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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. x^2 is divisible by both 40 and 75. If x has exactly three  Question banks Downloads My Bookmarks Reviews Important topics
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Founder  Joined: 18 Apr 2015
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x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
Expert's post 00:00

Question Stats: 30% (02:12) correct 69% (01:39) wrong based on 33 sessions

$$x^2$$ 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

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Director Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 356 , given: 66

Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
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! Director Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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Kudos [?]: 671  , given: 148

Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
1
KUDOS
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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Intern Joined: 14 Jun 2018
Posts: 36
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Kudos [?]: 7 , given: 100

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.
Founder  Joined: 18 Apr 2015
Posts: 6920
Followers: 114

Kudos [?]: 1344 , given: 6318

Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
Expert's post
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
_________________ Intern Joined: 09 Jul 2018
Posts: 10
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Re: x^2 is divisible by both 40 and 75. If x has exactly three [#permalink]
2
KUDOS
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

$$40 = 2*2*2*5$$ and $$75 = 3*5*5$$

For $$x^2$$ to be divisible by 40 and 75, its prime-factorization must include at least three 2's (since there are three 2's within 40), at least one 3 (since
there is one 3 within 75), and at least two 5's (since there are two 5's within 75):
$$2^3 * 3^1 * 5^2$$

However, since $$x^2$$ is a perfect square, its prime-factorization must have an EVEN NUMBER of every prime factor.
Since the prime-factorization of x must include $$2^3$$, $$3^1$$ and $$5^2$$ -- but $$x$$ must have an even number of each of these prime factors -- the least possible option for $$x^2$$ is as follows:
$$2^4 * 3^2 * 5^2$$
Since the least possible option for $$x^2 = 2^4 * 3^2 * 5^2$$, the least possible option for $$x = 2^2 * 3 * 5 = 60$$.

Implication:
$$x$$ must be a MULTIPLE OF 60.
In addtion, since $$x$$ must have exactly three distinct prime factors, it cannot be divisible by any prime number other than 2, 3 and 5.

Since 30 and 200 are not divisible by 60, eliminate A and C.
Since 420 is divisible by 7 -- a prime number other than 2, 3 and 5 -- eliminate E.

[Reveal] Spoiler:
B, D

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Available for tutoring in NYC and long-distance. Re: x^2 is divisible by both 40 and 75. If x has exactly three   [#permalink] 09 Jul 2018, 14:44
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