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If x is divisible by 6 and 9, then x must be a multiple of:

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If x is divisible by 6 and 9, then x must be a multiple of:  [#permalink]

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New post 01 Nov 2018, 03:30
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Question Stats:

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If x is divisible by 6 and 9, then x must be a multiple of:

I. 3
II. 18
III. 27

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III

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If x is divisible by 6 and 9, then x must be a multiple of:  [#permalink]

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New post 02 Nov 2018, 19:08
1
1
Baten80 wrote:
If x is divisible by 6 and 9, then x must be a multiple of:

I. 3
II. 18
III. 27

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III


If x is a divisible by 6 and 9, it has to be a multiple of LCM of 6 and 9 and thus multiple of all factors of the LCM.

Now LCM is : 6=2*3 and 9 =3*3, LCM = 2*3*3=18
Thus factors of 18 are 1, 2, 3, 6, 9, 18
Thus I and II are correct..

B

We cannot say anything about 27 since if the number is 36, it is NO but if number is 54, it is yes..
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If x is divisible by 6 and 9, then x must be a multiple of:  [#permalink]

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New post 02 Nov 2018, 23:22
2
Baten80 wrote:
If x is divisible by 6 and 9, then x must be a multiple of:

I. 3
II. 18
III. 27

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III


x is a multiple of 6 so it has 2 and 3.
x is a multiple of 9, so it has two 3s.

So x has a 2 and two 3s at least.
x = 2 * 3 * 3 * k
This means x is a multiple of 3 and 18. But we cannot say anything about 27 since we do not know if x has three 3s.

Answer (B)
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Re: If x is divisible by 6 and 9, then x must be a multiple of:  [#permalink]

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New post 02 Nov 2018, 23:26
Baten80 wrote:
If x is divisible by 6 and 9, then x must be a multiple of:

I. 3
II. 18
III. 27

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III



At first determine the minimum value of x

lcm of 6 and 9 will help determine minimum value.

lcm ( 9 and 6) = 18

18 is divisible by 3 and 18.

The best answer is B.
GMAT Club Bot
Re: If x is divisible by 6 and 9, then x must be a multiple of: &nbs [#permalink] 02 Nov 2018, 23:26
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If x is divisible by 6 and 9, then x must be a multiple of:

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