not be an integer
Using both statements together:
m/18 is an integer
So, m/9 is an integer
n/40 is an integer
So, n is divisible by 40

So, n/20 is an integer
So, both statements together are sufficient
12. The problem consists of a question followed by 2 statements. Decide whether the data in the
statements are sufficient to answer the question. Choose the option accordingly.
Is value of Z3 + Z2 is negative, where Z is an integer?
I: Value of Z3 is less than Z.
II: Value of Z5 is greater than Z.
A. Both statements taken together are sufficient to answer the question, but neither statement alone is
sufficient
B. Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.
C. Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.
D. Either statement alone is sufficient.
E. Both statements together are not sufficient to answer the question.
Correct Answers : D. Either statement alone is sufficient
Explanation :
Note:
· If power of a negative number is odd, then its value will be negative.
· If power of a negative number is even, then its value will be positive.
· If power of a positive number is even/odd, its value will be positive.
From statement I: Value of Z3 is less than Z.
Value of Z3 is less than Z and Z is an integer means the value of Z is less than -1.
Then, in Z3 + Z2:
Z3 will be negative and Z2 will be positive and numerical value of Z3 will be more than numerical value of Z2.
When a large negative number is added to a small positive number, then the result obtained is negative.
Therefore, Z3 + Z2 will be negative.
From statement II: Value of Z5 is greater than Z.


5
Value of Z is greater than Z means the value of Z is greater than 1.
Then, in Z3 + Z2:
Z3 and Z2 will be positive and numerical value of Z3 will be more than numerical value of Z2.
Since, addition of two positive numbers is positive, so, Z3 + Z2 will be positive.
Hence, either statement I or II alone is sufficient to find the answer.
13. Directions : Study the data carefully and answer the following questions.
Anchal and Amandeep started a business by investing in the ratio of 6: 5 and after 6 month Abhishek joined
the business with 33(1/3)% more than the initial investment of Anchal and at that time Amandeep invested
again 20% more than his initial investment. Further 6 more months, Anchal, Amandeep and Abhishek
invested again in the ratio 2: 3: 5. After 2 years, Amandeep withdraw 1/3rd of his last investment for his
child's education and at that time Anchal and Abhishek again invested in the ratio 5: 6 and further 6
months more, Anchal again invested 20% more than his last investment. They invested the whole amount
for three years and the profit earned in the business is proportional to the investment and the period of
investment.
Which of the following statement/statements is/are sufficient to answer?
If at the end of three years, total profit earned by them is Rs. 439890, then what is the share of profit of
Anchal?
Statement I: The investment by Abhishek after 2 years is 50% more than the investment by Amandeep
after 1 year.
Statement II: The initial investment of Abhishek is 4000 more than the initial investment of Anchal which is
50% less than the investment by Amandeep after 1 year.
Statement III: The investment by Anchal after 2.5 years is 50% more than the initial investment by
Abhishek.
A. Only I and II together are sufficient
B. Either I and II together or II and III together are sufficient
C. Either I and II together or I and III together are sufficient
D. Either I and III together or II and III together are sufficient
E. Any two statements together are sufficient
Correct Answers : E. Any two statements together are sufficient

Explanation :
Let initial investment by Anchal and Amandeep is Rs. 6x and 5x respectively.
After 6 months,
Initial investment by Abhishek is Rs. 4/3 * 6x = Rs. 8x
And, Amandeep again invested = 6/5 * 5x = Rs. 6x
After 1 year,
Invested by Anchal, Amandeep and Abhishek are Rs. 2y, Rs. 3y and Rs. 5y respectively.
After 2 years,
Investment by Anchal and Abhishek are 5z and 6z respectively.
Amount withdraw by Amandeep = 1/3 * 3y = y
After 2.5 years,
Investment by Anchal = 6/5 * 5z = 6z
So, ratio of profit of Anchal, Amandeep and Abhishek
= [6x * 12 + (6x + 2y) * 12 + (6x + 2y + 5z) * 6 + (6x + 2y + 5z + 6z) * 6] :
[5x * 6 + (5x + 6x) * 6 + (5x + 6x + 3y) * 12 + (5x + 6x + 3y - y) * 12] :
[8x * 6 + (8x + 5y) * 12 + (8x + 5y + 6z) * 12]
= (18x + 4y + 8z): (30x + 5y): (20x + 10y + 6z)
Total profit = Rs. 439890
From I and II:
The initial investment of Abhishek is 4000 more than the initial investment of Anchal which is 50% less than
the investment by Amandeep after 1 year.
8x = 4000 + 6x
=> 2x = 4000
=> x = 2000

