Question

# A certain number 'C' when divided by N1 it leaves a remainder of 13 and when it is divided by N2 it leaves a remainder of 1, where N1 and N2 are the positive integers. Then the value of N1+N2 is, if N1N2=54:

A
36
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B
27
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C
54
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D
can't be determined uniquely
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Solution

## The correct option is D can't be determined uniquelyC = N1Q1 + 13 and C = N2Q2 + 1 where Q1 Q2 are the quotients and hence Q1 and Q2must be integers So, N1Q1+13=N2Q2+1 N2Q2−N1Q1=1245N1Q2−N1Q1=12N1(4Q2−5Q1)=60 where N1 and (4Q2−5Q1) both will be integers so that N1 can be one of the values of factors of 60 i.e., 1, 2, 3, 4, 15, 20, 30 and 60. But N1 can not be less than the remainder 13. So the possible values are 15, 20, 30 and 60. Thus we see that the corresponding values of N2 are 12, 16, 24 and 48. So there are more than one possible values of N1 and N2. Thus there is no unique value of N1+N2. Hence (d) is correct option.

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