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

Question

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

virtualanimosity · Answer

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

ezinis · Answer

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

sdas · Answer

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)

Bunuel · Answer

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.

sdas · Answer

Thanks Bunuel to rectify my careless approach. Of course 2 is prime...
+1 to you

gracie · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards