Question

the numbers 272738 and 232342 when divided by n a two digit number leave a remainder of 13 and 17 respectively. find the sum of the digits of n?

Answer 1

74. The numbers 272738 and 232342, when divided by n, a two digit number, leave a remainder of 13 and 17 respectively. Find the sum of the digits of n?

A. 7

B. 8

C. 5

D. 4

Answer: Option A

Explanation :

From the given information, (272738 - 13, 232342 - 17) are exactly divisible by that two digit number.

We have to find the HCF of the given numbers 272725, 232325.

HCF = 25.

So sum of the digits = 7.

Answer 2

The options for this question are missing. Here are the missing options:

a. 7

b. 8

c. 5

d. 4

Answer

As remainder is 13 & 17 so dividend must be greater than 17  

272738 = n*a+13 => 272725=n*a ---(1)

232342 = n*b+17 => 232325=n*b ---(2)

Last two digit of (1)&(2) is 25 so n must be 25, no other two digit no. greater than 25 satisfies this

272725=25*10909

232325=25*9293

n=25, sum of digits of n = 2+5 = 7

So the correct answer is option A: 7