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

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Director
Joined: 01 Apr 2008
Posts: 768
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
If positive integer k is divided by 6, the quotient is m and  [#permalink]

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Updated on: 23 Apr 2013, 12:37
8
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:37) correct 45% (01:43) wrong based on 372 sessions

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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

Originally posted by Economist on 06 Nov 2009, 23:06.
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.
Manager
Joined: 19 Aug 2009
Posts: 78

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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
Manager
Joined: 27 Oct 2009
Posts: 120
Location: Montreal
Schools: Harvard, Yale, HEC

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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
Senior Manager
Joined: 23 Mar 2011
Posts: 408
Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)

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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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Math Expert
Joined: 02 Sep 2009
Posts: 52294

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23 Apr 2013, 12:40
1
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.

Hope it's clear.
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Re: If positive integer k is divided by 6, the quotient is m and  [#permalink]

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23 Apr 2013, 13:17
Thanks Bunuel to rectify my careless approach. Of course 2 is prime...
+1 to you
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VP
Joined: 07 Dec 2014
Posts: 1152
If positive integer k is divided by 6, the quotient is m and  [#permalink]

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10 Feb 2018, 10:35
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

I. not true:
let k=8
8=6*1+2
8+1=9 (odd)
II. & III. not true:
let k=2
2=6*0+2
2 is prime and not divisible by 4
A
If positive integer k is divided by 6, the quotient is m and &nbs [#permalink] 10 Feb 2018, 10:35
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