When a certain number is divided by 7, the remainder is 0. If the rema

Question

When a certain number is divided by 7, the remainder is 0. If the remainder is not 0 when the number is divided by 14, then the remainder must be

(A) 1 
(B) 2
(C) 4 
(D) 6 
(E) 7

Kinshook · Answer

Since the number is divisible by 7, is may be written as 7k, where k is an integer Since remainder is not 0 when divided by 14, it may be written as 14x + c But since number is divisible by 7 => 14x + c is divisible by 7 14x is divisible by 7 => c is divisible by 7 => c=7 since 0

Lampard42 · Answer

The number must be a multiple of 7. The multiples of 7 are 14,21,28. So every 2nd multiple remainder when divided by 14 will be zero. So for other multiples remainder will always be 7. IMO E.

Archit3110 · Answer

test with no; 21,35 so on 
remainder would be 7
IMO E

ueh55406 · Answer

same here, tested a couple of number starting 21, 28, 35.. getting a consistent remainder, 7 for 21 and 35 so went with guessing for this one.

is there a more logical approach for these questions. what Bunuel has explained is fine, but I'm not sure if I'll be able to do that for larger numbers, say, had the question been to check what the remainder is when n is divided by 83

BrushMyQuant · Answer

Given that When a certain number is divided by 7, the remainder is 0. If the remainder is  not  0 when the number is divided by 14, then the remainder must be

A certain number is divided by 7, the remainder is 0

n -> Dividend (Assume)
7 -> Divisor
a -> Quotient (Assume)
0 -> Remainders
=> n = 7*a + 0 = 7a

Remainder when n is divided by 14, if not 0, will be

As the number is a multiple of 7, so it will be either an even multiple of 7 or an odd multiple.
It is not an even multiple of 7, as then it will becomes a multiple of 14 giving remainder with 14 as 0. (Which is not possible)

=> It is an odd multiple of 7. Example it can be 7 also

Remainder of 7 by 14 = 7

So,  Answer will be E 
Hope it helps!

Watch the following video to learn the Basics of Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

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.

When a certain number is divided by 7, the remainder is 0. If the rema

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

When a certain number is divided by 7, the remainder is 0. If the rema

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