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If positive integer k is divided by 6, the quotient is m and

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If positive integer k is divided by 6, the quotient is m and [#permalink] New post 06 Nov 2009, 23:06
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If positive integer k is divided by 6, the quotient is m and the remainder is 2, then which of the following must be true?

I. k + m is even

II. k cannot be a prime number

III. k is divisible by 4

A. None
B. I
C. II
D. III
E. I and II only
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Apr 2013, 12:37, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: Division [#permalink] New post 06 Nov 2009, 23:52
Economist wrote:
If positive integer k is divided by 6, the quotient is m and the remainder is 2, then which of the following must be true?

I. k + m is even

II. k cannot be a prime number

III. k is divisible by 4

a. none
b. I
c. II
d. III
e. I and II only


K=6m+2 ( dividend = quotent*divisor+ remainder
take a few example
k=2 ,m=0
k=8, m=1
k=14,m=2

thus ans if none of these
ans.a
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Re: Division [#permalink] New post 07 Nov 2009, 08:56
k = 6m+2 = 2(3m+1)
I. k + m = 2(3m+1) + m => even if only m is even, however m can be odd => not always true
II. k can not be a prime: not always true:
m=0 => k=2 : a prime
III. not true if m is even

Ans: none of the above
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Re: Division [#permalink] New post 23 Apr 2013, 12:24
Question is which "must be true"

So Ans is C (K cannot be prime, as primes cannot be divisible by 6 with remainder as 2)
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Re: Division [#permalink] New post 23 Apr 2013, 12:40
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Expert's post
sdas wrote:
Question is which "must be true"

So Ans is C (K cannot be prime, as primes cannot be divisible by 6 with remainder as 2)


That's not correct.

If positive integer k is divided by 6, the quotient is m and the remainder is 2, then which of the following must be true?

I. k + m is even
II. k cannot be a prime number
III. k is divisible by 4


A. None
B. I
C. II
D. III
E. I and II only

Positive integer k is divided by 6, the quotient is m and the remainder is 2 can be expressed as k=6m+2:

If m=0, then k=2=prime --> discard II and III.
If m=1, then k=8 --> k+m=9=odd --> discard I.

Answer: A.

Hope it's clear.
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Re: If positive integer k is divided by 6, the quotient is m and [#permalink] New post 23 Apr 2013, 13:17
Thanks Bunuel to rectify my careless approach. Of course 2 is prime...
+1 to you
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Re: If positive integer k is divided by 6, the quotient is m and   [#permalink] 23 Apr 2013, 13:17
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