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24 Sep 2021, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
58% (01:27) correct
42%
(01:17)
wrong
based on 184
sessions
History
Date
Time
Result
Not Attempted Yet
If a and b are integers and \(a^b = 16\), \(|a-b| = ?\)
(1) \(b ≠ 1\)
(2) \(a > 0\)
(1) \(b ≠ 1\)
(2) \(a > 0\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
24 Sep 2021, 02:16
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Bunuel
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
24 Sep 2021, 03:06
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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
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
