A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question: Is (x + y) an integer? 1. Statement-I: (2x+y) is an integer. 2. Statement-II: (x+2y) is an integer. Which one of the following is correct in respect of the above Question and the Statements?

Correct Option The Question asks whether (x + y) is an integer. Statement-I: (2x + y) is an integer. Consider an example: If 2x + y = 3. If x = 1, then y = 1, making x + y = 2 (an integer). However, if x = 1.5, then y = 0, making x + y = 1.5 (not an integer). Therefore, Statement-I alone is insufficient to determine if (x + y) is an integer. Statement-II: (x + 2y) is an integer. Consider an example: If x + 2y = 3. If y = 1, then x = 1, making x + y = 2 (an integer). However, if y = 1.5, then x = 0, making x + y = 1.5 (not an integer). Therefore, Statement-II alone is insufficient to determine if (x + y) is an integer. Combining Statement-I and Statement-II: - From Statement-I, (2x + y) is an integer. - From Statement-II, (x + 2y) is an integer. Adding these two expressions: (2x + y) + (x + 2y) = 3x + 3y = 3(x + y). Since the sum of two integers is an integer, 3(x + y) must be an integer. Let 3(x + y) = K, where K is an integer. This implies $x + y = \frac{K}{3}$. The expression $\frac{K}{3}$ may or may not be an integer. For instance, if K = 3, then x + y = 1 (an integer). If K = 4, then $x + y = \frac{4}{3}$ (not an integer). Thus, even by using both statements together, it cannot be definitively determined whether (x + y) is an integer. Incorrect Options Options 1, 2, and 3 are incorrect because, as demonstrated above, neither statement alone nor both statements combined are sufficient to answer the question.

IAS 2024 — CSAT Reasoning

2024mcqmedium

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?

Official previous-year question

Verified 2 Aug 2026.

Options

AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
BThe Question can be answered by using either Statement alone
CThe Question can be answered by using both Statements together, but cannot be answered using either Statement alone
DThe Question cannot be answered even by using both the Statements together.

Did you get this right?

Solution

Correct Option

The Question asks whether (x + y) is an integer.

Statement-I: (2x + y) is an integer.

Consider an example: If 2x + y = 3. If x = 1, then y = 1, making x + y = 2 (an integer). However, if x = 1.5, then y = 0, making x + y = 1.5 (not an integer). Therefore, Statement-I alone is insufficient to determine if (x + y) is an integer.

Statement-II: (x + 2y) is an integer.

Consider an example: If x + 2y = 3. If y = 1, then x = 1, making x + y = 2 (an integer). However, if y = 1.5, then x = 0, making x + y = 1.5 (not an integer). Therefore, Statement-II alone is insufficient to determine if (x + y) is an integer.

Combining Statement-I and Statement-II:

From Statement-I, (2x + y) is an integer.
From Statement-II, (x + 2y) is an integer.

Adding these two expressions: (2x + y) + (x + 2y) = 3x + 3y = 3(x + y).

Since the sum of two integers is an integer, 3(x + y) must be an integer. Let 3(x + y) = K, where K is an integer. This implies $x + y = \frac{K}{3}$ .

The expression $\frac{K}{3}$ may or may not be an integer. For instance, if K = 3, then x + y = 1 (an integer). If K = 4, then $x + y = \frac{4}{3}$ (not an integer).

Thus, even by using both statements together, it cannot be definitively determined whether (x + y) is an integer.

Incorrect Options

Options 1, 2, and 3 are incorrect because, as demonstrated above, neither statement alone nor both statements combined are sufficient to answer the question.

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Options

AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone

BThe Question can be answered by using either Statement alone

CThe Question can be answered by using both Statements together, but cannot be answered using either Statement alone

DThe Question cannot be answered even by using both the Statements together.

Solution

Correct Option

The Question asks whether (x + y) is an integer.

Statement-I: (2x + y) is an integer.

Statement-II: (x + 2y) is an integer.

Combining Statement-I and Statement-II:

From Statement-I, (2x + y) is an integer.
From Statement-II, (x + 2y) is an integer.

Adding these two expressions: (2x + y) + (x + 2y) = 3x + 3y = 3(x + y).

Since the sum of two integers is an integer, 3(x + y) must be an integer. Let 3(x + y) = K, where K is an integer. This implies $x + y = \frac{K}{3}$ .

The expression $\frac{K}{3}$ may or may not be an integer. For instance, if K = 3, then x + y = 1 (an integer). If K = 4, then $x + y = \frac{4}{3}$ (not an integer).

Thus, even by using both statements together, it cannot be definitively determined whether (x + y) is an integer.

Incorrect Options

Options 1, 2, and 3 are incorrect because, as demonstrated above, neither statement alone nor both statements combined are sufficient to answer the question.

IAS 2024 — CSAT Reasoning

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