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# Which of the following, if multiplied by x^3y^2z, would yield a produc

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Math Expert
Joined: 02 Sep 2009
Posts: 44655
Which of the following, if multiplied by x^3y^2z, would yield a produc [#permalink]

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10 Apr 2018, 03:59
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Difficulty:

25% (medium)

Question Stats:

71% (00:46) correct 29% (00:49) wrong based on 31 sessions

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Which of the following, if multiplied by $$x^3y^2z$$, would yield a product that is both a perfect cube and a perfect power of five?

A. $$x^5y^{15}z^{15}$$

B. $$x^{12}y^{13}z^{14}$$

C. $$x^2yz^2$$

D. $$x^2y^3z^4$$

E. $$yz^2$$
[Reveal] Spoiler: OA

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Intern
Joined: 04 Apr 2018
Posts: 21
Re: Which of the following, if multiplied by x^3y^2z, would yield a produc [#permalink]

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10 Apr 2018, 23:08

Product that is both a perfect cube and a perfect power of five would imply powers of 15.
Simply, addding exponent of x,y & z with the given (x^3*y^2*z) in option B would yield x^(3+12)*y^(2+13)*z^(1+14) which equals x^15*y^15*z^15 = (xyz)*15 which is both a perfect cube as well as perfect power of five.
Re: Which of the following, if multiplied by x^3y^2z, would yield a produc   [#permalink] 10 Apr 2018, 23:08
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