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# If a and b are integers and (3√a*√b)^6 = 500, then a + b cou

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If a and b are integers and (3√a*√b)^6 = 500, then a + b cou [#permalink]  21 Nov 2017, 00:58
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Question Stats:

50% (00:45) correct 50% (00:01) wrong based on 2 sessions
If a and b are integers and $$(\sqrt[3]{a}*\sqrt{b})^6 = 500$$, then a + b could equal

A. 2
B. 3
C. 4
D. 5
E. 6

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[Reveal] Spoiler: OA
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Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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Re: If a and b are integers and (3√a*√b)^6 = 500, then a + b cou [#permalink]  01 Dec 2017, 21:40
1
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Bunuel wrote:
If a and b are integers and $$(\sqrt[3]{a}*\sqrt{b})^6 = 500$$, then a + b could equal

A. 2
B. 3
C. 4
D. 5
E. 6

From the above equation we get,

$$[(a^{1/3}) X (b^{1/2})]^6 = 500$$

or$$a^2 X b^3 = 5^3 X 2^2$$

Thus we can write as , a= 2 and b = 5.

But a+b = 7 that is not in the option. However a could be = 2 or -2 (since square of any negative number is positive)

that is $$2^2 = (-2)^2$$

Now when a= -2 and b= 5, we have = -2 + 5 =3 . Hence option B
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Re: If a and b are integers and (3√a*√b)^6 = 500, then a + b cou   [#permalink] 01 Dec 2017, 21:40
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