Data Sufficiency MCQ Quiz - Objective Question with Answer for Data Sufficiency - Download Free PDF
Last updated on Jul 7, 2025
Latest Data Sufficiency MCQ Objective Questions
Data Sufficiency Question 1:
Directions: Below question is followed by two statements labeled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:
There are four consecutive even integers. Find the average of these integers?
Statement I: The largest number is 6 more than the smallest number.
Statement II: The second smallest number is 20% less than the third number.
Answer (Detailed Solution Below)
Data Sufficiency Question 1 Detailed Solution
Let the four consecutive even integers be:
x, (x + 2), (x + 4), (x + 6)
The average of these numbers =
⇒ [x + (x + 2) + (x + 4) + (x + 6)] ÷ 4 = (4x + 12) ÷ 4 = x + 3
Statement I: The largest number is 6 more than the smallest number.
⇒ (x + 6) = x + 6 ⇒ Always true for consecutive even numbers.
This confirms the numbers are in the pattern we assumed, but does not give the value of x.
Thus, Not sufficient to find the average.
Statement II: The second smallest number is 20% less than the third number.
Second smallest = (x + 2)
Third number = (x + 4)
⇒ (x + 2) = (x + 4) – 20% of (x + 4)
⇒ x + 2 = 0.8(x + 4)
⇒ x + 2 = 0.8x + 3.2
⇒ x - 0.8x = 3.2 - 2 ⇒ 0.2x = 1.2 ⇒ x = 6
Now we can find all the numbers:
⇒ x = 6 ⇒ Numbers: 6, 8, 10, 12
⇒ Average = (6 + 8 + 10 + 12) ÷ 4 = 36 ÷ 4 = 9
Thus, Sufficient to find the average.
Therefore, the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient.
Data Sufficiency Question 2:
Directions: Below question is followed by two statements labeled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:
What is the difference between the amounts invested in Scheme X and Scheme Y?
Statement I:
Rahul invests a total of ₹10,000 in Scheme X (for 2 years) and Scheme Y (for 3 years). Scheme Y offers 12% simple interest per annum.
Statement II:
Scheme X offers 8% compound interest annually. The total interest earned from both schemes after their respective periods is ₹2,390.
Answer (Detailed Solution Below)
Data Sufficiency Question 2 Detailed Solution
Let: x = amount invested in Scheme X 10000 – x = amount invested in Scheme Y
From Statement I alone: We only know x + (10000 – x) = 10000, and Scheme Y’s rate and period, but no interest amounts ⇒ cannot find x.
From Statement II alone: We know Scheme X rate (8% compounded annually for 2 years) and Scheme Y rate (12% simple for 3 years), and total interest = ₹2390, but we don’t know the total principal (10000) ⇒ cannot determine x.
Using I and II together:
Interest from X = x × [(1.08)² – 1] = 0.1664x
Interest from Y = (10000 – x) × (12% × 3) = 0.36 (10000 – x) = 3600 – 0.36x
Total interest = 0.1664x + (3600 – 0.36x) = 3600 – 0.1936x = 2390 ⇒ 3600 – 2390 = 0.1936x ⇒ 1210 = 0.1936x ⇒ x = 6250
⇒ Amount in Y = 10000 – 6250 = 3750
⇒ Difference = 6250 – 3750 = ₹2500
Thus, the data given in both Statements I and II together are necessary to answer the question.
Data Sufficiency Question 3:
Directions: Below question is followed by two statements labeled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:
The total number of employees in Companies X and Y is equal. Find the number of female employees in X and Y combined?
Statements:
I: The male-to-female ratio in X is 4:3 and in Y is 5:2. The ratio of junior to senior male employees in X is 3:5.
II: The ratio of junior to senior female employees in Y is 1:2. The sum of senior male employees in X and senior female employees in Y is 630.
Answer (Detailed Solution Below)
Data Sufficiency Question 3 Detailed Solution
Let that total number be T.
Statement I:
Male : Female in X = 4 : 3 → So in X, male = 4x and female = 3x ⇒ total in X = 7x
Male : Female in Y = 5 : 2 → So in Y, male = 5y and female = 2y ⇒ total in Y = 7y
Now, we are given that total employees in X = total employees in Y
⇒ 7x = 7y ⇒ x = y
Now:
Female in X = 3x
Female in Y = 2x (since y = x)
Total females = 3x + 2x = 5x
But x is unknown.
