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# x > 0 and x^4 = 625

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x > 0 and x^4 = 625 [#permalink]  05 Mar 2017, 08:41
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Expert's post
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Question Stats:

80% (00:32) correct 19% (00:45) wrong based on 57 sessions

$$x > 0$$ and $$x^4 = 625$$

 Quantity A Quantity B The greatest prime factor of 36x x

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Kudos [?]: 1782 [0], given: 397

Re: x > 0 and x^4 = 625 [#permalink]  11 Mar 2017, 06:57
Expert's post
Explanation

First, find x:
$$x^4 = 625$$ or $$x = 5$$ or $$-5$$

However, the question states that x > 0, so x = 5

Now find 36x:

$$36x$$ or $$(36)(5)$$ or $$180$$.

Now prime factors of 180 are 2, 3, and 5.

Prime factors of 5 is 5.

Greatest prime factor of both the quantities is 5. Hence C is correct.
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Kudos [?]: 101 [2] , given: 22

Re: x > 0 and x^4 = 625 [#permalink]  16 Mar 2018, 16:26
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KUDOS
correct: C
x^4 = 625
x = 5 (x > 0 so x can't be -5)
36x = 36 * 5 or 36 * -5
36 * 5 = 2 * 2 * 3 * 3 * 5 = 2^2 * 3^2 * 5 The prime factors are 2, 3 and 5. So the biggest prime factor of 36*x is 5

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Re: x > 0 and x^4 = 625 [#permalink]  17 Mar 2018, 08:44
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625 is a fairly common number on the GRE along with other powers of 5. Whenever I have a variable on a QC I like to ask myself can the number be Pos/neg, integer/non-int, or 0. Because $$x^4$$ is an integer, I know that X is also an integer, and that it must be positive (therefore not 0) as well.

Therefore, I know X is positive 5. For the greatest prime factor, I don't ever need to multiply 36 and 5 together. I can just do the prime factorization of 36 (2-2-3-3) and I have 5 so the greatest prime factor is 5 and both quantities are equal.

Remember if you can get away with not doing math on the quant section that's the way to go!
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Re: x > 0 and x^4 = 625   [#permalink] 17 Mar 2018, 08:44
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