A sequence S consists of 5 distinct positive integers. Are all the integers in the sequence divisible by 5?(1) The sum of all the integers in the sequence is divisible by 5.(2) The product of all the integers in the sequence is divisible by 5 but not by 10.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 askedc)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 'E'. Can you explain this answer?

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A sequence S consists of 5 distinct positive integers. Are all the integers in the sequence divisible by 5?

(1) The sum of all the integers in the sequence is divisible by 5.

(2) The product of all the integers in the sequence is divisible by 5 but not by 10.

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 'E'. Can you explain this answer?

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A sequence S consists of 5 distinct positive integers. Are all the int...

Steps 1 & 2: Understand Question and Draw Inferences

Sequence S consists of a₁,a₂,a₃,a₄,a₅

, where all the terms are integers > 0

To Find: Is a₁,a₂,a₃,a₄,a₅ divisible by 5?

Step 3: Analyze Statement 1 independently

(1) The sum of all the integers in the sequence is divisible by 5.

a₁+a₂+a₃+a₄+a₅=5x

, where x is an integer > 0.

Two cases arise:

All of a₁,a₂,a₃,a₄,a₅ are a multiple of 5. In this case all the terms are divisible by 5

Two or more terms sum up to a multiple of 5. In this case all the terms are not divisible by 5.

Insufficient to answer.

Step 4: Analyze Statement 2 independently

(2) The product of all the integers in the sequence is divisible by 5 but not by 10.

a₁∗a₂∗a₃∗a₄∗a₅=5y, where y is an integer > 0

For the product of the terms to be divisible by 5, any one or more of the terms should be divisible by 5.

So, 1 or all the 5 terms may be divisible by 5.

Also, as the product of the terms is not divisible by 10, none of the terms is even.

Insufficient to answer.

Step 5: Analyze Both Statements Together (if needed)

(1) a₁+a₂+a₃+a₄+a₅=5x

(2) a₁∗a₂∗a₃∗a₄∗a₅=5y and none of a₁,a₂,a₃,a₄,a₅ is even

Following cases may arise:

All the terms are odd multiples of 5.
1 or more terms are an odd multiple of 5 and the rest terms are odd and not a multiple of 5 but sum up to be a multiple of 5.

Insufficient to answer.

Answer: E

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A sequence S consists of 5 distinct positive integers. Are all the integers in the sequence divisible by 5?(1) The sum of all the integers in the sequence is divisible by 5.(2) The product of all the integers in the sequence is divisible by 5 but not by 10.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 askedc)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 'E'. Can you explain this answer?

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A sequence S consists of 5 distinct positive integers. Are all the integers in the sequence divisible by 5?(1) The sum of all the integers in the sequence is divisible by 5.(2) The product of all the integers in the sequence is divisible by 5 but not by 10.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 askedc)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 'E'. 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 A sequence S consists of 5 distinct positive integers. Are all the integers in the sequence divisible by 5?(1) The sum of all the integers in the sequence is divisible by 5.(2) The product of all the integers in the sequence is divisible by 5 but not by 10.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 askedc)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 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sequence S consists of 5 distinct positive integers. Are all the integers in the sequence divisible by 5?(1) The sum of all the integers in the sequence is divisible by 5.(2) The product of all the integers in the sequence is divisible by 5 but not by 10.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 askedc)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 'E'. Can you explain this answer?.

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