The CAT QA section requires speed and accuracy, along with a thorough understanding of the Data Sufficiency. This article provides a set of MCQs on Data Sufficiency to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
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CAT MCQs on Data Sufficiency
1. What is the number of matches played by the champion?
A. The entry list for the tournament consists of 83 players.
B. The champion received one bye.
A. The entry list for the tournament consists of 83 players.
B. The champion received one bye.
A
If A alone but not B alone is sufficient
B
If B alone but not A alone is sufficient
C
If both A and B together are sufficient
D
If A alone is sufficient and B alone is sufficient
2. If the number of players in the first round was between 65 and 128, what is the exact value of \(n\)?
A. Exactly one player received a bye in the entire tournament.
B. One player received a bye while moving on to the fourth round from the third round.
A. Exactly one player received a bye in the entire tournament.
B. One player received a bye while moving on to the fourth round from the third round.
A
If A alone but not B alone is sufficient
B
If B alone but not A alone is sufficient
C
If both A and B together are sufficient
D
If A alone is sufficient and B alone is sufficient
3. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, \( W_I \), of Section I is smaller than the average weight \( W_{II} \) of Section II. If the heaviest student, Deepak, of Section II is moved to Section I, and the lightest student, Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched.
A: \( W_{II} - W_I = 1.0 \)
B: Moving Deepak from Section II to I (without any move to II) makes the average weights of the two sections equal.
A: \( W_{II} - W_I = 1.0 \)
B: Moving Deepak from Section II to I (without any move to II) makes the average weights of the two sections equal.
A
if the question can be answered using A alone but not B alone.
B
if the question can be answered using B alone but not A alone.
C
if the question can be answered using A and B together, but not using either A or B alone.
D
if the question cannot be answered even using A and B together.
4. ABC Corporation needs at least 400 kilolitres of water in its factory at all times. It considers a spherical tank with uniform wall thickness. The outer diameter of the tank is 10 m. Is the tank capacity adequate?
A: The inner diameter of the tank is at least 8 meters.
B: The tank weighs 30,000 kg when empty, and is made of material with density 3 g/cc.
A: The inner diameter of the tank is at least 8 meters.
B: The tank weighs 30,000 kg when empty, and is made of material with density 3 g/cc.
A
if the question can be answered using A alone but not B alone.
B
if the question can be answered using B alone but not A alone.
C
if the question can be answered using A and B together, but not using either A or B alone.
D
if the question cannot be answered even using A and B together.
5. Consider integers \( x, y, z \). What is the minimum possible value of \( x^2 + y^2 + z^2 \)?
A: \( x + y + z = 89 \)
B: Among \( x, y, z \) two are equal.
A: \( x + y + z = 89 \)
B: Among \( x, y, z \) two are equal.
A
if the question can be answered using A alone but not B alone.
B
if the question can be answered using B alone but not A alone.
C
if the question can be answered using A and B together, but not using either A or B alone.
D
if the question cannot be answered even using A and B together.
6. Rahim plans to draw a square JKLM with point O on side JK but is not successful. Why?
A: The length of OM is twice that of OL.
B: The length of OM is 4 cm.
A: The length of OM is twice that of OL.
B: The length of OM is 4 cm.
A
if the question can be answered using A alone but not B alone.
B
if the question can be answered using B alone but not A alone.
C
if the question can be answered using A and B together, but not using either A or B alone.
D
if the question cannot be answered even using A and B together.
7. Given n2 = 123456787654321, find n
A
12344321
B
1235789
C
11111111
D
1111111
8. Expenses at a boarding house are partly fixed and are partly varying on the number of boarders at the house. The average expense per boarder is Rs. 700 with 25 boarders. The average expense comes to Rs. 600 when the number of boarders is 50. What will the average cost per boarder when the number of boarders is 100?
A
550
B
560
C
540
D
570
9. A pair of positive integers (x, y) satisfies the equation 4x − 17y = 1. x also satisfies the inequality x ≤ 1. Find the number of pairs (x, y) that will satisfy the above?
A
59
B
57
C
55
D
58
10. Given that X and Y are non-negative. What is the value of X?
I. 2X + 2Y ≤ 40
II. X − 2Y ≥ 20
I. 2X + 2Y ≤ 40
II. X − 2Y ≥ 20
A
If the question can be answered with the help of statement I alone
B
If the question can be answered with the help of statement II alone
C
If both, statement I and statement II are needed to answer the question
D
If the question cannot be answered even with the help of both the statements
11. What are the values of three integers \( a, b, \) and \( c \)? I. \( ab = 8 \)
I II. \( bc = 9 \)
I II. \( bc = 9 \)
A
If the question can be answered with the help of statement I alone
B
If the question can be answered with the help of statement II alone
C
If both, statement I and statement II are needed to answer the question
D
If the question cannot be answered even with the help of both the statements
12. Is the average of the largest and the smallest of four given numbers greater than the average of the four numbers? I. The difference between the largest and the second largest numbers is greater than the difference between the second smallest and the smallest numbers.
I II. The difference between the largest and the second largest numbers is less than the difference between the second largest and the second smallest numbers.
I II. The difference between the largest and the second largest numbers is less than the difference between the second largest and the second smallest numbers.
A
If the question can be answered with the help of statement I alone
B
If the question can be answered with the help of statement II alone
C
If both, statement I and statement II are needed to answer the question
D
If the question cannot be answered even with the help of both the statements
13. What are the ages of the three brothers? I. The product of their ages is 21.
I II. The sum of their ages is not divisible by 3.
I II. The sum of their ages is not divisible by 3.
A
If the question can be answered with the help of statement I alone
B
If the question can be answered with the help of statement II alone
C
If both, statement I and statement II are needed to answer the question
D
If the question cannot be answered even with the help of both the statements
14. Two types of widgets, namely type A and type B, are produced on a machine. The number of machine hours available per week is 80. How many widgets of type A must be produced? I. One unit of type A widget requires 2 machine hours and one unit of type B widget requires 4 machine hours.
I II. The widget dealer wants supply of at least 10 units of type A widget per week and he would not accept less than 15 units of type B widget.
I II. The widget dealer wants supply of at least 10 units of type A widget per week and he would not accept less than 15 units of type B widget.
A
If the question can be answered with the help of statement I alone
B
If the question can be answered with the help of statement II alone
C
If both, statement I and statement II are needed to answer the question
D
If the question cannot be answered even with the help of both the statements
15. What is the price of mangoes per kg? I. Ten kg of mangoes and two dozens of oranges cost Rs. 252.
I II. Two kg of mangoes could be bought in exchange for one dozen oranges.
I II. Two kg of mangoes could be bought in exchange for one dozen oranges.
A
If the question can be answered with the help of statement I alone
B
If the question can be answered with the help of statement II alone
C
If both, statement I and statement II are needed to answer the question
D
If the question cannot be answered even with the help of both the statements
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