And, 6x = 50/100 * 3y
=> y = 6 * 2000 * 100/50 * 1/3
=> y = 8000
The investment by Abhishek after 2 years is 50% more than the investment by Amandeep after 1 year.
6z = 150/100 * 3y
=> z = 1/6 * 150/100 * 3 * 8000
=> z = 6000
= (18x + 4y + 8z): (30x + 5y): (20x + 10y + 6z)
= (18 * 2000 + 4 * 8000 + 8 * 6000): (30 * 2000 + 5 * 8000): (20 * 2000 + 10 * 8000 + 6 * 6000)
= 116000: 100000: 156000
= 116: 100: 156
= 29: 25: 39
So, share of profit of Anchal = 439890 * 29/(29 + 25 + 39) = Rs. 137170
Hence, statement I and II together are sufficient
From II and III:
The initial investment of Abhishek is 4000 more than the initial investment of Anchal which is 50% less than
the investment by Amandeep after 1 year.
8x = 4000 + 6x
=> 2x = 4000
=> x = 2000
And, 6x = 50/100 * 3y
=> y = 6 * 2000 * 100/50 * 1/3
=> y = 8000
The investment by Anchal after 2.5 years is 50% more than the intial investment by Abhishek.

6z = 150/100 * 8x
=> z = 1/6 * 150/100 * 8 * 2000
=> z = 4000
= (18x + 4y + 8z): (30x + 5y): (20x + 10y + 6z)
= (18 * 2000 + 4 * 8000 + 8 * 4000): (30 * 2000 + 5 * 8000): (20 * 2000 + 10 * 8000 + 6 * 4000)
= 100000: 100000: 144000
= 100: 100: 144
= 25: 25: 36
So, share of profit of Anchal = 439890 * 25/(25 + 25 + 36) = Rs. 127875
Hence, statement II and III together are sufficient
From I and III:
The investment by Abhishek after 2 years is 50% more than the investment by Amandeep after 1 year.
6z = 150/100 * 3y
=> z = 1/6 * 3/2 * 3 * y
=> z = 3y/4
=> y = 4z/3
The investment by Anchal after 2.5 years is 50% more than the intial investment by Abhishek.
6z = 150/100 * 8x
=> z = 1/6 * 3/2 * 8 * x
=> z = 2x
=> x = z/2
= (18 * z/2 + 4 * 4z/3 + 8z): (30 * z/2 + 5 * 4z/3): (20 * z/2 + 10 * 4z/3 + 6z)
= (9z + 16z/3 + 8z): (15z + 20z/3): (10z + 40z/3 + 6z)

= 67: 65: 88
So, share of profit of Anchal = 439890 * 67/(67 + 65 + 88) = Rs. 133966.5
Hence, statement I and III together are sufficient
Therefore, any two statement together are sufficient
14. Each of the questions below consists of a question and three statements numbered I, II and III given
below it. You have to decide whether the data provided in the statements are sufficient to answer the
question. Read all the statements and give answer.
There are 5 artists, 8 dancers, some players and some singers in a locality. Find the probability of selecting
2 artists and 2 singers from the locality.
Statement I: Probability of selecting one player from the locality is 1/5.
Statement II: A committee of four members is to be formed such that the committee contains 1 artist, 1
dancer, 1 player and 1 singer. The number of ways in which this can be possible is 480.
Statement III: Probability of selecting one artist from the locality is ¼.
A. Only I and II
B. Any two of the three
C. All I, II and III
D. Only I and either II or III
E. Cannot be answered even after combining all the statements.
Correct Answers : D. Only I and either II or III
Explanation :
Artists = 5
Dancers = 8
Let, Players = m
And Singers = n
Total = 5 + 8 + m + n = 13 + m + n

From I and II:
m/(13 + m + n) = 1/5
=> 5m = 13 + m + n
=> 5m - m - n = 13
=> 4m - n = 13 ------------ (i)
And
5
c1 x 8c1 x mc1 x nc1 = 480
=> 5 x 8 x m x n = 480
=> m x n = 480/40
=> mn = 12
=> n = 12/m ------------- (ii)
From (i) and (ii)
4m - 12/m = 13
=> 4m2 - 12 = 13m
=> 4m2 - 13m - 12 = 0
=> 4m2 - 16m + 3m - 12 = 0
=> 4m(m - 4) + 3(m - 4) = 0
=> (m - 4)(4m + 3) = 0
=> m = 4, -3/4(rejected)
=> m = 4
From (ii)
n = 12/4 = 3
Hence, Players = 4
And Singers = 3
Total = 13 + 4 + 3 = 20

