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x^3-y^3 = 90 and x-y = 3. What is the value of xy?

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x^3-y^3 = 90 and x-y = 3. What is the value of xy?  [#permalink]

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New post 03 Apr 2019, 04:23
1
6
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

57% (01:54) correct 43% (02:45) wrong based on 28 sessions

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[GMAT math practice question]

\(x^3-y^3 = 90\) and \(x-y = 3\). What is the value of \(xy\)?

\(A. 3\)
\(B. 4\)
\(C. 5\)
\(D. 6\)
\(E. 7\)

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Re: x^3-y^3 = 90 and x-y = 3. What is the value of xy?  [#permalink]

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New post 03 Apr 2019, 05:58
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Math Revolution GMAT Instructor
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Re: x^3-y^3 = 90 and x-y = 3. What is the value of xy?  [#permalink]

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New post 05 Apr 2019, 01:42
1
=>

\(x^3-y^3 = (x-y)(x^2+xy+y^2) = 90\)
Since \(x – y = 3, x^2+xy+y^2 = 30\)
Now, \(9 = (x-y)^2 = x^2 – 2xy + y^2 = x^2+xy+y^2 – 3xy = 30 – 3xy.\)
So, \(3xy = 21\) and \(xy = 7.\)

Therefore, the answer is E.
Answer: E
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Re: x^3-y^3 = 90 and x-y = 3. What is the value of xy?   [#permalink] 05 Apr 2019, 01:42
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x^3-y^3 = 90 and x-y = 3. What is the value of xy?

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