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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, 20:34
1
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:19) correct 25% (01:16) wrong based on 109 sessions

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GMAT 1: 730 Q50 V38
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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, 22:44
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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, 09:39
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  [#permalink]

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New post 02 Jun 2020, 08:31
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Top Contributor
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


There are at least two different ways to solve this question:
1) Determine what properties of x are required so that x is divisible by 15 but not divisible by 20, and then use those results to identify the correct answer
2) Test values

When it comes to solving Integer Properties questions, testing values is often a very fast and effective approach. So let's do that.

Important: The question asks "x CANNOT be divisible by which of the following?"
So if we can show that x CAN be divisible by a certain value, we can ELIMINATE that answer choice.

If x is divisible by 15 but not divisible by 20, then x COULD be 30
Check the answer choices....
Since 30 IS divisible by 6, 10 and 30, we can ELIMINATE answer choices A, B and D

Now let's test another possible value of x

If x is divisible by 15 but not divisible by 20, then x COULD be 150
Since 150 IS divisible by 150, we can ELIMINATE answer choice E.

By the process of elimination, the correct answer is C

Cheers,
Brent
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Re: If x is an integer divisible by 15 but not divisible by 20, then x   [#permalink] 02 Jun 2020, 08:31

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

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