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What is a–b? (1) a^3 – b^3 = 117 (2) a^2 + ab + b^2 = 39

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Expert Post
Math Expert
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V
Joined: 02 Sep 2009
Posts: 42628

Kudos [?]: 135818 [0], given: 12715

What is a–b? (1) a^3 – b^3 = 117 (2) a^2 + ab + b^2 = 39 [#permalink]

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New post 08 Oct 2017, 05:32
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (00:51) correct 29% (01:29) wrong based on 42 sessions

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Kudos [?]: 135818 [0], given: 12715

Intern
Intern
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B
Joined: 19 Sep 2016
Posts: 35

Kudos [?]: 2 [0], given: 3

Re: What is a–b? (1) a^3 – b^3 = 117 (2) a^2 + ab + b^2 = 39 [#permalink]

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New post 08 Oct 2017, 06:31
OA-C, statement 1 can be rewritten as (a-b)^3+3ab(a-b)=117. Which can be further simplified as (a-b)[(a-b)^2+3ab]=117. So (a-b) is dependant on value of 'ab' and hence insufficient.
Statement 2, can be simplified as (a-b)^2+2ab+ab=39, so it becomes
(a-b)^2+3ab=39. Since value again dependant on value of 'ab', so again insufficient.
St 1+ st2 - (a-b)=117/39 and further (a-b)=3. So my answer is C.

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Kudos [?]: 2 [0], given: 3

Manager
Manager
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B
Joined: 14 Sep 2016
Posts: 148

Kudos [?]: 5 [0], given: 36

Re: What is a–b? (1) a^3 – b^3 = 117 (2) a^2 + ab + b^2 = 39 [#permalink]

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New post 08 Oct 2017, 07:17
a^3-b^3 = (a-b)(a^2+ab+b^2)

1) a^3-b^3 = 117, Insufficient
2) (a^2+ab+b^2), Insufficient

Taking both option together we can derive the value of (a-b)

Answer C

Kudos [?]: 5 [0], given: 36

Re: What is a–b? (1) a^3 – b^3 = 117 (2) a^2 + ab + b^2 = 39   [#permalink] 08 Oct 2017, 07:17
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What is a–b? (1) a^3 – b^3 = 117 (2) a^2 + ab + b^2 = 39

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