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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42
GPA: 3.82
x^3-y^3 = 90 and x-y = 3. What is the value of xy?  [#permalink]

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03 Apr 2019, 04:23
1
6
00:00

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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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 21 Feb 2019 Posts: 125 Location: Italy Re: x^3-y^3 = 90 and x-y = 3. What is the value of xy? [#permalink] ### Show Tags 03 Apr 2019, 05:58 Solution attached. Attachments Scan.pdf [298.22 KiB] Downloaded 31 times  To download please login or register as a user Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8235 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: x^3-y^3 = 90 and x-y = 3. What is the value of xy? [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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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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