5 3 20
Required probability = ( c2 x c2)/ c4
= (10 x 3)/4845
= 2/323
From I and III:
m/(13 + m + n) = 1/5
=> 5m = 13 + m + n
=> 5m - m - n = 13
=> 4m - n = 13 ------------ (i)
And
5/(13 + m + n) = ¼
=> 20 = 13 + m + n
=> m + n = 20 - 13
=> m + n = 7 ------------------ (iii)
Adding (i) and (iii)
4m - n + m + n = 13 + 7
=> 5m = 20
=> m = 20/5
=> m = 4
From (ii)
4+n=7
=> n = 7 - 4
=> n = 3
Hence, Players = 4
And Singers = 3
Total = 13 + 4 + 3 = 20

5 3 20
Required probability = ( c2 x c2)/ c4
= (10 x 3)/4845
= 2/323
From II and III:

5
c1 x 8c1 x mc1 x nc1 = 480
=> 5 x 8 x m x n = 480
=> m x n = 480/40
=> mn = 12
=> n = 12/m ------------- (ii)
And
5/(13 + m + n) = ¼
=> 20 = 13 + m + n
=> m + n = 20 - 13
=> m + n = 7 ------------------ (iii)
From (ii) and (iii)
m + 12/m = 7
=> m2 + 12 = 7m
=> m2 - 7m + 12 = 0
=> m2 - 4m - 3m + 12 = 0
=> m(m - 4) - 3(m - 4) = 0
=> (m - 3)(m - 4) = 0
=> m = 3, 4
From (iii)
n = 4, 3
Required value cannot be determined.

Hence, only I and either II or III together are sufficient.
15. The problem below consists of a question and three statements numbered I, II and III given below it.
You have to decide whether the data provided in the statements are sufficient to answer the question.
Read all the statements and give answer.
Find the time taken by the train A to cross another train of length 380 m running in the direction of the
train with the speed of 40 Km/h
Statement I: The train A can cross a platform of length 780 m in 90 seconds.
Statement II: The train A can cross a tree in 31.5 seconds.
Statement III: The train A can cross another train of length 440 m coming from the opposite direction with
the speed of 38 Km/h in 36 seconds.
A. All I, II and III together are sufficient
B. Any two statements together are sufficient
C. Only statement I and either statement II or III together are sufficient
D. Only statements II and III together are sufficient
E. Only statement II and either statement I or III together are sufficient
Correct Answers : B. Any two statements together are sufficient
Explanation :
Let, length of the train be l metres
And speed of the train be s Km/h.
From I and II:
l + 780 = s x 5/18 x 90
=> l + 780 = 25s
=> l = 25s - 780 ------------ (i)
l = s x 5/18 x 31.5
=> l = 8.75s ----------- (ii)
From (i) and (ii)

8.75s = 25s - 780
=> 25s - 8.75s = 780
=> 16.25s = 780
=> s = 780/16.25
=> s = 48 Km/h
From (ii)
l = 8.75 x 48 = 420 m
Let, required time = t seconds
420 + 380 = (48 - 40) x 5/18 x t
=> 800 = 8 x 5/18 x t
=> t = 800/8 x 18/5
=> t = 360 seconds
From I and III:
l + 780 = s x 5/18 x 90
=> l + 780 = 25s
=> l = 25s - 780 ------------ (i)
l + 440 = (s + 38) x 5/18 x 36
=> l + 440 = (s + 38) x 10
=> l + 440 = 10s + 380
=> l = 10s + 380 - 440
=> l = 10s - 60 -------------- (iii)
From (i) and (iii)
25s - 780 = 10s - 60
=> 25s - 10s = 780 - 60
=> 15s = 720

=> s = 720/15
=> s = 48 Km/h
From (i)
l = 25 x 48 - 780
=> l = 1200 - 780
=> l = 420 m
420 + 380 = (48 - 40) x 5/18 x t
=> 800 = 8 x 5/18 x t
=> t = 800/8 x 18/5
=> t = 360 seconds
From II and III:
l = s x 5/18 x 31.5
=> l = 8.75s ----------- (ii)
l + 440 = (s + 38) x 5/18 x 36
=> l + 440 = (s + 38) x 10
=> l + 440 = 10s + 380
=> l = 10s + 380 - 440
=> l = 10s - 60 -------------- (iii)
From (ii) and (iii)
8.75s = 10s - 60
=> 10s - 8.75s = 60
=> 1.25s = 60
=> s = 60/1.25
=> s = 48 Km/h

