Data sufficiency

2019 · Q29

A five-storeyed building with floors from I to V is painted using four different colours and only one colour is used to paint a floor.

Consider the following statements:

1.The middle three floors are painted in different colours.

2.The second (II) and the fourth (IV) floors are painted in different colours.

3.The first (I) and the fifth (V) floors are painted red.

To ensure that any two consecutive floors have different colours

1. (a)Only statement 2 is sufficient
2. (b)Only statement 3 is sufficientUPSC key
3. (c)Statement 1 is not sufficient, but statement 1 along with statement 2 is sufficient
4. (d)Statement 3 is not sufficient, but statement 3 along with statement 2 is sufficient

2019 · Q58

Consider two statements S1 and S2 followed by a question:

S1: p and q both are prime numbers.

S2: p + q is an odd integer.

Question: Is pq an odd integer?

Which one of the following is correct?

1. (a)S1 alone is sufficient to answer the question
2. (b)S2 alone is sufficient to answer the questionUPSC key
3. (c)Both S1 and S2 taken together are not sufficient to answer the question
4. (d)Both S1 and S2 are necessary to answer the question

2020 · Q17

Two Statements S1 and S2 are given below followed by a Question:

S1: There are not more than two figures on any page of a 51-page book.

S2: There is at least one figure on every page.

Question:

Are there more than 100 figures in that book?

Which one of the following is correct in respect of the above Statements and the Question?

1. (a)Both S1 and S2 are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
2. (b)S1 alone is sufficient to answer the Question.
3. (c)S1 and S2 together are not sufficient to answer the Question.UPSC key
4. (d)S2 alone is sufficient to answer the Question.

2020 · Q28

Two Statements S1 and S2 are given below with regard to four numbers P, Q, R and S followed by a Question:

S1: R is greater than P as well as Q.

S2: S is not the largest one.

Question:

Among four numbers P, Q, R and S, which one is the largest?

Which one of the following is correct in respect of the above Statements and the Question?

1. (a)S1 alone is sufficient to answer the Question.
2. (b)S2 alone is sufficient to answer the Question.
3. (c)S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.UPSC key
4. (d)S1 and S2 together are not sufficient to answer the Question.

2020 · Q29

Two Statements S1 and S2 are given below followed by a Question:

S1: n is a prime number.

S2: n leaves a remainder of 1 when divided by 4.

Question:

If n is a unique natural number between 10 and 20, then what is n?

Which one of the following is correct in respect of the above Statements and the Question?

1. (a)S1 alone is sufficient to answer the Question.
2. (b)S2 alone is sufficient to answer the Question.
3. (c)S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
4. (d)S1 and S2 together are not sufficient to answer the Question.UPSC key

2020 · Q30

Two Statements S1 and S2 are given below with regard to two numbers followed by a Question:

S1: Their product is 21.

S2: Their sum is 10.

Question:

What are the two numbers?

Which one of the following is correct in respect of the above Statements and the Question?

1. (a)S1 alone is sufficient to answer the Question.
2. (b)S2 alone is sufficient to answer the Question.
3. (c)S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.UPSC key
4. (d)S1 and S2 together are not sufficient to answer the Question.

2020 · Q36

Three Statements S1, S2 and S3 are given below followed by a Question:

S1: C is younger than D, but older than A and B.

S2: D is the oldest.

S3: A is older than B.

Question:

Who among A, B, C and D is the youngest?

Which one of the following is correct in respect of the above Statements and the Question?

1. (a)S1 alone is sufficient to answer the Question.
2. (b)S1 and S2 together are sufficient to answer the Question.
3. (c)S2 and S3 together are sufficient to answer the Question.
4. (d)S1 and S3 together are sufficient to answer the Question.UPSC key

2021 · Q38

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?

1. (a)Statement-1 alone is not sufficient to answer the Question
2. (b)Statement-2 alone is not sufficient to answer the Question
3. (c)Either Statement-1 alone or Statement-2 alone is sufficient to answer the QuestionUPSC key
4. (d)Both Statement-1 and Statement-2 are required to answer the Question

2021 · Q39

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?

