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28 Nov 2017, 23:29
Kudos
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D
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:
51% (01:16) correct
49%
(01:24)
wrong
based on 121
sessions
History
Date
Time
Result
Not Attempted Yet
If a, b, and c are different integers, is (a − b)^c > 0 ?
(1) b < a
(2) c = 2a
(1) b < a
(2) c = 2a
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
29 Nov 2017, 00:52
Kudos
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imo D
question basically asks is \((a − b)^c\) positive?
1)b<a means (a-b) is positive
=> positive number to the power of c (irrespective of sign of c) is positive
example: \(2^(-2)\) = 0.25
S, \((a − b)^c\) is positive
sufficient
2) c = even
(a − b)^c [/m] is positive irrespective of the sign of (a-b)
example: \(-3^(-2)\)= 9
sufficient
--D--
question basically asks is \((a − b)^c\) positive?
1)b<a means (a-b) is positive
=> positive number to the power of c (irrespective of sign of c) is positive
example: \(2^(-2)\) = 0.25
S, \((a − b)^c\) is positive
sufficient
2) c = even
(a − b)^c [/m] is positive irrespective of the sign of (a-b)
example: \(-3^(-2)\)= 9
sufficient
--D--
06 Sep 2021, 07:41
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Bookmarks
Bunuel
Target question: Is \((a − b)^c > 0\) ?
Key Property: there are two different ways for \((a − b)^c\) to be greater than zero:
(i) The base, \((a - b)\), is positive (in which case the exponent can have any value)
(ii) The exponent, \(c\), is EVEN (in which case the base can have any value)
Statement 1: b < a
Subtract \(b\) from both sides of the inequality to get: \(0 < a - b\).
Since \((a - b)\) is positive, we know that \((a − b)^c \) is POSITIVE. (by property i)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: c = 2a
Since \(a\) is an INTEGER, we know that \(c\) is a multiple of 2, which means \(c\) is EVEN
By property ii, we can be certain that \((a − b)^c \) is POSITIVE.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