From (ii)
l = 8.75 x 48
=> l = 420 m
420 + 380 = (48 - 40) x 5/18 x t
=> 800 = 8 x 5/18 x t
=> t = 800/8 x 18/5
=> t = 360 seconds
Hence, any two of the three statements are sufficient.
16. The question consists of three statements numbered “I, II and III” given below it. You have to decide
A, B, C and D together can complete a piece of work in 3.75 days. Find the time taken by A and D together
to complete the whole work.
Statement I: A and B together can complete the whole work in 7.5 days, while C and D together can
complete 80% of the work in 6 days.
Statement II: If all of them together completed the work and for this Rs. 2400 is given as wage, out of which
amount received by A and D together is Rs. 1650.
Statement III: A is twice efficient as C and B is 60% less efficient than D.
A. The data in both statements II and III together are necessary to answer the question, while data in
statement I alone is not sufficient to answer the question.
B. The data in both statements I and III together are necessary to answer the question, while data in
statement II alone is not sufficient to answer the question.
C. The data in both statements I and II together are necessary to answer the question, while data in
statement III alone is not sufficient to answer the question.
D. The data either in both statement I and statement II together or in both statement II and III together are
necessary to answer the question.
E. The data in either statement II alone or in statement I and statement III together are necessary to
answer the question.

Correct Answers : E. The data in either statement II alone or in statement I and statement III together are
Explanation :
Let efficiency of A, B, C and D be a, b, c and d units per day respectively.
Statement I:
Total time taken by C and D together to complete the whole work = 6 × 100/80 = 7.5 days
So, efficiency of A + B = efficiency of C + D
So, a + b = c + d
Statement I alone is not sufficient to answer the question.
Statement II:
Efficiency of (A + D)/Efficiency of (A + B + C + D) = 1650/2400 = 11/16
So, Total amount of work to be completed = 16 × 3.75 = 60 units
Time taken by A and D together to complete the whole work = 60/11 days
Statement II alone is sufficient to answer the question.
Statement III:
a = 2c
b = 0.4 × d
Statement III alone is not sufficient to answer the question.
Combining statement I and III:
2c + 0.4d = c + d
c = 0.6d
So, a = 2 × 0.6d = 1.2d
Efficiency of A and D together = a + d = 2.2d units per day
Efficiency of A, B, C, D together = 2 × (a + b) = 2 × (1.2d + 0.4d) = 3.2d units per day
Total amount of work to be completed = 3.2d × 3.75 = 12d

Amount of time taken by A and D together to complete the work = 12d/2.2d = 60/11 days
So, the data in statement I and statement III together are sufficient to answer the question.
Present age of Kunal, Kamal, Kaushal and Kartik is (x – 2) years, (x + 2) years, (x + 8) years and (x – 4) years
respectively. Find present age of Kaushal.
Statement I: Average present age of Kunal and Kartik together is (x – 16) years less than average age of
Kamal and Kaushal together after 6 years.
Statement II: Average present age of Kunal and Kamal taken together is 5 years less than average present
age of Kamal and Kaushal taken together.
Statement III: Average age of Kunal and Kaushal after 12 years is 12 years more than average age of Kamal
and Kartik after 4 years.
A. The data in statement I alone is sufficient to answer the question, while the data in statement II and
statement III alone are not sufficient to answer the question.
B. The data either in statement II alone is sufficient or both in statement I and statement III together are
C. The data in both statements II and III together are necessary to answer the question, while data in
D. The data in both statements I and III together are necessary to answer the question, while data in
E. The data in both statements I and II together are necessary to answer the question, while data in
Correct Answers : A. The data in statement I alone is sufficient to answer the question, while the data in
statement II and statement III alone are not sufficient to answer the question.
Explanation :
Statement I:
[(x – 2) + (x – 4)]/2 = [(x + 2) + (x + 8) + 12]/2 – (x – 16)
(2x – 6)/2 = (2x + 22)/2 – (x – 16)
x – 3 = x + 11 – x + 16

x – 3 = 27
x = 30
Present age of Kaushal = x + 8 = 38 years
Therefore, statement I alone is sufficient to answer the question.
Statement II:
[(x – 2) + (x + 2)]/2 = [(x + 2) + (x + 8)]/2 – 5
x=x+5–5
x=x
So, we can’t determine the present age of Kaushal
Therefore, statement II alone is not sufficient to answer the question.
Statement III:
[(x – 2) + (x + 8) + 24]/2 = [(x + 2) + (x – 4) + 8]/2 + 12
(2x + 30)/2 = (2x + 6)/2 + 12
x + 15 = x + 3 + 12
x=x
So, we can’t determine the present age of Kaushal.
Therefore, statement III alone is not sufficient to answer the question.
Find the value of a two-digit number.
Statement I: The sum of the digits is 11, while their product is 18.
Statement II: The sum of squares of digits is 85.
Statement III: The square of the units place digit is 77 more than the square of the tens place digit.
A. The data in both statements II and III together are necessary to answer the question, while data in

