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Trying to get my head around this divisibility question

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Trying to get my head around this divisibility question

by ramapra » Tue Nov 29, 2011 12:09 am
This is from the Kaplan Premier 2011 edition page 467 , question 10 .

If R is an integer , is R evenly divisible by 3 ?

1) 2R is evenly divisible by 3.
2) 3R is evenly divisible by 3.

Kaplan's solution lists 1) as being sufficient .
The solution somehow equates being evenly divisible to being a multiple , which IMHO is incorrect .

Lets take R as being 6 and 15 respectively
According to 1) 2 x R is an even multiple of 3 , which will be 12 and 30 respectively and 2R/3 in this case will be 4 and 10 respectively . In both cases its an even multiple of 3 but clearly does not prove sufficient .

Is this a typo or am I misunderstanding the question ?

Thanks
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by shankar.ashwin » Tue Nov 29, 2011 12:46 am
Statement 1:

2*R is divisible by 3.

2 is not divisible by 3, so R MUST be divisible by 3 (for 2R to be divisible by 3) - Sufficient

Statement 2:

3*R is divisible by 3.

Here, 3 is divisible by 3, so R can take any integer value and 3R would be divisible by 3. So we cannot tell if R is divisible by 3. - Insufficient.

A
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by ramapra » Tue Nov 29, 2011 1:01 am
1) is sufficient for divisibility but not for even divisibility .

The questions asked is for even divisibility
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by shankar.ashwin » Tue Nov 29, 2011 1:03 am
Even divisibility is nothing but a number when divided leaves a remainder of 0.

So, divisibility test and evenly divisible are the same thing.

ramapra wrote:1) is sufficient for divisibility but not for even divisibility .

The questions asked is for even divisibility
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by ramapra » Tue Nov 29, 2011 1:05 am
Doesnt evenly divisible mean that the quotient is a multiple of 2 ?
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by ramapra » Tue Nov 29, 2011 1:05 am
ah got it . thanks for the clarification .
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