If a and b are integers and a^b = 16, |a - b| = ? (1) b ≠ 1 (2) a 0

Question

If a and b are integers and  a^b = 16 ,  |a-b| = ?

(1)  b ≠ 1 
(2)  a > 0

Project DS Butler Data Sufficiency (DS3) 
 For DS butler Questions  Click Here

errorlogger · Answer

a^b = 16
Possibilities:
 4^2 = 16, (-4)^2 = 16, (16)^1 = 16, (2)^4 = 16, (-2)^4 = 16 
So, a could be 4, -4, 16, 2, -2
b could be 2, 1, 4
1)b not = 1
So, b could be 2, 4 and a could be any number from the above findings. - Insufficient!
2)a > 0
So, a could be 4, 16, 2
and b could be any number from the above findings - Insufficient!
Combining (1) & (2):
Only possibilities are 2^4 or 4^2, |a-b| = 2 - Sufficient!
IMO C

Boho · Answer

If a and b are integers and  a^b = 16 ,  |a-b| = ?

Statement (1)  b ≠ 1 
(a, b) = (2, 4), (4, 2), (-2, 4), (-4, 2)
|a-b| = 2, or 6

Statement (2)  a > 0 
(a, b) = (2, 4), (4, 2), (16, 1)
|a-b| = 2, or 15

Combined 
|a-b| = 2

Sufficient 
(C) is correct

Victor19 · Answer

Answer is C.
For a^b = 16 we can have 2^4, (-2)^4, 4^2, (-4)^2, 16^1. For 2^4 and 4^2 we get |a-b| = 2. For 16^1, |a-b| = 15. For (-2)^4 and (-4)^2 we |a-b| = 6. So, we have 3 different answers. Let us see if the statements help us narrow down to one answer.

Statement 1 : This eliminates the option where a=16, b=1. But still |a-b| can be 2 or 6.
Insufficient.

Statement 2 : This eliminates options with negative values of a. Still we have |a-b| = 2 or 15.
Insufficient.

Combining both, we have only |a-b| = 2. Hence together they are sufficient. So answer is C.

Posted from my mobile device

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

JerryAtDreamScore · Answer

Breaking Down the Info:

We may have  4^2 = (-4)^2 = 2^4 = (-2)^4 = 16^1 = 16

Rephrase the question:

What is the positive difference between a and b? Note that some of our options give the same positive difference.

Statement 1 Alone:

This only rules out one option; we still have 4 options which can give us a positive difference of 6 or 2. Then this statement is insufficient.

Statement 2 Alone:

We can have  4^2 = 2^4 = 16^1 = 16 . We still have two difference positive differences, so this statement is insufficient.

Both Statements Combined:

Now we ruled out  16^1 = 16 , so we have only  4^2 = 2^4 = 16  which both give a positive difference of 2. Then combined it is sufficient.

Answer: C

If a and b are integers and a^b = 16, |a - b| = ? (1) b ≠ 1 (2) a > 0

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions