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x^2 is divisible by both 40 and 75. If x has exactly three

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x^2 is divisible by both 40 and 75. If x has exactly three [#permalink] New post 12 Aug 2017, 10:10
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x^2 is divisible by both 40 and 75. If x has exactly three distinct prime factors, which of the following could be the value of x?

Indicate all values that apply.

❑ 30

❑ 60

❑ 200

❑ 240

❑ 420

[Reveal] Spoiler: OA
B, D

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Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink] New post 24 Sep 2017, 06:46
Probably there exist a faster way to solve this question. By the way, I used this one. In order to be a right answer, the square of X must be divisible for both 40 and 75 and X must have only three distinct prime factors.
Thus, I have checked for which of the numbers these two requirements are satisfied and they are for 60 and 240, thus answers B and D!
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Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink] New post 24 Sep 2017, 14:06
Carcass wrote:
x^2 is divisible by both 40 and 75. If x has exactly three distinct prime factors, which of the following could be the value of x?

Indicate all values that apply.

❑ 30

❑ 60

❑ 200

❑ 240

❑ 420

[Reveal] Spoiler: OA
B, D


The factors of 40 = 2*2*2*5 and factors of 75 = 3*5*5

since x^2 is divisible by both 40 and 75

so x must have = 2^2*3*5 = 60. ( numerator should be the LCM of 40 and 75 ie 2^3*3*5^2)

So check the option which is divisible by 60

Only option B and option D satisfy the condition.
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Re: x^2 is divisible by both 40 and 75. If x has exactly three   [#permalink] 24 Sep 2017, 14:06
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x^2 is divisible by both 40 and 75. If x has exactly three

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