1. (a)Statement-1 alone is sufficient to answer the Question
2. (b)Statement-2 alone is sufficient to answer the Question
3. (c)Both Statement-1 and Statement-2 are required to answer the QuestionUPSC key
4. (d)Neither Statement-1 alone nor Statement-2 alone is sufficient to answer the QuestionUPSC key

2021 · Q47

Consider two Statements and a Question:

Statement-1: The last day of the month is a Wednesday.

Statement-2: The third Saturday of the month was the seventeenth day.

Question: What day is the fourteenth of the given month?

Which one of the following is correct in respect of the Statements and the Question?

1. (a)Statement-1 alone is sufficient to answer the Question
2. (b)Statement-2 alone is sufficient to answer the QuestionUPSC key
3. (c)Both Statement-1 and Statement-2 are required to answer the Question
4. (d)Neither Statement-1 alone nor Statement-2 alone is sufficient to answer the Question

2022 · Q19

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?

1. (a)Statement-1 alone is sufficient to answer the Question
2. (b)Statement-2 alone is sufficient to answer the Question
3. (c)Both Statement-1 and Statement-2 are sufficient to answer the Question
4. (d)Both Statement-1 and Statement-2 are not sufficient to answer the QuestionUPSC key

2022 · Q25

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?

1. (a)Statement-1 alone is sufficient to answer the Question
2. (b)Statement-2 alone is sufficient to answer the Question
3. (c)Both Statement-1 and Statement-2 are sufficient to answer the Question
4. (d)Both Statement-1 and Statement-2 are not sufficient to answer the QuestionUPSC key

2022 · Q37

Consider the Question and two Statements given below in respect of three cities P, Q and R in a State:

Question: How far is city P from city Q?

Statement-1: City Q is 18 km from city R.

Statement-2: City P is 43 km from city R.

Which one of the following is correct in respect of the Question and the Statements?

1. (a)Statement-1 alone is sufficient to answer the Question
2. (b)Statement-2 alone is sufficient to answer the Question
3. (c)Both Statement-1 and Statement-2 are sufficient to answer the Question
4. (d)Both Statement-1 and Statement-2 are not sufficient to answer the QuestionUPSC key

2022 · Q48

Six persons A, B, C, D, E and F are sitting equidistant from 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?

1. (a)Statement-1 alone is sufficient to answer the Question
2. (b)Statement-2 alone is sufficient to answer the Question
3. (c)Both Statement-1 and Statement-2 are sufficient to answer the Question
4. (d)Both Statement-1 and Statement-2 are not sufficient to answer the QuestionUPSC key

2022 · Q49

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 Statements?

1. (a)Statement-1 alone is sufficient to answer the Question
2. (b)Statement-2 alone is sufficient to answer the Question
3. (c)Both Statement-1 and Statement-2 are sufficient to answer the QuestionUPSC key
4. (d)Both Statement-1 and Statement-2 are not sufficient to answer the Question

2022 · Q50

Six lectures A, B, C, D, E and F, each of one hour duration, are scheduled between 8:00 a.m. and 2:00 p.m.

Consider the Question and two Statements given below:

Question: Which lecture is in the third period?

Statement-1: Lecture F is preceded by A and followed by C.

Statement-2: There is no lecture after lecture B.

Which one of the following is correct in respect of the Question and the Statements?

1. (a)Statement-1 alone is sufficient to answer the Question
2. (b)Statement-2 alone is sufficient to answer the Question
3. (c)Both Statement-1 and Statement-2 are sufficient to answer the Question
4. (d)Both Statement-1 and Statement-2 are not sufficient to answer the QuestionUPSC key

2023 · Q38

Consider the following statements:

1.A is older than B.

2.C and D are of the same age.

3.E is the youngest.

4.F is younger than D.

5.F is older than A.

How many statements given above are required to determine the oldest person/persons?

1. (a)Only two
2. (b)Only three
3. (c)Only four
4. (d)All fiveUPSC key

2023 · Q39

Consider the following including the Question and the Statements:

There are 5 members A, B, C, D, E in a family.