C. The data in both statements I and II together are necessary to answer the question, while data in
D. The data in statement I alone is sufficient to answer the question, while the data in statement II and
statement III alone are not sufficient to answer the question.
E. The data either in either statement II alone, or in statement I and statement III together are sufficient to
answer the question.
Correct Answers : B. The data in both statements I and III together are necessary to answer the question,
while data in statement II alone is not sufficient to answer the question.
Explanation :
Let the two-digit number be 10x + y.
Statement I:
x + y = 11
And, x × y = 18
(x – y)2 = (x + y)2 – 4xy
(x – y)2 = 121 – 4 × 18
(x – y)2 = 49
x–y=7
So, x = 9 and y = 2
So, the number can be 92 or 29.
So, data in statement I alone is not sufficient to answer the question.
Statement II:
x2 + y2 = 85
So, data in statement II alone is not sufficient to answer the question.
Statement III:
y2 – x2 = 77

So, data in statement III alone is not sufficient to answer the question.
Combining statement I and III:
The number will be 29.
There are four students namely Abhay, Anil, Aniket and Arpit. Abhay, Anil and Arpit secured 65%, 40% and
52% marks respectively in an examination. Find individual marks of Abhay, Anil, Aniket and Arpit.
Statement I: Aniket got 12 marks more than that by Arpit while 7.5 marks less than Abhay’s marks.
Statement II: Total of Abhay’s and Anil’s marks is 157.5.
Statement III: Aniket obtained 90 marks, which is 12 marks more than Arpit’s mark.
A. The data in statements I alone, II alone and III alone are sufficient to answer the question.
C. The data either in statement II alone or in statement I and statement III together are sufficient to answer
the question.
D. The data either in statement I alone or data in statement II and statement III are necessary to answer
the question.
E. The data in both statements I and II together are necessary to answer the question, while statement III
alone is not sufficient to answer the question.
Correct Answers : A. The data in statements I alone, II alone and III alone are sufficient to answer the
question.
Explanation :
Let maximum marks for the exam is y.
Statement I:
Let total marks obtained by Aniket is x
Marks obtained by Arpit = x – 12
Marks obtained by Abhay = x + 7.5
Difference between marks obtained by Abhay and Arpit = (x + 7.5) – (x – 12) = 19.5

So, 0.65y – 0.52y = 19.5
0.13y = 19.5
y = 150
So, marks obtained by Abhay = 0.65 × 150 = 97.5
Marks obtained by Anil = 0.4 × 150 = 60
Marks obtained by Arpit = 0.52 × 150 = 78
Marks obtained by Aniket = 78 + 12 = 90
Statement II:
0.65y + 0.4y = 157.5
1.05y = 157.5
y = 150
Statement III:
Marks obtained by Arpit = 90 – 12 = 78
0.52y = 78
y = 150

So, data in statement III alone is sufficient to answer the question.
Direction (20-24) : In each of the following question, a question is followed by two or three statements.
Read all the statements and find that which statement are required to answer the question and answer
accordingly.
20. If an agent received commission of 2% of sales he has booked in a month, what was the sales booked
by the agent in the month of October 2017?
Statement I: The sales booked by the agent in the month of October in 2017 minus agents commission was
235000.
Statement II: The selling price of the sales booked by the agent in the month of October 2017 was 125% of
the original purchase price of Rs. 255000.
A. Neither (I) nor (II)
B. Either (I) or (II)
C. Both (I) and (II)
D. Only (II)
E. Only (I)
Correct Answers : B. Either (I) or (II)
Explanation :
If we consider the first statement we come to know that the
difference between the sales he booked in the month of October and the agents commission = 235000
let he booked X, then commission = 2X/100
X – 2X/100 = 235000
So, statement (I) is alone sufficient to answer the question.
Statement II
If we consider statement II, we get that sales price is 125% of original purchase price
Sales price = 255000 * 125/100 = 318750
And we know his commission is 2% of the sales he booked.
So, by using this we can get the answer.


