If Z is a positive integer such thata)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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GMAT Exam > GMAT Questions > If Z is a positive integer such thata)Stateme...

If Z is a positive integer such that

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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Verified Answer

If Z is a positive integer such thata)Statement (1) ALONE is sufficien...

Steps 1 & 2: Understand Question and Draw Inferences

Given:

Z is a positive integer
Z = 81(Y⁴ – 7)³ . . . (1)

We need to find the value of Y.

Step 3: Analyze Statement 1 independently

Squaring both sides:
- Z⁵ = 3⁵⁰
Taking 5^th root on both sides:
- Z = 3¹⁰ . . . (2)
Put (2) in (1):
- 3¹⁰ = 3⁴(Y⁴ – 7)³
- 3⁶ = (Y⁴ – 7)³
Taking the cube-root on both sides:
- 3² = Y⁴ – 7
- Y⁴ = 9 + 7 = 16
- Y⁴ = 2⁴ = (-2)⁴
- Y = 2 or -2

Not sufficient to determine a unique value of Y.

Step 4: Analyze Statement 2 independently

(2) |Y-1| < 4

Distance of Y from 1 on the number line is less than 4 units

-3 < Y < 5

Multiple values of Y possible. Not sufficient.

Step 5: Analyze Both Statements Together (if needed)

From St. 1, Y = 2 or – 2
From St. 2, -3 < Y < 5
- This inequality is satisfied by both 2 and -2

So, even after combining both statements, we have 2 possible values of Y

Since we couldn’t find a unique value of Y, the correct answer. Is Option E.

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Most Upvoted Answer

If Z is a positive integer such thata)Statement (1) ALONE is sufficien...

Steps 1 & 2: Understand Question and Draw Inferences

Given:

Z is a positive integer
Z = 81(Y⁴ – 7)³ . . . (1)

We need to find the value of Y.

Step 3: Analyze Statement 1 independently

Squaring both sides:
- Z⁵ = 3⁵⁰
Taking 5^th root on both sides:
- Z = 3¹⁰ . . . (2)
Put (2) in (1):
- 3¹⁰ = 3⁴(Y⁴ – 7)³
- 3⁶ = (Y⁴ – 7)³
Taking the cube-root on both sides:
- 3² = Y⁴ – 7
- Y⁴ = 9 + 7 = 16
- Y⁴ = 2⁴ = (-2)⁴
- Y = 2 or -2

Not sufficient to determine a unique value of Y.

Step 4: Analyze Statement 2 independently

(2) |Y-1| < 4

Distance of Y from 1 on the number line is less than 4 units

-3 < Y < 5

Multiple values of Y possible. Not sufficient.

Step 5: Analyze Both Statements Together (if needed)

From St. 1, Y = 2 or – 2
From St. 2, -3 < Y < 5
- This inequality is satisfied by both 2 and -2

So, even after combining both statements, we have 2 possible values of Y

Since we couldn’t find a unique value of Y, the correct answer. Is Option E.

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If Z is a positive integer such thata)Statement (1) ALONE is sufficien...

Steps 1 & 2: Understand Question and Draw Inferences

Given:

Z is a positive integer
Z = 81(Y⁴ – 7)³ . . . (1)

We need to find the value of Y.

Step 3: Analyze Statement 1 independently

Squaring both sides:
- Z⁵ = 3⁵⁰
Taking 5^th root on both sides:
- Z = 3¹⁰ . . . (2)
Put (2) in (1):
- 3¹⁰ = 3⁴(Y⁴ – 7)³
- 3⁶ = (Y⁴ – 7)³
Taking the cube-root on both sides:
- 3² = Y⁴ – 7
- Y⁴ = 9 + 7 = 16
- Y⁴ = 2⁴ = (-2)⁴
- Y = 2 or -2

Not sufficient to determine a unique value of Y.

Step 4: Analyze Statement 2 independently

(2) |Y-1| < 4

Distance of Y from 1 on the number line is less than 4 units

-3 < Y < 5

Multiple values of Y possible. Not sufficient.

Step 5: Analyze Both Statements Together (if needed)

From St. 1, Y = 2 or – 2
From St. 2, -3 < Y < 5
- This inequality is satisfied by both 2 and -2

So, even after combining both statements, we have 2 possible values of Y

Since we couldn’t find a unique value of Y, the correct answer. Is Option E.

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If Z is a positive integer such thata)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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If Z is a positive integer such thata)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? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If Z is a positive integer such thata)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? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If Z is a positive integer such thata)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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