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

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
Is |a| > |b| ? (1) a − b > a^2 − b^2 (2) a > b  [#permalink]

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23 Aug 2018, 00:21
00:00

Difficulty:

85% (hard)

Question Stats:

51% (02:11) correct 49% (02:10) wrong based on 139 sessions

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Is |a| > |b| ?

(1) a − b > a^2 − b^2

(2) a > b

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7688
Re: Is |a| > |b| ? (1) a − b > a^2 − b^2 (2) a > b  [#permalink]

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23 Aug 2018, 01:06
1
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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Joined: 04 May 2018
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GMAT 1: 650 Q46 V34
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31 Dec 2018, 04:52
Is |a|>|b|?

(1) a−b>a^2−b^2

(2) a>b

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
VP
Joined: 09 Mar 2018
Posts: 1004
Location: India

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31 Dec 2018, 05:31
Is |a|>|b|?
(1) a−b>a^2−b^2
(2) a>b

Statement (1)
when you solve this inequality,
a-b > a^2 - b^2
will give you
=> 0 > a^2 - b^2 - (a-b)
=> a-b (a+b-1) < 0

Now there can be 2 cases that a-b > 0 and a+b-1 < 0 or a-b < 0 and a+b-1 > 0

Satisfying the above will not give you a definite answer, as if you take Case 1, a > b and a+b < 1

the question |a|>|b| can be No when a = -1 and b = -2 and Yes when a = 1 and b =-7 -> %

Statement (2), just mentions a > b, which can take both the cases as mentioned in %

Combining both the statements will give the mentioned scenario in %

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examPAL Representative
Joined: 07 Dec 2017
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31 Dec 2018, 05:33

we can solve this question by using numbers.
1) 1) a−b>a^2−b^2:
this can be true for a=2, b=1 - for which |2|>|1| - yes!
but it can also be true for a=1, b=-2, for which |1|<|-2| - no!

2) a>b:
same example as before - this is true for both (2,1), for which the answer is yes, and (1,-2) - for which it is no - contradicting answers - insufficient!

Combined: since both examples ((2,1) & (1,-2)) hold for both statements - combining them adds nothing. we can still get either a "yes" or a "no" . insufficient!
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Posts: 55277
Re: Is |a| > |b| ? (1) a − b > a^2 − b^2 (2) a > b  [#permalink]

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31 Dec 2018, 05:51
ajtmatch wrote:
Is |a|>|b|?

(1) a−b>a^2−b^2

(2) a>b

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

____________________
Merging topics.
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Re: Is |a| > |b| ? (1) a − b > a^2 − b^2 (2) a > b   [#permalink] 31 Dec 2018, 05:51
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