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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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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, 06:32
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (00:45) correct 31% (01:12) wrong based on 54 sessions

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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, 07:31
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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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, 08:17
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
Re: What is a–b? (1) a^3 – b^3 = 117 (2) a^2 + ab + b^2 = 39 &nbs [#permalink] 08 Oct 2017, 08:17
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