Previous Year Topic Wise Questions With Solutions: Data Sufficiency

Q1. A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. 
Question: Is (p + q)² - 4pq, where p, q are natural numbers, positive? 
Statement I: p < q. 
Statement II: p > q. 
Which one of the following is correct in respect of the above Question and the Statements?    (2025)
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone. 
(b) The Question can be answered by using either Statement alone. 
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone. 
(d) The Question can be answered even without using any of the Statements.

Q2. A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. 
Question: 
Let P, Q, R, S be distinct non-zero digits. 
If PP × PQ = RRSS, where P ≤ 3 and Q ≤ 4, then what is Q equal to? 
Statement I: R = 1. 
Statement II: S = 2. 
Which one of the following is correct in respect of the above Question and the Statements?     (2025)
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone. 
(b) The Question can be answered by using either Statement alone. 
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone. 
(d) The Question can be answered even without using any of the Statements.

Q3. A question is given followed by two Statements I and II. Consider the Question and the Statements. 
Question: What are the unique values of x and y, where x, y are distinct natural numbers? 
Statement-I : x/y is odd. 
Statement-II : xy = 12
Which one of the following is correct in respect of the above Question and the Statements?     (2024)
(a) The question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone 
(b) The Question can be answered by using either Statement alone 
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone 
(d) The Question cannot be answered even by using both the Statements together

Q4. A Question if given followed by two Statements I and II. Consider the Question and the Statements. 
Question: Is (x+y) an integer? 
Statement-I : (2x+y) is an integer. 
Statement-II : (x+2y) is an integer. 
Which one of the following is correct in respect of the above Question and the Statements?      (2024)
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone 
(b) The Question can be answered by using either Statement alone 
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone 
(d) The Question cannot be answered even by using both the Statements together

Q5. A Question is given followed by two Statement I and II. Consider the Question and the Statements. 
A person buys three articles p, q and r for ₹50. The price of the article q is ₹16 which is the least. 
Question: What is the price of the article p? 
Statement-I : The cost of p is not more than that of r. 
Statement-II : The cost of r is not more than that of p. 
Which one of the following is correct in respect of the above Question and the Statements?       (2024)
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone 
(b) The Question can be answered by using either Statement alone 
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone 
(d) The Question cannot be answered even by using both the Statements together

Q6. A Question is given followed by two Statements I and II. Consider the Question and the Statements. P, Q, R and S appeared in a test. Question: Has P scored more marks than Q? 
Statement-I: The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S. 
Statement-II: The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R. 
Which one of the following is correct in respect of the above Question and the Statements?        (2024)
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone 
(b) The Question can be answered by using either Statement alone 
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone 
(d) The Question cannot be answered even by using both the Statements together

Q7. Read the following passage and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Household finance in India is unique. We have a tendency to invest heavily in physical assets such as gold and property. Steps to encourage the financialization of savings are critical. A populace accustomed to traditional processes will not simply jump into financialization. Hurdles to change include onerous bureaucracy, a scepticism of organized financial institutions, a lack of basic information about which of the myriad services and providers is best for each family, and how (and even if) one can make the transition between them if necessary.
Regarding the financialization of household savings, which of the following statements best reflect the solutions that are implied by the passage? 
1. A flexible environment is needed to develop solutions. 
2. Households need customized solutions. 
3. Innovations in financial technology are required
Select the correct answer using the code given below:     (2023)
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3

Q8. Questions: Is (p + q- r) greater than (p - q + r), where p, q and r are integers? 
Statement-1: (p - q) is positive. 
Statement-2: (p-r) is negative. 
Which one of the following is correct in respect of the above Question and the Statements?      (2023)
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone. 
(b) The Question can be answered by using either Statement alone. 
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone. 
(d) The Question cannot be answered even by using both the Statements together.

Q9. Consider a 3-digit number. 
Question: What is the number? 
Statement-1: The sum of the digits of the number is equal to the product of the digits. 
Statement-2: The number is divisible by the sum of the digits of the number. 
Which one of the following is correct in respect of the above Question and the Statements?       (2023)
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone. 
(b) The Question can be answered by using either Statement alone. 
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone. 
(d) The Question cannot be answered even by using both the Statements together.

Q10. Consider the Question and two Statements given below:
Question: Is x an integer?
Statement-1: x/3 is not an integer.
Statement-2: 3x is an integer.
Which one of the following is correct in respect of the Question and the Statements?    (2022)
(a) Statement-1 alone is sufficient to answer the Question
(b) Statement-2 alone is sufficient to answer the Question
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question
(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

Q11. Consider the Question and two Statements given below: 
Question: Is Z brother of X? 
Statement-1:" X is a brother of Y and Y is a brother of Z. 
Statement-2: X, Y and Z are siblings. 
Which one of the following is correct in respect of the Question and the Statements? (2022)
(a) Statement-1 alone is sufficient to answer the Questions 
(b) Statement-2 alone is sufficient to answer the Question 
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question 
(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

Q12. Six Persons A, B, C, D, E and F are sitting equidistant form each other around a circular table (facing the centre of the table). Consider the Question and two statements given below: Question: Who is sitting on the immediate left of A? 
Statement-1: B is sitting opposite to C and D is sitting opposite to E. 
Statement -2: F is sitting on the immediate left of B. 
Which one of the following is correct in respect of the Question and the Statements?      (2022)
(a) Statement-1 alone is sufficient to answer the question 
(b) Statement-2 alone is sufficient to answer the question 
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question 
(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

Q13. Consider the Question and two Statements given below: 
Question: What is the age of Manisha? 
Statement-1: Manisha is 24 years younger than her mother. 
Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3: 5. 
Which one of the following is correct in respect of the Question and the Statement?       (2022)
(a) Statements-1 alone is sufficient to answer the Question 
(b) Statement-2 alone is sufficient to answer the question 
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question 
(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

Q14. There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B. Consider the following statements:
1. The average score of Class-B will definitely decrease. 
2. The average score of Class-A will definitely increase.
Which of the above statements is/are correct?       (2021)
(a) 1 only 
(b) 2 only 
(c) Both 1 and 2 
(d) Neither 1 nor 2

Q15. Consider two Statements and a Question: 
Statement-1: Priya is 4 ranks below Seema and is 31st from the bottom. 
Statement-2: Ena is 2 ranks above Seema and is 37th from the bottom. 
Question: What is Seema's rank from the top in the class of 40 students? 
Which one of the following is correct in respect of the Statements and the Question?        (2021)
(a) Statement-1 alone is not sufficient to answer the Question 
(b) Statement-2 alone is not sufficient to answer the Question 
(c) Either Statement-1 alone or Statement-2 alone is sufficient to answer the Question 
(d) Both Statement-1 and Statement-2 are required to answer the Question

Q16. Consider two Statements and a Question: 
Statement-1: Each of A and D is heavier than each of B, E and F, but none of them is the heaviest. 
Statement-2: A is heavier than D, but is lighter than C. 
Question: Who is the heaviest among A, B, C, D and E? 
Which one of the following is correct in respect of the Statements and the Question?         (2021)
(a) Statement-1 alone is sufficient to answer the Question 
(b) Statement-2 alone is sufficient to answer the Question 
(c) Both Statement-1 and Statement-2 are required to answer the Question 
(d) Neither Statement-1 alone nor Statement-2 alone is sufficient to answer the Question