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Is |a| > |b| ? (1) a − b > a^2 − b^2 (2) a > b

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Joined: 02 Sep 2009
Posts: 49254
Is |a| > |b| ? (1) a − b > a^2 − b^2 (2) a > b  [#permalink]

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New post 23 Aug 2018, 00:21
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

52% (01:46) correct 48% (02:11) wrong based on 56 sessions

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Math Expert
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Joined: 02 Aug 2009
Posts: 6787
Re: Is |a| > |b| ? (1) a − b > a^2 − b^2 (2) a > b  [#permalink]

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New post 23 Aug 2018, 01:06
1
Is |a| > |b| ?


(1) a − b > a^2 − b^2
\(a − b > a^2 − b^2..........a − b -( a^2 − b^2)>0...............(a-b)(1-(a+b)>0\)
two cases
    # a-b>0 or a>b, 1-(a+b)>0 or 1>a+b, a=-2 and b=-3, here |a|<|b| OR a=1 and b=-0.5, here |a|>|b|......
    # a-b<0 or a<b, 1-(a+b)<0 or 1<a+b, a=2 and b=3, here |a|<|b| .
But we do not know if a<b
insuff

(2) a > b
2>-3 or 3>2 give different answers
clearly insuff

combined..
one case still remains..
# a-b>0 or a>b, 1-(a+b)>0 or 1>a+b,
a=-2 and b=-3, here |a|<|b| OR
a=1 and b=-0.5, here |a|>|b|.
insufficient

E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is |a| > |b| ? (1) a − b > a^2 − b^2 (2) a > b &nbs [#permalink] 23 Aug 2018, 01:06
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