Even the ratio of junior to senior male employees in X (3:5) is irrelevant here unless we know a value.
So, Statement I alone is NOT sufficient.
Statement II:
Ratio of junior to senior female in Y = 1:2
Let junior female = a, senior female = 2a ⇒ total female in Y = a + 2a = 3a
Senior male in X + senior female in Y = 690
We don’t know total male in X or how many are senior → cannot extract female number in X.
Also, we cannot connect this info to total employees (T) or get specific values.
So, Statement II alone is NOT sufficient.
Now combine both statements:
From Statement I:
Female in X = 3x
Female in Y = 2x
Total females = 5x
From Statement II:
Senior male in X + senior female in Y = 690
→ From Statement I, male in X = 4x
→ Ratio of junior to senior male = 3:5
⇒ So, senior male in X = 5 parts out of (3+5) = 5/8 of 4x
⇒ Senior male in X = (5/8) × 4x = (20x)/8 = 2.5x
Female in Y = 2x
→ From Statement II, ratio of junior:senior = 1:2 ⇒ senior = 2 parts out of 3 ⇒ 2/3 of 2x = (4x)/3
Now:
2.5x + (4x)/3 = 690
(7.5x + 4x)/3 = 690
(11.5x)/3 = 690
11.5x = 2070
x = 180
Now we can compute:
Female in X = 3x = 540
Female in Y = 2x = 360
Total females = 900
Thus, Both statements together are necessary.
Data Sufficiency Question 4:
In the question, two quantities I, and II are given. You have to solve both the quantities and establish the correct relation between Quantity - I and Quantity - II and choose the correct option accordingly.
The number of male managers in company P is 20% more than that of female managers, while the number of male non - managers and female non – manager in same company is 25% more than the male manager and female manager respectively. Difference between total male and total female in the office is 90. Out of total male non – manager 50% are male clerk. Number of female clerks is 25 more than the number of male clerks
Quantity I: Number of female clerks is what percent of number of male manager?
Quantity II: Number of male clerks is what percent of number of female manager?
Answer (Detailed Solution Below)
Data Sufficiency Question 4 Detailed Solution
Calculation
Let, Number of female managers = x
Then,
Male managers = 1.2x (20% more than female managers)
Male non-managers = 25% more than male managers
= 1.25 × 1.2x = 1.5x
Female non-managers = 25% more than female managers
= 1.25 × x = 1.25x
Total males and total females
Total males = male managers + male non-managers
= 1.2x + 1.5x = 2.7x
Total females = female managers + female non-managers
= x + 1.25x = 2.25x
Difference between total males and females = 90
Or, 2.7x − 2.25x = 0.45x = 90
⇒ x=90 / 0. 45 = 200
Female managers = x = 200
Male managers = 1.2x = 240
Male non-managers = 1.5x = 300
Female non-managers = 1.25x = 250
Male clerks = 50% of male non-managers = 50% of 300 = 150
Female clerks = male clerks + 25 = 150 + 25 = 175
Quantity I: Female clerks as % of male managers
[175/240] × 100 ≈ 72.92% ≈ 73%
Quantity II: Male clerks as % of female managers
[150/200] × 100 = 75%
⇒75%
So, Quantity I
Data Sufficiency Question 5:
In the question, two quantities I, and II are given. You have to solve both the quantities and establish the correct relation between Quantity - I and Quantity - II and choose the correct option accordingly.
The average of the current ages of A, B, and C is 39 years. D’s present age is 125% percent of A’s current age. Eight years from now, the ratio of A’s age to B’s age will be 5:6. At present, C’s age is 5 years older than of B. Also, Difference between age of B and D is 0.
Quantity I: Sum of age of A and C?
Quantity II: Sum of age of B and D?