Question: What is the relation of E to B?

Statement-1: A and B are a married couple.

Statement-2: D is the father of C.

Statement-3: E is D’s son.

Statement-4: A and C are sisters.

Which one of the following is correct in respect of the above Question and Statements?

1. (a)Statement-1, Statement-2 and Statement-3 are sufficient to answer the Question.
2. (b)Statement-1, Statement-3 and Statement-4 are sufficient to answer the Question.
3. (c)All four statements together are sufficient to answer the Question.UPSC key
4. (d)All four statements are not sufficient to answer the Question.

2023 · Q56

Question: Is p greater than q?

Statement-1: p × q is greater than zero.

Statement-2: $p^{2}$ is greater than $q^{2}$.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
2. (b)The Question can be answered by using either Statement alone.
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. (d)The Question cannot be answered even by using both the Statements together.UPSC key

2023 · Q57

Question: 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?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
2. (b)The Question can be answered by using either Statement alone.
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.UPSC key
4. (d)The Question cannot be answered even by using both the Statements together.

2023 · Q58

In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink.

Question: How many persons attended the party?

Statement-1: 50 persons took milk.

Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.UPSC key
2. (b)The Question can be answered by using either Statement alone.
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. (d)The Question cannot be answered even by using both the Statements together.

2023 · Q59

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?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
2. (b)The Question can be answered by using either Statement alone.
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. (d)The Question cannot be answered even by using both the Statements together.UPSC key

2023 · Q60

For five children with ages a < b < c < d < e; any two successive ages differ by 2 years.

Question: What is the age of the youngest child?

Statement-1: The age of the eldest is 3 times the youngest.

Statement-2: The average age of the children is 8 years.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
2. (b)The Question can be answered by using either Statement alone.UPSC key
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. (d)The Question cannot be answered even by using both the Statements together.

2024 · Q59

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:

What are the values of m and n, where m and n are natural numbers?

Statement–I:

m + n > mn and m > n.

Statement–II:

The product of m and n is 24.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. (b)The Question can be answered by using either Statement alone
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement aloneUPSC key
4. (d)The Question cannot be answered even by using both the Statements together

2024 · Q60

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:

What is the time required to download the software?

Statement–I:

The size of the software is 12 megabytes.

Statement–II:

The transfer rate is 2·4 kilobytes per second.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. (b)The Question can be answered by using either Statement alone
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement aloneUPSC key
4. (d)The Question cannot be answered even by using both the Statements together

2024 · Q64

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?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. (b)The Question can be answered by using either Statement alone
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement aloneUPSC key
4. (d)The Question cannot be answered even by using both the Statements together

2024 · Q65

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

A certain amount was distributed among X, Y and Z.

Question:

Who received the least amount?

Statement–I:

X received $\dfrac{4}{5}$ of what Y and Z together received.

Statement–II:

Y received $\dfrac{2}{7}$ of what X and Z together received.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. (b)The Question can be answered by using either Statement alone
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement aloneUPSC key
4. (d)The Question cannot be answered even by using both the Statements together

2024 · Q66

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:

If the average marks in a class are 60, then what is the number of students in the class?

Statement–I:

The highest marks in the class are 70 and the lowest marks are 50.

Statement–II:

Exclusion of highest and lowest marks from the class does not change the average.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. (b)The Question can be answered by using either Statement alone
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. (d)The Question cannot be answered even by using both the Statements togetherUPSC key

2024 · Q67

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

There are three distinct prime numbers whose sum is a prime number.

Question:

What are those three numbers?

Statement–I:

Their sum is less than 23.

Statement–II:

One of the numbers is 5.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement aloneUPSC key
2. (b)The Question can be answered by using either Statement alone
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. (d)The Question cannot be answered even by using both the Statements together

2024 · Q68

A Question is 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?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. (b)The Question can be answered by using either Statement alone
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. (d)The Question cannot be answered even by using both the Statements togetherUPSC key

2024 · Q69

A Question is given followed by two Statements 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?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. (b)The Question can be answered by using either Statement alone
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement aloneUPSC key
4. (d)The Question cannot be answered even by using both the Statements together

2024 · Q70

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?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. (b)The Question can be answered by using either Statement alone
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. (d)The Question cannot be answered even by using both the Statements togetherUPSC key

2024 · Q73

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.