Hence both the statements are independently sufficient.
21. Car A is travelling 3/4th of the speed that car B is travelling at. How fast A is travelling?
Statement I: If both cars decrease their speeds by 5 km/h. Car A would be travelling at 2/3rd the speed of
B.
Statement II: If both cars increase their speeds by 10 km/h A would be travelling at 1/2nd the speed of car
B.
A. Only (I)
B. Only (II)
C. Either (I) or (II)
D. Neither (I) nor (II)
E. Both (I) and (II)
Correct Answers : C. Either (I) or (II)
Explanation :
Let car B’s speed is = X km/h
Car A’s speed will be = 3X/4 km/h
Statement I
If both cars decrease their speeds by 5 km/h
A’s speed = (3X/4) – 5 km/h
B’s speed = X – 5 km/h
Car A’s speed = 2/3 of car B’s speed
(3X/4) – 5 = 2/3(X-5)
By solving this we can find out A’s speed.
Now by statement II
If both the cars increase their speeds by 10km/h
A’s speed = (3X/4) +10 km/h
B’s speed = X + 10 km/h


A’s speed = ½ B’s speed
(3X/4) +10 = ½(X+10)
By solving this we can find out the value of X.
Hence both the statements are independently sufficient to solve
22. In an election 3 candidates P. Q and R were represented. How many votes did each of them received?
Statement I: P receives 248 votes more than Q and 399 votes more than R.
Statement II:Total votes cast where 1153
A. Only (I)
B. Only (II)
Correct Answers : E. Both (I) and (II)
Explanation :
Let P receives P votes
Q receives Q votes
And R receives R votes
Statement I
P = Q + 248
P = R + 499
Statement I alone isn’t sufficient
Statement II
Total votes cast were 1153,
P + Q + R = 1153
P + (P – 248) + (P – 399) = 1153

3P = 1800
P = 600
Hence statement I and II both are required.
23. Amit purchased 20 packets of shampoo, some of which contains chemical. How many of the packets
did not contains chemical?
Statement I: Of the packets Amit purchased, the number of packets contains chemical is 25% of total
packets.
Statement II: Of the packets purchased, the number of packets containing chemical is odd.
A. Only (I)
B. Only (II)
Correct Answers : A. Only (I)
Explanation : by statement I
Total number of shampoo packets purchased by Amit = 20
Packets that contains chemical = 20/4 = 5 packets
So, packets that don’t contain chemical are = 15
Hence statement I alone is sufficient.
Statement II does not give any data that can be helpful to solve that’s why it isn’t sufficient
24. Square A has sides of length 8 cm. is the area of the square B is exactly half of the area of square A?
Statement I: The length of the diagonal of square B is equal to the length of one side of square A.
Statement II: The perimeter of square B is twice the length of the diagonal of square A
A. Only (I)
B. Only (II)


Correct Answers : C. Either (I) or (II)
Explanation : the side of square A = 8 cm

Area of the square A = 64 cm square
By statement I
Let length of the side of square B is = X cm
Now diagonal = X√2
X√2=8
So, X = 4√2
Area of square B = 32
And area of square A = 64
32/64 = 1/2
Hence, option I is alone sufficient.
Statement II
The perimeter of square B is twice the length of the diagonal of square A
Side of square A = 8
Diagonal = 8√2
2(8√2)= Perimeter of square B
Let side of square B is X
4X =16√2
X =4√2
Area of square B = 32
32/64 = ½
So, statement II is sufficient alone
25. In the question, a question is given followed by information in three statements. You have to
consider the information in all the three statements and decide the information in which of the
statement(s) is not necessarily required to answer the questions and therefore can be dispensed with
Indicate your answer accordingly.
What is the marked price of an article?
I. The cost price of the article is Rs. 680
II. The selling price after offering 6% discount on the marked price is Rs. 799.
III. The profit earned would have been 25% if no discount had been offered.
A. Only I

B. Only III
C. Only II or III
D. Only II
E. Only I and II
Correct Answers : D. Only II
Explanation : Selling price (S.P.) = Marked price (M.P.) – Discount
We can find the M.P. of the article by statement II and by using the above formula.
By using statements I and III, and by using the above formula we can find the M.P. of the article.
As statement II alone is sufficient to answer the question.
∴ Statements I or III is not necessarily required to answer the question.
26. The following question consists of a question followed by three statements numbered I, II and III.
Decide if data given in the statements are sufficient to answer the questions below.
In which year was Sanam born?
Statements:
I. Sanam is six years older than Gopla
II. Gopla's brother was born in 1972.
III. Sanam's brother is two years younger than Gopla's brother who was eight years younger than Gopla
A. Only I and II
B. Only II and III
C. Only I and III
D. All I, II and III
E. None of these
Correct Answers : D. All I, II and III
Explanation : From I, we know that Sanam is six years older than Gopla.
From II, we know that Gopla's brother was born in 1972.

