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

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Senior Manager
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 422
If x is divisible by 6 and 9, then x must be a multiple of:  [#permalink]

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01 Nov 2018, 04:30
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Difficulty:

15% (low)

Question Stats:

77% (00:49) correct 23% (01:05) wrong based on 98 sessions

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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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Joined: 02 Aug 2009
Posts: 7982
If x is divisible by 6 and 9, then x must be a multiple of:  [#permalink]

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02 Nov 2018, 20:08
1
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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Re: If x is divisible by 6 and 9, then x must be a multiple of:  [#permalink]

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03 Nov 2018, 00:22
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.

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Karishma
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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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03 Nov 2018, 00:26
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

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.

Re: If x is divisible by 6 and 9, then x must be a multiple of:   [#permalink] 03 Nov 2018, 00:26
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