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Question

A number when divided by 18 leaves a remainder 7. The same number when divided by 12 leaves a remainder n. How many values can n take?

CAT 2021

A
2
CORRECT ANSWER WRONG ANSWER
B
0
CORRECT ANSWER WRONG ANSWER
C
1
CORRECT ANSWER WRONG ANSWER
D
3
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(A)

Explanatory Answer :

18a+7=12b+n

18a+7= 25,43,61,79

check remainder in all these cases it is following pattern of either 1 or 7

other method

18a+7=(12+6)a+7=12a+(6a+7)

so we can say no when divided by 12 gives remainder as 6a+7 i.e. 13,19,25 as remainder while dividing by 12 can't be greater than 12 hence 1,7.