From III, Sanam's brother is two years younger than Gopla's brother who was eight years younger than
Gopla.
Combining all the statements we get,
From II and III, we get Gopla's brother was 8 years younger to him i.e. Gopla was born in 1964.
From I, we find that Sanam is 6 years older than Gopla. Thus, Sanam was born in 1958.
Hence, all I, II and III are required to answer the above question
27. In this question, a question is given followed by information in three statements. You have to
What is Jitan’s share in the profit earned at the end of two years. in a joint business run by Jitan, Kiran and
Karan?
I. Jitan invested Rs. 1,36,000 to start the business
II. Kiran and Karan joined Jitan’s business after four months, investing amount in the ratio of 7 : 5
III. Total amount invested by Kiran and Karan is Rs. 3.6 lakh.
A. Only II
B. Only III
C. Only either II or II
D. Information in all the three statements is required for answering the question
E. The question cannot be answered even with the information in all the three statements
Correct Answers : E. The question cannot be answered even with the information in all the three
statements
Explanation : From the given three statements we cannot get the value of total profit.
∴ The question cannot be answered even with the information in all the three statements
28. In this question, a question is given followed by information in three statements. You have to consider
the information in all the three statements and decide the information in which of the statement(s) is not
necessarily required to answer the questions and therefore can be dispensed with Indicate your answer
accordingly.
What is Anushka’s present age?


I. Anushka’s present age is double the age of her son.
II. The ratio of the present ages of Anushka and her mother is 3 : 4
III. Four years. hence the ratio of Anushka’s age to her son’s will be 5 : 4
A. Only II
B. Only III
C. Either I or II
D. Either II or III only
E. None of these
Correct Answers : A. Only II
Explanation :
By using statement I alone, we cannot find Anushka’s age as we must know the age of her son.
By using statement II alone, we cannot find Anushka’s age as we must know the age of her mother.
By using statement I & statement III, we can find the ages of both Anushka and her son by proper Algebra.
∴ Statement II is not necessarily required to answer the question.
29. In these questions, a question is given followed by information in three statements. You have to
What is the monthly income of Vivek?
I. Vivek’s expenditure is 88% of his monthly income and the rest are his savings.
II. The monthly savings of Vivek is Rs. 5,760
III. Out of Vivek’s total monthly earnings, one - fifth is spent on cab and an amount of Rs. 30,240 on other
items
A. Only II
B. Only III
C. Only II or III
D. The question cannot be answered even with the information in all the three statements

E. None of these
Correct Answers : B. Only III
Explanation : By using statement I and II we can get the answer as follows:
Vivek’s expenditure is 88% of his income and the rest is his savings.
⇒ Vivek’s savings = 100 – 88 = 12%
The monthly savings of Vivek is Rs. 5,760.
⇒ 12% = 5760
⇒ 100% = 5760/0.12 = Rs. 48,000
∴ Vivek’s monthly income = Rs. 48,000
30. What will be the speed of boat A in still water when travelling in a river?
I: Time taken by boat B to go 40 km upstream is 24 minutes less than the time taken by boat A to cover
same distance in upstream.
II: Total time taken by boat A to go 15 km upstream and comes back to the same point is 1.125 hours.
III: In a race of 3.6 km in the river boat B beats the boat A by 720 meters and 400 meters when travelling in
upstream and downstream respectively.
A. Only I and II together are sufficient.
B. Either I and III together or II and III together are sufficient.
C. Either II alone or I and III together are sufficient.
D. Either I alone or II and III together are sufficient.
E. Combination of any two of them together is sufficient.
Correct Answers : B. Either I and III together or II and III together are sufficient.
Explanation : Let the speed of boats A and B in still water is 'a' and 'b' respectively and speed of stream is
'x' km/h.
From I:
According to the question:
[40/(a - x)] = [40/(b - x)] + (24/60)

[40/(a - x)] = [40/(b - x)] + 0.4 ......... (1)
Statement I alone is not sufficient.
From II:
[15/(a - x)] + [15/(a + x)] = 1.125 ....... (2)
Statement II alone is not sufficient.
From III:
3.6 * [(a - x)/(b - x)] = 3.6 - (720/1000)
3.6 * [(a - x)/(b - x)] = 2.88 ........ (3)
3.6 * [(a + x)/(b + x)] = 3.6 - (400/1000)
3.6 * [(a + x)/(b + x)] = 3.2 ......... (4)
Statement III alone is not sufficient.
From I and II:
From statement I we get:
[40/(a - x)] = [40/(b - x)] + 0.4 ......... (1)
From statement II we get:
[15/(a - x)] + [15/(a + x)] = 1.125 ....... (2)
After combining both the equations there are total three variables 'a', 'b' and 'x' in two equations.
Statement I and II together are not sufficient.
From I and III:
From statement I we get:
[40/(a - x)] = [40/(b - x)] + 0.4 ......... (1)
From statement III we get:
3.6 * [(a - x)/(b - x)] = 2.88 ........ (3)

