Previous Year Topic Wise Questions With Solutions: Data Sufficiency | CSAT Preparation - UPSC PDF Download

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.

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Ans: (b)
(p + q)² – 4pq, where p and q are natural numbers.
= p² + q² + 2pq – 4pq
= p² + q² – 2pq
= (p – q)²
The expression (p – q)² will be positive if p > q or q > p.
However, if p = q, then (p – q)² = 0, which is not a positive number.
Thus, the question can be answered if we know that p ≠ q, i.e. if either statement I or II is correct.
Hence, option (b) is correct.

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.

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Ans: (d)
Here, P, Q, R, S are distinct non-zero digits and PP × PQ = RRSS, where P ≤ 3 and Q ≤ 4.
Thus, P can be 1, 2 or 3 and Q can be 1, 2, 3 or 4.
However, if P is either 1 or 2, we cannot obtain a 4-digit number when we multiply PP × PQ.
So, P must be 3.
Now, 33 × 31 or 33 × 32 or 33 × 34 are the only possible combinations. (Q cannot be 3, as P and Q must be distinct.)
Let’s check them one by one: 33 × 31 = 1023
It doesn't satisfy the given condition.
33 × 32 = 1056
It doesn't satisfy the given condition.
33 × 34 = 1122
It satisfies the given condition, as 1122 is of the form RRSS. Also, P, Q, R, S are distinct. So,
Q = 4.
We can find the value of Q without using any of the given statements.
Hence, option (d) is the correct answer.

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

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Ans: (c)
Given that, x and y are distinct natural numbers. 
Using statement-I alone: x/y = odd 3/1 = 3, 6/2 = 3 …..and so on.
This statement alone is not sufficient, as so many possibilities are there.
Using statement-II alone: xy = 12
The values of x and y may be 12 & 1, 4 & 3, or 6 & 2. So, this statement alone is also not sufficient.
On combining statement-I and statement-II: 12/1 = 12, which is not odd. 4/3 is a fraction.
Now, 6/2 = 3, which is an odd number.
Hence, unique values of x and y are 6 and 2 respectively.
Hence, the question can be answered by using both the statements together, but cannot be answered using either statement alone.

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

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Ans: (d)
Using statement-I alone: 2x + y is an integer. If x = 1.5 and y = 2, then: 2x + y = 3 + 2 = 5, which is an integer.
But, x + y = 1.5 + 2 = 3.5, which is not an integer.
If x = 1 and y = 2, then: 2x + y = 2 + 2 = 4, which is an integer. Also, x + y = 1 + 2 = 3, which is an integer.
So, with the help of statement –I alone, we cannot say that x+y is an integer or not.
Using statement-II alone: x + 2y is an integer. If y = 1.5 and x = 2, then: x + 2y = 2 + 3 = 5, which is an integer.
But, x + y = 2 + 1.5 = 3.5, which is not an integer. If x = 1 and y = 2, then:
x + 2y = 1 + 4 = 5, which is an integer. Also, x + y = 1 + 2 = 3, which is an integer.
So, with the help of statement –II alone, we cannot say that x+y is an integer or not.
On combining statement-I and statement-II: 2x + y is an integer. Also, x + 2y is an integer.
But even if it’s true, x+y may be an integer or not. Let’s illustrate with an example. If x = 1.33 and y = 2.33, 
then: x + 2y = 1.33 + 4.67 = 6, which is an integer. 2x + y = 2.66 + 2.33 = 5, which is an integer.
But, x + y = 1.33 + 2.33 = 3.66, which is not an integer.
So, even after combining both of the statements, we cannot say that x+y is an integer or not.

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

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Ans: (c)
p + r + q = Rs. 50, wherein q = Rs. 16 So, p + r = 50 – 16
Or p + r = 34 (i)
Also, it is given that the price of q is the least.
Using statement-I alone: p ≤ r
It alone is not sufficient.
Using statement-II alone: r ≤ p
It alone is not sufficient.
On combining statement-I and statement-II:
We can say that p = r.
Therefore, from equation (i), we get: p + r = 34
Or p = r = 17
Therefore, the price of the article p = Rs. 17
Hence, the question can be answered by using both the statements together, but cannot be answered using either statement alone.

