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Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
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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

Show: :: 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]
IlCreatore wrote:
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!


I saw that your method by using the calculator of GRE might take more than 1.5 minutes. However, the method in the second post takes less time.
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Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
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GRE almost never requires intensive calculation.

In my opinion, you rarely have to use the calc. The fastest way is to rely on your math skills.

Regards
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Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
I thought E is correct 420/60=7
(420^2)/40 = 4410
(420^2)/75 = 2352
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Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
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mageed wrote:
I thought E is correct 420/60=7
(420^2)/40 = 4410
(420^2)/75 = 2352


We're told that x has exactly three distinct prime factors
420 has FOUR distinct prime factors, since 420 = (2)(2)(3)(5)(7)
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Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
pranab223 420 is divisible by 60 amongst the answer choices too. Can you explain this line: "so x must have = 22∗3∗522∗3∗5 = 60. ( numerator should be the LCM of 40 and 75 ie 23∗3∗5223∗3∗52)." Thank you!
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Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
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Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
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