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Is n a multiple of 15

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by sanjana » Sat Oct 10, 2009 7:11 am
Is the integer n a multiple of 15?

1)n is a multiple of 20
2)n+6 is a multiple of 3

[spoiler]0A : C[/spoiler]

I picked E,

1) n can be 20,40,60,80..
May or may not be a multiple of 15 hence insufficient.

2)n+6 is a multiple of 3
n could be 0,3,6,9, etc hence insufficient

Was not able to derive anything combining them as well,
Can someone help?
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by rohan_vus » Sat Oct 10, 2009 7:21 am
Pretty straight forward .

From stmnt (1) you now n is divisible by 2 and 5 ..
From stmnt (20) you know n is divisible by 3 ..as n + 6 can only be divisble by 3 if n alone is divisible by 3 since 6 is already a multiple of 3.

So , combining both stmnts u can infer n is divisible by 2 , 5 and 3 .. 2, 5 and 3 are prime numbers , thus n is a multiple of 2 * 5 * 3 ..=> 15 * 2..in other words its a multiple of 15 ..
60 , 120 , 180 , etc...
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by sanjana » Sun Oct 11, 2009 8:11 pm
Thanks! yeah that was pretty straight forward..
From this can we conclude that whenever we are faced with such questions, always look for the Prime Divisors and then combine them to get the answer..?
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