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

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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 V
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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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
_________________
Intern  B
Joined: 04 May 2018
Posts: 31
GMAT 1: 650 Q46 V34 GMAT 2: 680 Q49 V34 Is |a|>|b|?  [#permalink]

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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

D) EACH statement ALONE is sufficient to answer the question asked

E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
VP  G
Joined: 09 Mar 2018
Posts: 1004
Location: India
Re: Is |a|>|b|?  [#permalink]

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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 %

Making the answer as E.
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examPAL Representative P
Joined: 07 Dec 2017
Posts: 1061
Re: Is |a|>|b|?  [#permalink]

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The answer is E.

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!
two contradicting answers - insufficient!

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

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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

D) EACH statement ALONE is sufficient to answer the question asked

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