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If a certain number is divisible by 12 and 10, it is NOT necessarily

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Bunuel
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If a certain number is divisible by 12 and 10, it is NOT necessarily [#permalink] New post   20 Dec 2015, 05:45
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If a certain number is divisible by 12 and 10, it is NOT necessarily divisible by which of the following?

A. 4
B. 6
C. 15
D. 20
E. 24
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Re: If a certain number is divisible by 12 and 10, it is NOT necessarily [#permalink] New post   20 Dec 2015, 08:18
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If a certain number is divisible by 12 and 10, it is NOT necessarily divisible by which of the following?

let the certain number be 60, which is both divisible by 12 and 10.

60/24 = 5/2

E. 24
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Re: If a certain number is divisible by 12 and 10, it is NOT necessarily [#permalink] New post   03 Jan 2019, 21:08
Find the LCM (12,10)
12= 2*2*3
10= 2*5
=> LCM= 2*2*3*5 = 60
60 is not divisible by 24. =>E
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Re: If a certain number is divisible by 12 and 10, it is NOT necessarily [#permalink] New post   04 Jan 2019, 00:42
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Bunuel wrote:
If a certain number is divisible by 12 and 10, it is NOT necessarily divisible by which of the following?

A. 4
B. 6
C. 15
D. 20
E. 24


When we say a number is divisible by 12, it means it has two 2s and a 3 as factors (12 = 2*2*3)
When we say a number is divisible by 10, it means it has a 2 (which we knew already) and a 5 as factors (10 = 2*5)

So the number must have at least two 2s, a 3 and a 5 as factors.

A. 4 = 2*2 (a factor)
B. 6 = 2*3 (a factor)
C. 15 = 3*5 (a factor)
D. 20 = 2*2*5 (a factor)
E. 24 = 2*2*2*3 (may not be a factor because it needs three 2s)

Answer (E)
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Re: If a certain number is divisible by 12 and 10, it is NOT necessarily [#permalink]
04 Jan 2019, 00:42
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