Answer (Detailed Solution Below)
Data Sufficiency Question 5 Detailed Solution
Calculation
Let A = 4x
Given:
D = 125% of A
⇒ D = [5/4] × A = 5x
B = D
⇒ B = 5x
C = B + 5 = 5x + 5
Average of A, B, and C = 39
⇒ A + B + C = 3 × 39 = 117
So, A + B + C = 4x + 5x + (5x + 5) = 14x + 5 = 117
⇒ 14x = 112
⇒ x = 112/14=8
A = 4x =32
B = D = 5x = 40
C = 5x + 5 = 45
Quantity I: A + C = 32 + 45 = 77
Quantity II: B + D = 40 + 40 = 80
Quantity I
Top Data Sufficiency MCQ Objective Questions
You are given a question followed by two statements numbered I and II. You have to decide whether the data provided on the statements are sufficient to answer the question.
What is the value of 'x'?
Statements :
I. x + 2y = 6
II. 3x + 6y = 18
Answer (Detailed Solution Below)
Data Sufficiency Question 6 Detailed Solution
Download Solution PDFStatement I:
⇒ x + 2y = 6
Here, we cannot find the value of x with the help of only one equation
Hence, Statement I alone is insufficient
Statement II:
⇒ 3x + 6y = 18
Here, we cannot find the value of x with the help of only one equation
Hence, Statement II alone is insufficient
From Statement I and II:
⇒ x + 2y = 6 ----(1)
⇒ 3x + 6y = 18 ----(2)
Multiplying equation (1) by 3 we get
⇒ 3(x + 2y) = 6 × 3
⇒ 3x + 6y = 18 ----(3)
Here, both equations (2) and (3) is same so we can not find the value of x
∴ Statements I and II together are not sufficient
Confusion Points
The second equation is only the multiple of first, so we cannot find the values of x and y
Given below are two quantities named A & B. Based on the given information; you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
Quantity A: If x is 20% more than y and y is 62.5% less than 840, then find the value of x.
Quantity B: 420
Answer (Detailed Solution Below)
Data Sufficiency Question 7 Detailed Solution
Download Solution PDFQuantity A:
⇒ y = (100 – 62.5)% of 840
⇒ y = 37.5% of 840
⇒ y = 3/8 × 840 = 315
Now,
⇒ x = (100 + 20)% of y
⇒ x = 1.2 × 315 = 378
⇒ Quantity A = 378
Quantity B: 420
∴ Quantity A
Consider the given question and decide which of the following statement(s) is/are sufficient to answer the question.
What is the average daily wage of X, Y and Z?
Statements:
- Y’s salary is half of (X + Z)
- X and Y together earn Rs. 40 more than Z and Z earns Rs. 500
Answer (Detailed Solution Below)
Data Sufficiency Question 8 Detailed Solution
Download Solution PDFFrom statement 2,
Earning of Z = Rs. 500
Earning of X and Y = Rs. 500 + 40 = Rs. 540.
⇒ Required average of daily wages = (X + Y + Z)/3 = (540 + 500)/3 = Rs. 1040/3
∴ 2 alone is sufficient while 1 alone is insufficient.
The question below consists of a question followed by two statements labeled as 1 and 2. You have to decide whether these statements are sufficient to answer the question.
Question: What is the value of X+Y ?
Statements:
1. X - 2Y = 5
2. X2 – 25 = 4XY - 4Y2
Answer (Detailed Solution Below)
Data Sufficiency Question 9 Detailed Solution
Download Solution PDFFrom Statement 1: X - 2Y = 5
cannot find the value of X and Y.
From statement 2: X2 – 25 = 4XY - 4Y2
X2 – 25 = 4XY - 4Y2 -------(1)
X2 - 4XY + 4Y2 = 25
(X - 2Y)2 = 25
X - 2Y = 5
cannot find the value of X and Y.
So, same equation in both the statements.
Hence, option (3) is the correct answer.
Confusion PointsHere, after calculation, we got only 1 equation, hence we cannot conclude the exact values of X and Y.
Consider the given question and decide which of the following statement(s) is/are sufficient to answer the question.
Is (X – 5) even? X is a real number.
Statement:
- X – 15 belongs to integer
- X – 10 is an odd integer
Answer (Detailed Solution Below)
Data Sufficiency Question 10 Detailed Solution
Download Solution PDFStatement 1:
X – 15 = integer
⇒ X is also an integer
Statement 2:
X – 10 = odd integer
⇒ X is an odd integer.
⇒ (X – 5) is even.
∴ Statement 2 alone is sufficient while statement 1 alone is insufficient.
