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If x is an integer divisible by 15 but not divisible by 20, then x

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If x is an integer divisible by 15 but not divisible by 20, then x  [#permalink]

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New post 10 Sep 2017, 21:34
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A
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C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (01:00) correct 28% (00:48) wrong based on 95 sessions

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Re: If x is an integer divisible by 15 but not divisible by 20, then x  [#permalink]

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New post 10 Sep 2017, 23:44
as per my understanding
x is divisible by 15 => so x has a 3 and 5 in it ( as 15 =3*5)
but x is not divisible by 20 => as 20 = 2*2*5.. and x already has a 5 in it by above statement than:
either x does not have a 2 in it making x divisible by 2*5=10 but not by 20
or x does not have a 4 in it making x divisible by 5 but not by 20

Find x cannot be divisible by which number ?
Now we have to find a Must be condition , so it need to be true always.

Going by options:
A) 6 => 2*3 => x already have a 3, it can or cannot have a 2
B)10 => 2* 5 => x already have a 5, it can or cannot have a 2
C) 12 => 3*4 => x already have a 3, it cannot have a 4 in it. As if x have a 4 in it x will become divisible by 20. Answer
D) 30 => 3*2*5 => x already have a 3 and 5, it can or cannot have a 2
E) 150 => 15*2*3 => x already have a 15, it can or cannot have additional 2 and 3 in it.

So Answer: C
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Re: If x is an integer divisible by 15 but not divisible by 20, then x  [#permalink]

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New post 14 Sep 2017, 10:39
Bunuel wrote:
If x is an integer divisible by 15 but not divisible by 20, then x CANNOT be divisible by which of the following?

A. 6
B. 10
C. 12
D. 30
E. 150


Since x is divisible by 15 and not 20, and 15 = 5 x 3 and 20 = 2^2 x 5, we see that x will never be divisible by a number with two 2s in its prime factorization. Thus, x will not be divisible by 12, because 12 = 2^2 x 3^1.

Answer: C
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Re: If x is an integer divisible by 15 but not divisible by 20, then x &nbs [#permalink] 14 Sep 2017, 10:39
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