Does ablie between 0 and 1, exclusive?(1) -a- 1(2) b is a positive odd integera)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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Does a^b lie between 0 and 1, exclusive?

(1) |a| < 1

(2) b is a positive odd integer

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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Does ablie between 0 and 1, exclusive?(1) |a| < 1(2) b is a positi...

Steps 1 & 2: Understand Question and Draw Inferences

Given: Two numbers a and b

To Find: Is 0 < a^b < 1

Following cases are possible:

a ≥ 1 →

If b≥ 0, then a^b ≥ 1. So, the answer to the question is NO
If b < 0, then 0 < a^b< 1. So, the answer to the question is YES

2. 0 < a < 1 → Irrespective of the value of b, 0 < a^b < 1 So, the answer to the question is YES

3. If a = 0 → Irrespective of the value of b, a^b = 0. So, the answer to the question is NO.

4. -1 < a < 0 →

If b is even, 0 < a^b < 1 So, the answer to the question is YES.
If b is odd, -1 < a^b < 0. So, the answer to the question is NO.

5. a ≤ -1 →

If b is even,ab≥1. So, the answer to the question is NO.
If b is odd, ab≤1. So, the answer to the question is NO

So, the answer to the question will be YES, if:

a ≥ 1 and b < 0 OR

0 < a < 1 OR
-1 < a < 0 and b is even

And the answer to the question will be NO, if:

a ≥ 1 and b ≥ 0 OR
a = 0 OR
-1 < a < 0 and b is odd OR
a ≤ -1

So, we can answer the given question with a unique answer for the above cases.

Step 3: Analyze Statement 1 independently

(1) |a| < 1

This means, -1 < a < 1. So, following cases can occur:
- -1 < a < 0 → As we have seen from our analysis above that in this case the answer to the question may be YES or NO
  - Now, we don’t need to analyse other cases as we do not have unique from this case itself, but we will do so for the sake of completing the analysis.
- a = 0 → The answer to the question is NO in this case
- 0 < a < 1 → The answer to the question is YES in this case.
- As we do not have a unique answer , we cannot say for sure if 0 < a^b < 1

Insufficient to answer

Step 4: Analyze Statement 2 independently

(2) b is a positive odd integer

We have seen from our analysis in steps 1&2 that we need to find the range of values of a to answer this question.
As we do not know the value of a, the statement is insufficient to tell if 0 < a^b < 1

Insufficient to answer

Step 5: Analyze Both Statements Together (if needed)

(1)From Statement 1, -1 < a < 1

(2) From Statement 2, b > 0

Following cases are possible:

-1 < a < 0 → We have seen from our analysis in steps 1&2 that if b is odd, the answer to the question is NO.
a = 0 → We have seen from our analysis in steps 1&2 that in this case the answer to the question is NO.
0 < a < 1 → We have seen from our analysis in steps 1&2 that in this case the answer to the question is YES

As we do not have a unique answer, the combination of statements is insufficient to answer.

Answer: E

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Does ablie between 0 and 1, exclusive?(1) |a| < 1(2) b is a positive odd integera)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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Does ablie between 0 and 1, exclusive?(1) |a| < 1(2) b is a positive odd integera)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 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Does ablie between 0 and 1, exclusive?(1) |a| < 1(2) b is a positive odd integera)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 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Does ablie between 0 and 1, exclusive?(1) |a| < 1(2) b is a positive odd integera)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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