If x and y are positive integers, what is the remainder when y is divided by x?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?

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GMAT Exam > GMAT Questions > If x and y are positive integers, what is the...

If x and y are positive integers, what is the remainder when y is divided by x?

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Correct answer is option 'D'. Can you explain this answer?

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If x and y are positive integers, what is the remainder when y is divi...

Steps 1 & 2: Understand Question and Draw Inferences

Given: x, y are integers > 0
y = ax + r , where a is a positive integer and r is an integer such that 0 ≤ r < x

To Find: Value of r for which we need to find the value of x and y.

Step 3: Analyze Statement 1 independently

As 149 is expressed as an integer raised to a power, we need to find that integer. As this integer will be a factor of 149, we need to find if 149 can be expressed as a factor raised to its power. So, let’s check its divisibility by the prime numbers.
- Divisibility by 2: As 149 is odd, it is not divisible by 2
- Divisibility by 3: As the sum of the digits of 149 (i.e. 14) is not divisible by 3, 149 will not be divisible by 3
- Divisibility by 5: As the units digit of 149 is neither 0 nor 5, it is not divisible by 5
- Divisibility by 7: We can see that 149 when divided by 7, leaves a remainder 2. So, it is not divisible by 7
- Divisibility by 11: 149 when divided by 11 leaves a remainder 4. So, it is not divisible by 11
- Divisibility by 13: We see that 149 when divided by 13 leaves a remainder 6. So, it is not divisible by 13.
Since 12² < 149 < 13² and 149 is not divisible by any prime number till 13, we can say that 149 is a prime number.
As 149 is a prime number, any integer apart from 149 raised to any power will not result in 149.
- Only possible option is x + y = 149 and y – x = 1
2 equations, 2 variables, we can find unique values of x and y and hence find the remainder.

Sufficient to answer.

Step 4: Analyze Statement 2 independently

So, we need to express 149 as a product of 2 integers. For expressing 149 as a product of 2 integers, we need to find the factors of 149.
As we have found above that 149 is a prime number, the only possible case of expressing 149 as a product of 2 integers is 149 * 1
y + x = 149 and y – x = 1
2 equations, 2 variables, we can find unique values of x and y and hence find the remainder.

Sufficient to answer.

Step 5: Analyze Both Statements Together (if needed)

As we have a unique answer from steps 3 and 4, this step is not required.

Answer: D

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If x and y are positive integers, what is the remainder when y is divided by x?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?

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If x and y are positive integers, what is the remainder when y is divided by x?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If x and y are positive integers, what is the remainder when y is divided by x?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are positive integers, what is the remainder when y is divided by x?a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?.

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