If x is a multiple of 18 and 60, then x must be divisible by which of

Question

If x is a multiple of 18 and 60, then x must be divisible by which of the following?

I. 24
II. 36
III. 45

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III

gmatophobia · Accepted Answer

Given x is a multiple of 18 and 60

If x is a multiple of 18, x has  2 * 3^2  in its prime box (or as its prime factors)

If x is a multiple of 60, x has  2^2 * 3 * 5  in its prime box (or as its prime factors)

Therefore at the minimum x has  2^2 * 3^2 * 5  in its prime box (or as its prime factors). This is the LCM of 18 and 60.

Answer choice elimination

I. 24 →  3 * 2^3

We know that x has at least two threes, so x is divisible by 3. However, it's not guaranteed that x has three twos. Hence, x MAY be divisible by 24, it's not a MUST be a true statement.  We can eliminate I.

II. 36 →  3^2 * 2^2

We know that x has at least two threes and two twos, x MUST be divisible by 36.

III. 45 →  5 * 3^2

As x must have two threes and one five, x MUST be divisible by 45.

Option D

JeffTargetTestPrep · Answer

If x is divisible by 18 = (2)(3^2) and by 60 = (2^2)(3)(5), then x must also be divisible by LCM(18,60) = (2^2)(3^2)(5).

I. 24 = (2^3)(3). Since 24 is not a factor of LCM(18,60), x is  not necessarily  divisible by 24.

II. 36 = (2^2)(3^2). Since 36 is a factor of LCM(18,60), x  must be  divisible by 36.

III. 45 = (3^2)(5). Since 45 is a factor of LCM(18,60), x  must be  divisible by 45.

Answer: D

soysaucess · Answer

18 = 2 * 3^2
60 = 2^2 * 3 * 5

Since x is a multiple of the two numbers, x must at least contain:   2^2 * 3^2 * 5

24 = 2^3 * 3 
 36 = 2^2 * 3^2 
 45 = 3^2 * 5

For x to be divisible of a number, it must contain all of its factors. Hence, only 36 and 45 work.

epry10 · Answer

I guess my flaw was thinking that I had to do 18 x60 and THEN prime factorize, hence why I got E. Can someone clarify why that's wrong please?

Bunuel · Answer

x being a multiple of 18 and 60 does not mean x = 18 * 60. It means x is a multiple of the least common multiple (LCM) of 18 and 60, which is (2^2)(3^2)(5).

sujoykrdatta · Answer

If x is a multiple of 18 and 60, it is a multiple of their LCM (not their product). Their LCM is 180
So, the answer is II and III =>  Ans D

Take for example: A number is a multiple of 4 and 6. The number is a multiple of 12 (12 is a multiple of 4 and 6; so the smallest such number is 12) - It does not necessarily have to be 24. Hope that helps.

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If x is a multiple of 18 and 60, then x must be divisible by which of

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If x is a multiple of 18 and 60, then x must be divisible by which of

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