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Re: If n and k are positive integers, is n/k an even integer? [#permalink]

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02 Sep 2010, 14:04

If n and k are positive integers, is n/k an even integer? (1) n is divisible by 8. (2) k is divisible by 4.

Explanation 1) n is divisible by 8 --> 8/8 = 1 (odd) 8/3 ,8/5 gives nothing not even an integer 2) k is divisible by 4 --> 25/4 = gives nothing not even an integer

combining both

16/12 --> gives nothing not even an integer

answer E...... _________________

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n/k= 8a/4b= 2a/b so n/k= 2a/b if a and b are 2 and 2 the answer is yes=2*2/2=2 (n/k is even) but if a and b are 3 and 2 then 2*3/2=3 (the answer is no. 3 is odd)

Re: If n and k are positive integers, is n/k an even integer? [#permalink]

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03 Mar 2015, 10:23

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While it might be easy to run through this question without taking any notes (and still get it correct), there's something to be said for practicing to PROVE that your answer is correct. This level of attention to detail will help you to hone your skills on ALL DS questions.

We're told that N and K are positive integers. We're asked if N/K is an EVEN INTEGER. This is a YES/NO question.

Fact 1: N is divisible by 8

IF.... N = 8 K = 1 Then 8/1 = 8 and the answer to the question is YES

IF.... N = 8 K = 8 Then 8/8 = 1 and the answer to the question is NO Fact 1 is INSUFFICIENT

Fact 2: K is divisible by 4

IF.... N = 8 K = 4 Then 8/4 = 2 and the answer to the question is YES

IF... N = 7 K = 4 Then 7/4 = 1.75 and the answer to the question is NO Fact 2 is INSUFFICIENT

Combined, we know... N is divisible by 8 K is divisible by 4

IF.... N = 8 K = 4 Then 8/4 = 2 and the answer to the question is YES

IF.... N = 8 K = 8 8/8 = 1 and the answer to the question is NO Combined, INSUFFICIENT

Re: If n and k are positive integers, is n/k an even integer? [#permalink]

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20 Dec 2015, 10:54

The question asks whether n/k = 2n

Each statement alone is insufficientt

Combining the two statements n/k can be written as (8 * something)/(4 * something)

While at first chance it may seem that 8 gets cancelled by 4, leaves a 2 and rest multiplied by 2 is even. But we don't know the something/something else. it may be 2 * 7/9 which is not an integer at all (n and k are positive integers, this does not imply their division is one too)

Hence, E _________________

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Re: If n and k are positive integers, is n/k an even integer?
[#permalink]
20 Dec 2015, 10:54

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