(b - x) = 1.25(a - x)
b = 1.25a - 1.25x + x
b = 1.25a - 0.25x
3.6 * [(a + x)/(b + x)] = 3.2 ......... (4)
Put the value of 'b' in equation (4):
3.6 * [(a + x)/(1.25a - 0.25x + x)] = 3.2
9(a + x) = 8(1.25a + 0.75x)
9a + 9x = 10a + 6x
a = 3x
b = 1.25a - 0.25x
b = 3.5x
Now, put the value of 'a' and 'b' in equation (1):
[40/(3x - x)] = [40/(3.5x - x)] + 0.4
(20/x) - (16/x) = 0.4
4/x = 0.4
x = 10
a = 3x = 30
Hence, speed of boat A in still water = 30 km/hr
Statement I and III together are sufficient.
From II and III:
From statement II we get:
[15/(a - x)] + [15/(a + x)] = 1.125 ........ (2)
From statement III we get:
3.6 * [(a - x)/(b - x)] = 2.88 ........ (3)
(b - x) = 1.25(a - x)

b = 1.25a - 1.25x + x
b = 1.25a - 0.25x
3.6 * [(a + x)/(b + x)] = 3.2 ......... (4)
Put the value of 'b' in equation (4):
3.6 * [(a + x)/(1.25a - 0.25x + x)] = 3.2
9(a + x) = 8(1.25a + 0.75x)
9a + 9x = 10a + 6x
a = 3x
Now, put the value of 'a' in equation (2):
[15/(3x - x)] + [15/(3x + x)] = 1.125
(7.5/x) + (3.75/x) = 1.125
11.25/x = 1.125
x = 10
a = 3x = 30
Hence, speed of boat A in still water = 30 km/h
Statement II and III together are sufficient.

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Quant Data Sufficiency Practice Questions 2021

Statement I: 3x > 210 while 2y < 170.

3x > 210 i.e. x > 70 while 2y < 170 = y< 85

So the value of ‘5x – 3y’ = 5 × 77 – 3 × 80 = 145

So, data in statement I alone is sufficient to answer the question.

y – x satisfies only for ‘x’ = 77 and y = 80.

So the value of ‘5x – 3y’ = 5 × 77 – 3 × 80 = 145

So, data in statement II alone is sufficient to answer the question.

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Explanation : Statement I: Let the cost price of item A = Rs. x

So the cost price of item B = Rs. 1000 – x

Selling price of item A = Rs. 1.2x

Selling price of item B = 0.90 × (1000 – x) = Rs. 900 – 0.9x

According to question: 1.2x + 900 – 0.9x = 1000 + 80

So the cost price of item A = Rs. 600

So, data in statement I alone is sufficient to answer the question.

Selling price of item B = 1080 – 720 = Rs. 360

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Cost price of item A can’t be determined.

So, data in statement II alone is not sufficient to answer the question.

So according to question: 0.331x + 0.39y = 5827 …… (i)

Amount invested by Rahul can‘t be determined

So data in statement I alone is not sufficient to answer the question.

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So according to question: 0.21x + 0.26y = 3810 ……. (ii)

Amount invested by Rahul can‘t be determined

So data in statement II alone is not sufficient to answer the question.

Combining statement I and II:

Solving equations (i) and (ii) we get x = 7000 and y = 9000

So the total amount invested by Rahul = 7000 + 9000 = Rs. 16,000

Sum of the present ages of Deepak and Suresh = 31 × 2 = 62 years

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So the present age of Deepak = 70 + 62 – 90 = 42 years

So, data in statement I alone is sufficient to answer the question.

Let the present age of Suresh be ‘x’ years

So the present age of Harish = 1.4x years

Present age of Deepak = 1.4x × 3/2 = 2.1x years

According to question: x + 1.4x + 2.1x = 3 × 30

So the present age of Deepak = 2.1 × 20 = 42 years

So, data in statement II alone is sufficient to answer the question.

(I) He bought b at the rate of Rs 29 per kg

(I) He bought a at Rs 8 higher than the rate of b per kg 1

(III) He bought a at the rate of Rs 34 per kg

A. Either (I) or (II)

B. Any two of these

D. Only I and III

E. I, II and III together are not sufficient

Correct Answers : E. I, II and III together are not sufficient

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A. Per day efficiency of Rony, Rudra and Rohan is in the ratio 3 : 2 : 4

A. Either B alone or A and C together

B. Any two of them

C. Either A and B or B and C

D. Only A and B together

E. All statements are required

Correct Answers : C. Either A and B or B and C

From A per day efficiency = 3 : 2 : 4

From B) time taken by Rony and Rudra together = 7.2 days

Either B and A or B and C questions can be solved