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Prime Box - Manhattan Gmat

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Prime Box - Manhattan Gmat

by shanice » Sun Apr 08, 2012 9:41 pm
Hi guys,

Has anyone tried using prime box to solve Primes & Divisibility questions? I'm really having a headache with this one.

For example:If s is a multiple of 12 and t is a multiple of 12, is 7s+5t a multiple of 12?

Answer : Yes

Here is my understanding for the following:-

S is a multiple of 12 - It means S is divisible by 12 or 12 is a factor of S. Am I right?
t is a multiple of 12 - It means t is divisible by 12 or 12 is a factor of t. Am I right?

The prime factors of 12 are 2x2x3. I stopped until here. I don't know how to link this prime factors of 12 to the question.

Please help.
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by Shalabh's Quants » Sun Apr 08, 2012 9:54 pm
shanice wrote:Hi guys,

Has anyone tried using prime box to solve Primes & Divisibility questions? I'm really having a headache with this one.

For example:If s is a multiple of 12 and t is a multiple of 12, is 7s+5t a multiple of 12?

Answer : Yes

Here is my understanding for the following:-

S is a multiple of 12 - It means S is divisible by 12 or 12 is a factor of S. Am I right?
t is a multiple of 12 - It means t is divisible by 12 or 12 is a factor of t. Am I right?

The prime factors of 12 are 2x2x3. I stopped until here. I don't know how to link this prime factors of 12 to the question.

Please help.
Well you are correct. I could not understand why prime no. is being dragged into. At least in this particular question there is no need.

Q. Is 7s+5t a multiple of 12?

As s & t are multiple of 12 hence s can be written as s = 12 n and t can be written as t = 12 m;

where n & m are quotients.

=> (7s+5t)/12 = [7(12n)+5(12m)]/12 = 12.(7n+5m)/12 = (7n+5m).

So 7s+5t a multiple of 12.
Shalabh Jain,
e-GMAT Instructor
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