A number when divided by d leaves a remainder 5 and when divided by 2d

Question

A number when divided by d leaves a remainder 5 and when divided by 2d leaves a remainder 11. What remainder shall be obtained if thrice the number is divided by 2d?

A. 6
B. 9
C. 11
D. 23
E. 33

Source - Indian MBA college entrance test

ProfChaos · Answer

chetan2u ,  Bunuel ,  VeritasKarishma ,  yashikaaggarwal ,  generis

HELP!

chetan2u · Answer

Hi

The increase in remainder from 5 to 11 tells us that d is 6, and the number can be taken as 11..
11 divided by 6 gives 5 as the remainder and 11 divided by 12 gives remainder 11.
So, 11*3=33 when divided by 12 gives a remainder 9.

Or 
n=dx+5, and n=2dy+11
So dx+5=2dy+11....d(x-2y)=6
Now d gives a remainder of 5, so d>5. Thus only possible value is 6 as d*(x-2y)=6=6*1=3*2
Now we can take the number as 11 itself and find the answer as also shown above.

KarishmaB · Answer

A number say N when divided by d (split into groups of d each) leaves remainder 5. When N is divided by 2d (two groups of d each are combined now), it leaves remainder 11. This means one group of d was leftover which could not be combined with another group of d and hence it was added to the remainder. Thi means d = 11 - 5 = 6 and 2d = 12 3N will mean now we have 3 times the groups of 12 and 3 groups of 11 leftover. These 3 groups of 11 i.e. 33 will make further two groups of 12 leaving us with 33 - 2 * 12 = 9. So remainder in this case will be 9. Check: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... unraveled/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... y-applied/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... emainders/

GMATGuruNY · Answer

Let N = the number.

A number when divided by d leaves a remainder 5 .
In other words, N is a MULTIPLE OF D plus 5 more:
N = d+5, 2d+5,  3d+5 , 4d+5...

When divided by 2d, the number leaves a remainder 11. 
In other words, N is a MULTIPLE OF 2D plus 11 more:
N =  2d+11 , 4d+11, 6d+11, 8d+11...

Since the two lists represent options for the same number -- N -- choose an expression in the first list that can logically be equal to an expression in the second list.
Since d must be a NONNEGATIVE INTEGER, the green expression in the first list is the smallest option that could be equal to the blue expression in the second list:
 3d+5  =  2d+11 
d = 6

Since d=6, the blue expression yields the following option for N:
2d+11 = 2*6 + 11 = 23

What remainder shall be obtained if thrice the number is divided by 2d? 
3N = 3*23 = 69
2d = 2*6 = 12
 \frac{69}{12} = 5  R9

B

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A number when divided by d leaves a remainder 5 and when divided by 2d

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