N is positive integer and when N is divided by 24, the remainder is 16

Question

N is positive integer and when N is divided by 24, the remainder is 16. What is the remainder, when N is divided by 18?

(A) 4
(B) 12
(C) 16
(D) 24
(E) Cannot be determined

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GMATWhizTeam · Answer

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prateek25 · Answer

N = 24T +16 where T is an integer

T=1, N/18 gives a remainder 4 
T=2, N/18 gives a remainder 10
T=3, N/18 gives a remainder 16
T=4, N/18 gives a remainder 4

We need to know the exact value of N to determine the remainder. Answer should be E.

debjit1990 · Answer

Ans: E

N=24q+16
N=+ve int
let q=0, N=16 16%18=16
q=1,N=40 40%18=4
q=2,N=64 64%18=10
q=3,N=24*3+16 (24*3+16)%18=16

So, it cannot be determined.

shameekv1989 · Answer

N is positive integer and when N is divided by 24, the remainder is 16. What is the remainder, when N is divided by 18?

(A) 4
(B) 12
(C) 16
(D) 24
(E) Cannot be determined

Values that N can take => 16, 40, 64... that will yield 16 as a remainder when divided by 24.

Remainders when N divided by 18 :-
16/18 => 16
40/18 => 4
64/18 => 10

Hence remainder can not be determined

Answer - E

Groo · Answer

1)  When N is divided by 24, the remainder is 16  
 Values of N can be 16, 40, 64, 88 ...
 
2)  Remainders when N divided by 18  : 
16 when N=16; 4 when N= 40; 10 when N=64

There is no unique remainder, thus Answer is  E

GMATWhizTeam · Answer

The official solution is shared. You can access it from the post right below the question. Feel free to ask any doubts that you may have. We are happy to help.

Mrpd · Answer

N = 24*x + 16
N = (18+6)*x + 16
N = 18*x + 6*x + 16

The remainder is 6*x + 16. As we don't x, the remainder cannot be determined.

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N is positive integer and when N is divided by 24, the remainder is 16

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N is positive integer and when N is divided by 24, the remainder is 16

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