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

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Ans: (d)
Using statement-I alone: P + Q = R + S ….…(i) So, from statement –I alone we cannot say that P scored more than Q or not. 
Using statement-II alone: (P + S) > (Q + R).....................(ii) So, from statement –II alone also, we cannot say that P scored more than Q or not. 
And even after combining both the statements, we cannot definitely say that P scored more that Q or not. 
Therefore, this question cannot be answered even by using both of 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

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Ans: (a)
The passage highlights the critical need to encourage the financialization of savings. However, it also opines that people would only jump into financialization after addressing some hurdles. 
Statement 1 is correct: The line “Hurdles to change include onerous bureaucracy…” implies a rigid and challenging environment creating challenges in the financialization of household savings. Thus, a flexible environment is required to develop solutions to address the challenges related to the financialization of savings. Thus, it is a correct statement. 
Statement 2 is correct: The line “A lack of basic information about which of the myriad services and provers is best for each family.” reflects that families do not have information and access to solutions that meet their specific needs. This can be solved by providing customized solutions to each household. Thus, it is a correct statement. 
Statement 3 is incorrect: The passage focuses more on the scepticism of organized financial institutions and the lack of knowledge among households. While financial technology innovations can be beneficial in improving access to information and services, they are not directly implied as a solution in the passage.

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.

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Ans: (c)
Statement 1: (p - q) is positive.
This is possible only when p > q
Statement 2: (p - r) is negative.
This is possible only when p < r
Now, (p + q - r) – (p – q + r) = 2q – 2r
So, we basically need to find out if q > r, or not. For this, we obviously have to use both the given statements.
Using both of the statements, we get:
r > p > q
So, q < r
It means that, (p + q - r) – (p – q + r) = 2q – 2r < 0
In other words, (p + q - r) is not greater than (p – q + r).
Hence, option (c) is correct.

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.

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Ans: (d)
Statement 1: The sum of the digits of the number is equal to the product of the digits.
If the 3-digit number is 123, 132, 213, 231, 312, or 321, then the sum of the digits of the number would be equal to the product of the digits.
As, 1 + 2 + 3 = 1 × 2 × 3
Or 6 = 6
So, Statement 1 alone is not sufficient.
Statement2: The number is divisible by the sum of the digits of the number.
We can see that, 132/6 = 22, and 312/6 = 52
So, Statement 2 alone is not sufficient.
Even after using both the statements together, we cannot determine a unique 3-digit number.
Hence, option (d) is correct.

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

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Ans: (d)
Let’s consider the two statements one by one.
Statement 1: x/3 is not an integer.
x may or may not be an integer. For example, if x = 2, even then x/3 will not be an integer.
Statement 2: 3x is an integer.
x may or may not be an integer. For example, if x = 2/3, even then 3x will be an integer.
On combining the two statements, 3x is an integer, but x/3 is not.
x may or may not be an integer. 
For example, if x = 2, even then x/3 will not be an integer. 
But 3x = 6 will be an integer.
If x = 2/3, even then 3x will be an integer. 
But x/3 = 2/9 will not be an integer.

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

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Ans: (d)
Let’s consider the two statements one by one.
Statement 1: X is the brother of Y, and Y is the brother of Z.

But we do not know whether Z is a male or a female. So, we cannot say whether Z is the brother or sister of X.
Statement 2: X, Y, and Z are siblings. It tells us nothing much. 
Here, also gender of Z is not known. 
So, Z can be either brother or sister of X. 
Even if we combine the two statements, we cannot answer the given questions.

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

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Ans: (d)
It’s pretty evident that neither of the two statements is sufficient alone. 
Even on combining the two, we get two possible cases:

On observing the above two cases, we can see that the person who is sitting of the immediate left of A cannot be determined.

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

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Ans: (c)
It’s pretty evident that neither of the two statements is sufficient alone.
So, now let’s combine the two statements.
Let the present ages of Manisha and her mother be x and y respectively.
As per statement 1, y = x + 24
As per statement 2, (x + 5)/(y + 5) = 3/5
Or 5x + 25 = 3y + 15
Or 3y – 5x = 10
Or 3(x + 24) – 5x = 10
Or 3x + 72 – 5x = 10
Or 2x = 62
Or x = 31
So, Manisha is 31 years old at present. Both statements together are 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

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Ans: (a)
Average = Sum of observations / Number of observations 
Since 4 students are moved from A to B, therefore average of class B will definitely decrease as range of marks for class A is less than range of marks for class B. 
That is, the new students must be having less marks than the previous minimum marks of Class B. 
Statement 1 is correct.
However, we cannot be sure regarding the marks of the 4 students that have been moved from class A.
They may have marks close to 21, which will lead to decrease in the average marks of Class A. 
If they have marks close to 17, it will lead to increase in the average marks of Class A. 
Therefore, we cannot determine whether average of class A will increase or decrease. 
Statement 2 is incorrect.

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

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Ans: (c)
From Statement 1, we get:
From Statement 2, we get:
We know that, there are 40 students in the class. 
Seema’s rank from the top can be calculated using either of the statements. Hence, option (c) is correct.

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

View Answer  

Ans: (a)
From statement 1, we get: A & D > B, E & F
As none of them is the heaviest, we can conclude that C must be the heaviest. 
So, statement 1 alone is sufficient.
From Statement 2, we get: C > A > D
Using statement 2 alone we cannot determine the heaviest item.