Which of the following would result in a remainder of 7 when divided

Question

Which of the following would result in a remainder of 7 when divided by 12?

I. 151
II. 3,443
III. 5,995

A) I only
 B) I and II
 C) I and III
 D) II and III
 E) I, II and III

How come the answer is C? 5995 Divided by 12 doesn't leave a remainder 7. Any idea people?

jackyhd · Accepted Answer

say x div by 12, should check whether x div by 3 and 4. (x is div by 3 if sum of all digits of x is div by 3, and x is div by 4, if the number formed by tens and ones, is div by 4)

since remainder is 7, we have x=12q+7 (rearrange the equation: x-7=12q)

151-7=12q => 144=12q => q=12 yes
3443-7=3436 => 3436=12q => 3+4+3+6 =16 not div by 3 so not div by 12 no
5995-7=5988 => 5988=12q => 5+9+8+8=30 which is div by 3, and 88 is div by 4, so it's div by 12 yes

answer C

AKProdigy87 · Answer

151 = 12 *  12  +  7 
3443 = 286 *  12  +  11 
5995 = 499 *  12  +  7

Therefore, the answer is  C .

amit2k9 · Answer

for divisibility by 12,check for 3 and 4.
since after dividing remainder is 7,meaning after dividing by 3 remainder = 1 
and after dividing by 4 remainder = 3.

so check for 151 giving 1 and 3 respectively.

also for 5995 (sum of the digits = 28) hence dividing by 3 remainder = 1 (3*9=27)
also for 4 (6000 is divisible,similarly 5996 is divisible,hence 5992 is divisible)

thus 5995-5992=3 will be remainder after dividing by 4.

thus C it is.So,without actual dividing you can test like this.

mydreammba · Answer

Thanks Jack for the clear explanation

quantman3 · Answer

normal division looks much simpler ... and wont take much time as well

Ekland · Answer

the question is asking which will have a remainder 1 when divided by 3? answer C less than 15 seconds :-D

mahakmalik · Answer

It al comes down to basic in the end,I guess.
x=12q+7
151=12q+7
144=12q
q=12
like wise can be found for other two.

sq01 · Answer

If a number has a remainder of 7 when divided by 12 it will have a remainder of 1 when divided by 3 -->  1   2   3    4   5   6    7 . So all you have to do is divide all numbers by 3.

chetan2u · Answer

Hi,  sq01  and  Nez ,

It may not be correct idea to check only by 3 and take that as the answer..
You may have got the correct answer but may not be some other day in some other Q..

When 3 leaves a remainder of 1, the number div by 12 can leave a remainder of 1,4,7, or 10.. 
for example if one of the choice was 121. 121 leaves a remainder of 1 when div by 3, so you would mark tht as he answer.
But that would be wrong, since 121 leaves a remainder of 1, when div by 12..

therefore check for 3 and 4.. 
3 should leave a remainder 1, and 4 should leave a remainder of 3..
so if the number +1 is div by 4, that is our answer..

121 +1=122 this is not div by 4 as last two digits are not div by 4..
151 +1 = 152, 52 is div by 4, this is one of our answer.

Hope it helps

stonecold · Answer

only way to solve this question is via long division and see what is the remainder when the numbers are divided by 12

evillasis · Answer

My technique was the followin:

1. We need to confirm that these numbers have a reminder of 7 when divided by 12:

x/12=k+7 
 x=12k+7

what if we add 5 to each answee and check that the answer is divisible by 12?

x+5 = 12k + (7+5) = 12(k+1)

I. 151 -> 151+5 = 156  correct:divisible by 4 and by 3 
II. 3,443 -> 3448 ->  wrong: the sum of the digits is not multiple of 3 
III. 5,995 -> 6,000  clearly correct

Best,

Andres

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.

Which of the following would result in a remainder of 7 when divided

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

Which of the following would result in a remainder of 7 when divided

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