samarth1222 wrote:
hi
can someone provide the solution to this question I was not able to solve it ?
Surely! Ok so we are given that 85 when divided by \(n\) gives us a remainder of 7 and when divided by \(2n\) gives us a remainder of \(n+7\)
\(85 = n*C + 7\) and \(85 = (2n)C + (n+7)\) {Remainder expressions where C represents the Quotient}
Now \(85\) gives a remainder of \(7\) when divided by \(n\) => 2 things
a) \(n > 7\) (only then can it have a remainder greater than 7)
b) \(n\) is a factor of \(78\) (because only a number greater than 7 which is a factor of 78 can leave a remainder of 7 when it divides 85)
Now we know that \(n\) is a factor of \(78\), so we find all factors of \(78\)
\(78 = 2*3*13\), Factors = \(1, 2, 3, 6, 13, 26, 39, 78\)
\(n > 7 so 1, 2, 3, 6\) are out. Let us examine the other options
If \(n = 13: 2n = 26\): Remainder (\(\frac{85}{2n}\)) = \(16 ≠ n+7 (13+7=20)\)
If \(n = 26: 2n = 52\): Remainder (\(\frac{85}{2n}\)) = \(33 = n+7 (26+7=33)\)
If \(n = 39: 2n = 78\): Remainder (\(\frac{85}{2n}\)) = \(7 ≠ n+7 (39+7=46)\)
If \(n = 78: 2n = 156\): Remainder (\(\frac{85}{2n}\)) = \(85 = n+7 (78+7=85)\)
2 possible values satisfy. Hence
Answer = 2 (C)Hope its clear