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# If x is an integer, is 15 a factor of x?

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Math Expert
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If x is an integer, is 15 a factor of x?  [#permalink]

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27 Aug 2015, 00:51
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25% (medium)

Question Stats:

72% (00:58) correct 28% (01:19) wrong based on 148 sessions

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If x is an integer, is 15 a factor of x?

(1) 15 is a factor of 10x.
(2) 15 is a factor of 11x.

Kudos for a correct solution.

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Re: If x is an integer, is 15 a factor of x?  [#permalink]

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27 Aug 2015, 01:31
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Bunuel wrote:
If x is an integer, is 15 a factor of x?

(1) 15 is a factor of 10x.
(2) 15 is a factor of 11x.

Kudos for a correct solution.

Statement 1: 15 is a factor os 10x. Now, if x=3,we have 10x=30 and 15 will be factor of 30 but not a factor of 3
And, if x=15,10x=150 and 15 will be a factor of 15. Insufficient

Statement 2:15 is a factor of 11x: x has to be a mutilple of 15 in order for 11x to be a divisible by 15. Sufficient
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Re: If x is an integer, is 15 a factor of x?  [#permalink]

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27 Aug 2015, 02:21
Bunuel wrote:
If x is an integer, is 15 a factor of x?

(1) 15 is a factor of 10x.
(2) 15 is a factor of 11x.

Kudos for a correct solution.

IMO: B

Is 15 a factor of x?
or we can say does x consists of atleast one 3 and 5

St 1: 15 is a factor of 10x.

10x = 2*5*x
From this we can say x must consist of atleast one 3 and it may or may not have 5
Hence not suff

St 2:15 is a factor of 11x

11 is a prime number and has no common prime factors with 15.
Hence x must be a facor of 15 in order for 11x to be a factor of 15
Suff
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Re: If x is an integer, is 15 a factor of x?  [#permalink]

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28 Aug 2015, 11:59
1
If x is an integer, is 15 a factor of x?

(1) 15 is a factor of 10x.
(2) 15 is a factor of 11x

op 1 .
k=10x/15
therefore x could be 3,6,9,12,15,18,
If we compare 15 as a factor of X --then both yes and NO -- not sufficient

op2.
k=11x/15
any multiple of 11 is not divisble by 15 . Hence for 11x/15 to satisfy .... x must be divisible by 15 .

Hence ans B
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Re: If x is an integer, is 15 a factor of x?  [#permalink]

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28 Aug 2015, 17:07
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when X is integer, 15 is factor of x or not?
1. 15 is factor of 10X; so x may or may not have 5 in it. as 3&5 both should be there for 15 to be factor of x;insufficient
2. 15 is factor of 11x; so x has both 3 and 5; sufficient

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Re: If x is an integer, is 15 a factor of x?  [#permalink]

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28 Aug 2015, 17:16
1
IMHO,
the answer is B as well. Because X has to be a factor of 15, for 11x/15 to be an integer or no remainder only quotient.
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Re: If x is an integer, is 15 a factor of x?  [#permalink]

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17 Dec 2015, 10:50
If x is an integer, is 15 a factor of x?

Given; (1) 15 is a factor of 10x.

Factor of 15, must have a 3 & a 5 (min) as factors in it, now if 10x is divisible by 15 or 2 X 5 X x is divisible by 15 means 'x' must have a 3 as a factor but not necessarily a 5 as a factor .... hence insufficient

(2) 15 is a factor of 11x.

Now if 11x is divisible by 15 or we can say 11 X x is divisible by 15 means 'x' must have a 3 and a 5 as factors, since 11 is a prime no .... hence sufficient

So 'B' is the correct answer
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Re: If x is an integer, is 15 a factor of x?  [#permalink]

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22 Nov 2017, 13:05
If x is an integer, is 15 a factor of x?
The object is to find out if (15)(z) = x OR [after prime factorisation] (3)(5)(z) = (x) where z is some integer.
In other words, is x a multiple of 15?

(1) 15 is a factor of 10x.
Therefore (15)(q) = (10)(x) where q is some integer.
Find the prime factors of all numbers --> (3)(5)(q) = (5)(2)(x)
Cancel the 5 from each side --> (3)(q) = (2)(x)
It can't be determined if x = (3)(5)(z) OR if x is a multiple of 15. Insufficient.

(2) 15 is a factor of 11x.
Therefore (15)(p) = (11)(x) where p is some integer.
We can't cancel out any prime factors here, so therefore x must equal 15 or some multiple of 15. Sufficient.

Re: If x is an integer, is 15 a factor of x? &nbs [#permalink] 22 Nov 2017, 13:05
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