Question:

What is the difference of their ages?

Statement–I:

The age of P is greater than the age of Q.

Statement–II:

The sum of their ages is $\dfrac{11}{6}$ times their difference.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement aloneUPSC key
2. (b)The Question can be answered by using either Statement alone
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. (d)The Question cannot be answered even by using both the Statements together

2025 · Q68

A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: What is the smallest 1-digit number having exactly 4 distinct factors?

Statement I: 2 is one of the factors.

Statement II: 3 is one of the factors.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
2. (b)The Question can be answered by using either Statement alone.
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. (d)The Question can be answered even without using any of the Statements.UPSC key

2025 · Q69

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?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
2. (b)The Question can be answered by using either Statement alone.
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. (d)The Question can be answered even without using any of the Statements.UPSC key

2025 · Q70

A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: How is Q related to P?

Statement I: P has two sisters, R and S.

Statement II: R’s father is the brother of Q.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
2. (b)The Question can be answered by using either Statement alone.
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. (d)The Question cannot be answered even using any of the Statements.UPSC key

2025 · Q73

A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: In a football match, team P playing against Q was behind by 3 goals with 10 minutes remaining. Does team P win the match?

Statement I: Team P scored 4 goals in the last 10 minutes.

Statement II: Team Q scored a total of 4 goals in the match.

Which one of the following is correct in respect of the above Question and the Statements?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
2. (b)The Question can be answered by using either Statement alone.
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. (d)The Question cannot be answered even using any of the Statements.UPSC key

2025 · Q74

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?

1. (a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
2. (b)The Question can be answered by using either Statement alone.UPSC key
3. (c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. (d)The Question can be answered even without using any of the Statements.

2026 · Q1

Question: X receives three coins of different denominations: 1, 2, 5, 10 and 20. If the total amount received by X is m, does X receive a coin of denomination 5?

Statement I: m is not a prime number.

Statement II: The sum of the digits of m is greater than 5.

1. (a)Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statementUPSC key
2. (b)Select this option if the question can be answered using either statement alone
3. (c)Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
4. (d)Select this option if the question cannot be answered even using any of the statements

2026 · Q2

Question:

For two distinct real numbers x and y, which of them is bigger?

Statement I: $x^{2}$ < y < 1

Statement II: y < $\sqrt{x}$ < 1

1. (a)Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement
2. (b)Select this option if the question can be answered using either statement alone
3. (c)Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
4. (d)Select this option if the question cannot be answered even using any of the statementsUPSC key

2026 · Q3

Question:

If x and y are integers, then is x even?

Statement I: $x^{2}$$y^{2}$ is even.

Statement II: 1 + $x^{2}$ + $y^{2}$ is odd.

1. (a)Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement
2. (b)Select this option if the question can be answered using either statement alone
3. (c)Select this option if the question can be answered using both the statements together, but cannot be answered using either statement aloneUPSC key
4. (d)Select this option if the question cannot be answered even using any of the statements

2026 · Q4

Question:

X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of the numbers all of which are either from X or from Y. Is every number of T from Y?

Statement I: The sum of any two numbers belonging to T is even.

Statement II: If both p and q are picked from T, then (p − 1)q is even.

1. (a)Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement
2. (b)Select this option if the question can be answered using either statement alone
3. (c)Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
4. (d)Select this option if the question cannot be answered even using any of the statementsUPSC key

2026 · Q5

Question:

If x, y and z are integers, each greater than 1, then is x a prime number?

Statement I: $\mathrm{xy}^{2}$ = 116

Statement II: xz = 261

1. (a)Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statementUPSC key
2. (b)Select this option if the question can be answered using either statement alone
3. (c)Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
4. (d)Select this option if the question cannot be answered even using any of the statements