Directions: In the following question, two quantities A and B are given. You have to use your knowledge of mathematics to find the values of both A and B and choose the most appropriate relationship between the magnitudes of A and B from the given options.
Quantity A: Pipes X and Y can fill a tank in 15 hours and 20 hours respectively. There is a hole at 3/4th of the height of the tank which can drain water in 12 hours if it is at the bottom of the tank. How much time will it take to fill the tank?
Quantity B: 14 hours.
Answer (Detailed Solution Below)
Data Sufficiency Question 11 Detailed Solution
Download Solution PDFQuantity A -
Let the volume of tank = LCM of (15, 20, 12) = 60 units.
X's capacity = 60 / 15 = 4 units.
Y's capacity = 60 / 20 = 3 units.
Hole's emptying capacity = 60 / 12 = 5 units.
Time taken to fill (3 / 4)th tank = 45 / (4 + 3) = 6.42 units
Time taken for remaining (1 / 4)th tank = 15 / (4 + 3 - 5) = 7.5 units
Total time = 6.42 + 7.5 = 13.92 hours
Quantity B - 14 hours.
Hence, Quantity A
Confusion Points The statement that a hole at the bottom would have caused the tank to empty in 12 hours was made to give readers a sense of the pipe's flow rate, not to imply that the hole is at the bottom.
Consider the following question and decide which of the statements is sufficient to answer the question.
Question:
Find the value of m, slope of a line.
Statements:
1) y = mx + 2
2) Line passes through (2, 1)
Answer (Detailed Solution Below)
Data Sufficiency Question 12 Detailed Solution
Download Solution PDFStatement 1∶
y = mx + 2
We cannot find anything with statement 1.
Statement 2∶
Line passes thgough (2, 1)
We cannot find anything with statement 2.
Combining statement 1 and 2∶
∵ Line passes through (2, 1), it will satisfy the equation of line y = mx + 2
∴ Putting x = 2 and y = 1 in the equation of line
⇒ 1 = 2m + 2
⇒ m = -1/2
∴ Both statements 1 and 2 are sufficient.
Read the given question and decide which of the following information is sufficient to answer the question.
What is the value of ∠ACB?
Informations
1 | |
2 | ∠D = 60° |
Answer (Detailed Solution Below)
Data Sufficiency Question 13 Detailed Solution
Download Solution PDFCalculation:
Since angles by a chord on two different points on the same segment of a circle are equal.
∵ ∠D = 60°
So, ∠ACB = ∠D = 60°
Hence, Both 1 and 2 are sufficient (Option 2 is correct)
Consider the following question and statements and decide which of the statements is sufficient to answer the question.
What is the total weight of six boxes? Each of them is equal in weight.
Statements:
A. One-third of each boxes’ weight is 2 kg
B. The total weight of four boxes is 12 kg more than the total weight of two boxes.
Answer (Detailed Solution Below)
Data Sufficiency Question 14 Detailed Solution
Download Solution PDFStatement A:
⇒ One-third of each boxes’ weight is 2 kg
⇒ Weight of each box = 6 kg
⇒ So, the total weight of 6 boxes = 36 kg
Statement B:
The total weight of four boxes is 12 kg more than the total weight of two boxes
Let the weight of 1 box be x.
⇒ Given, 4x - 12 = 2x
⇒ x = 6 kg
⇒ So, the total weight of 6 boxes = 36 kg
∴ Both Statements 1 and 2 alone are sufficient
Question given below is followed by two statements
Is ‘a’ positive?
I) a + b is positive
II) a – b is positive.
Answer (Detailed Solution Below)
Data Sufficiency Question 15 Detailed Solution
Download Solution PDFFrom I
We know that a + b is positive ⇏ a is positive as b can be a large positive value when a is negative
For example,
Let the number of b be 2,
Then the number of a be -3
so, according to the statement
a + b = 2 + (-3) = -1 is negative
From II
We know that a - b is positive ⇏ a is positive as b can be a large negative value when a is negative
For example,
Let the number of b be 2,
Then the number of a be -3
so, according to the statement
a - b = 2 - (-3) = 5 is positive
Now, adding both i.e. I + II
(a + b) + (a - b) = positive
a is positive
Both the statements prove a is positive.