Is \(a > |b|?\)
(1) \(2^{a-b} > 16\)
(2) \(|a - b| < b\)
OA C
Source: e-GMAT
Is \(a > |b|?\)
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
- Followed by:247 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Since this question contains an absolute value, we must be sure to think about NEGATIVE as well as positive possibilities.Is \(a > |b|?\)
First, get like bases:(1) \(2^{a-b} > 16\)
\(2^{a-b}>2^4\)
We can infer:
\(a-b>4\)
\(a>b+4\)
Since a is greater than b+4, it must also be greater than b itself. But be careful! That doesn't mean a>|b|.
Think of examples where a and b are both negative:
a = -1
b = -6
This satisfies \(a>b+4\) but not \(a > |b|\)
This tells us that b must be positive, because it's greater than some absolute value. But this could be true whether a is greater than or less than b:(2) \(|a - b| < b\)
a = 3
b = 2
|3 - 2| < 2
\(a > |b|?\) --> yes
a = 2
b = 3
|2 - 3| < 3
\(a > |b|?\) --> no
This is insufficient.
(1) and (2) together
If \(a>b+4\) and \(b>0\), then a must be a positive number greater than b. Thus, the answer to \(a > |b|?\) is yes.
The answer is C.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
- Followed by:247 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
For more an ABSOLUTE VALUE with INEQUALITIES, see:
https://www.beatthegmat.com/if-x-is-not ... tml#793307
https://www.beatthegmat.com/if-x-y-is-x ... tml#793303
https://www.beatthegmat.com/gmat-prep-1 ... tml#765468
https://www.beatthegmat.com/if-x-is-not ... tml#793307
https://www.beatthegmat.com/if-x-y-is-x ... tml#793303
https://www.beatthegmat.com/gmat-prep-1 ... tml#765468
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education