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Positive integer x and 18 are both multiples of positive integer n. If

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Positive integer x and 18 are both multiples of positive integer n. If  [#permalink]

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New post 12 Apr 2018, 11:26
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Positive integer x and 18 are both multiples of positive integer n. If n > 1, which of the following is a possible value for 18 + x ?

a. 41
b. 67
c. 99
d. 103
e. 125

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Re: Positive integer x and 18 are both multiples of positive integer n. If  [#permalink]

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New post 12 Apr 2018, 20:58
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QZ wrote:
Positive integer x and 18 are both multiples of positive integer n. If n > 1, which of the following is a possible value for 18 + x ?

a. 41
b. 67
c. 99
d. 103
e. 125



18 has two prime numbers in it - 2 & 3
So n has to be MULTIPLE of atleast one of 2 and 3..

And since x is MULTIPLE of n, x will also be MULTIPLE of 2 or 3 or both.

If x is MULTIPLE of 2, x+18 will be EVEN...
But choices do not contain any even integer, so out

If x is MULTIPLE of 3, x+18 should be a MULTIPLE of 3..
Only 99 in Choices is MULTIPLE of 3

Hence C
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Re: Positive integer x and 18 are both multiples of positive integer n. If  [#permalink]

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New post 12 Apr 2018, 23:39
QZ wrote:
Positive integer x and 18 are both multiples of positive integer n. If n > 1, which of the following is a possible value for 18 + x ?

a. 41
b. 67
c. 99
d. 103
e. 125


If x and 18 are both multiples of n, then x + 18 must also be a multiple of n. This means that x + 18 must share some common factor with 18 (a factor which is greater than 1). Only 99 satisfies this (41, 67 and 103 are primes, 125 = 5^3 so none of them share any common factor, greater than 1, with 18).

Answer: C.
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Re: Positive integer x and 18 are both multiples of positive integer n. If  [#permalink]

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New post 13 Apr 2018, 00:29
QZ wrote:
Positive integer x and 18 are both multiples of positive integer n. If n > 1, which of the following is a possible value for 18 + x ?

a. 41
b. 67
c. 99
d. 103
e. 125


x and 18 are multiples of positive integer n. what could be the value of n. 18 can tell us the probable value of n. n could be 1, 18, 2, 9, 3, 6. it is also given in the question that n is greater that 1 (n>1). Now , we have to find out the value of 18+ x. In this point back solving is fine.

A) 41 ..........prime no. 18+x=41 . we are left with 23, which is also a prime . thus it can't be the multiple of n.
B)67............18+X=67.........x=49, which is not a multiple of n.
C)99..........18+x=99.........x=81......now it is a multiple of n. just look at the probable value of n. 9 is there.

So , the correct answer is C.

anyone can check rest of the options. only option C conforms our condition.
Re: Positive integer x and 18 are both multiples of positive integer n. If &nbs [#permalink] 13 Apr 2018, 00:29
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