Z=2a5b7cA positive integer Z can be expressed in terms of its prime factors as above, where a, b and c are positive integers. Is3-ab-9?(1) Z is divisible by 40 but not by 50(2)Zab=265274a)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 > Z=2a×5b×7cA positive integer Z can ...

Z=2^a×5^b×7^c

A positive integer Z can be expressed in terms of its prime factors as above, where a, b and c are positive integers. Is 3^|a−b|<9?

(1) Z is divisible by 40 but not by 50

(2) Z^a−b=2⁶×5²×7⁴

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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Z=2a×5b×7cA positive integer Z can be expressed in terms of ...

Steps 1 & 2: Understand Question and Draw Inferences

Given:

Step 3: Analyze Statement 1 independently

(1) Z is divisible by 40 but not by 50

40 = 2³*5
50 = 2*5²

The power of 2 in Z is at least 3
- a ≥ 3
The power of 5 in Z is 1.
- b = 1

Therefore, a – b ≥ 3 – 1

a – b ≥ 2

So, answer to the asked question is: NO

Statement 1 is sufficient to answer the question.

Step 4: Analyze Statement 2 independently

Equating the powers of a base on both sides of the equation:
- a(a - b) = 6. . . (1)
- b(a - b) = 2. . . (2)
Dividing (1) by (2)

The minimum value of b is 1 (b is a positive integer)
- So, minimum value of a – b = 2

Thus, the answer to the asked question is: NO

Statement 2 is sufficient to answer the question.

Step 5: Analyze Both Statements Together (if needed)

Since we’ve already arrived at unique answers in Steps 3 and 4, this step is not required

Answer: Option D

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Z=2a×5b×7cA positive integer Z can be expressed in terms of its prime factors as above, where a, b and c are positive integers. Is3|a−b|<9?(1) Z is divisible by 40 but not by 50(2)Za−b=26×52×74a)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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