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If a is an integer larger than 1, and x=60a, then x must be a multiple

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If a is an integer larger than 1, and x=60a, then x must be a multiple  [#permalink]

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New post 28 Sep 2016, 02:49
2
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A
B
C
D
E

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  25% (medium)

Question Stats:

83% (01:18) correct 17% (01:01) wrong based on 92 sessions

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If a is an integer larger than 1, and x=60a, then x must be a multiple  [#permalink]

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New post 28 Sep 2016, 13:55
Answer is C . X must be divisible by 60 .
a , an integer less than 1 means a could be 0,-1,-2,....... and x = 60a
so if a= 0, x = 0*60=0 is divisible by 12 ( recall 0 is divisible by any integer) if a= -1, then -60 is divisible by 12 but not 8,9,18 and 120 , if a-2 , then -120 is divisible by 60 and so on .



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Re: If a is an integer larger than 1, and x=60a, then x must be a multiple  [#permalink]

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New post 14 Jul 2017, 05:18
sajib2126 wrote:
Answer is C . X must be divisible by 60 .
a , an integer less than 1 means a could be 0,-1,-2,....... and x = 60a
so if a= 0, x = 0*60=0 is divisible by 12 ( recall 0 is divisible by any integer) if a= -1, then -60 is divisible by 12 but not 8,9,18 and 120 , if a-2 , then -120 is divisible by 60 and so on .



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Answer should be ???.

It is clearly mentioned that a>1, so for least value of a,suppose a = 2.
60*2=120
divisible by 8, 12..
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If a is an integer larger than 1, and x=60a, then x must be a multiple  [#permalink]

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New post 14 Jul 2017, 12:19
Bunuel wrote:
If a is an integer larger than 1, and x=60a, then x must be a multiple of which of the following?

A. 8
B. 9
C. 12
D. 18
E. 120

If you don't remember the rule below, do the prime factorization of 60 to get 2*2*3*5.

For each answer choice, see if you have enough prime factors from 60 to get what you need for the answer choice to be a factor of x = 60a.

A. 8 = 2*2*2. NO. We only have two 2s. "a" could be 2. It could also be 11.

B. 9 = 3*3. NO. We only have one 3. "a" could be 3. It could also be 11.

C. 12 = 2*2*3. YES. We have two 2s and one 3. Whatever else "a" is, x will be a multiple of 12. If you're like I, keep checking.

D. 18 = 2*3*3. NO. We only have one 3. "a" could be 3. It could also 11.

E. 120. NO.

I think it's the trap answer, because if a > 1, you're bound to consider that a equals 2, or to think that two integers multiplied means a factor of 2.

The latter might be true. But "a" might be or contain other factors that make x indivisible by 120. If a = 3, x = 180. That's not divisible by 120. It is divisible by 12.

The rule is: If x is a multiple of a number N, it is also always a multiple of the factors of that number N. Only choice that's a factor of N = 60 is 12. That's C.

Answer C

Hope it helps. :-)
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Re: If a is an integer larger than 1, and x=60a, then x must be a multiple  [#permalink]

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New post 16 Jul 2017, 17:41
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Bunuel wrote:
If a is an integer larger than 1, and x=60a, then x must be a multiple of which of the following?

A. 8
B. 9
C. 12
D. 18
E. 120


Since x = 60a and a is an integer greater than 1, x must be a multiple of 60. Furthermore, x must be a multiple of any factors of 60. Since the only answer choice that is a factor of 60 is 12, answer choice C is the correct answer.

Answer: C
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Re: If a is an integer larger than 1, and x=60a, then x must be a multiple   [#permalink] 16 Jul 2017, 17:41
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