Let \(X\) be the greatest number which, when it divides 2871, 4627 and 7700, leaves the same remainder \(Y\) in each case. What is the value of \(X-Y\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 202
If two numbers leave the same remainder on division by \(X\), their difference is divisible by \(X\), because the remainders cancel. So \(X\) is the HCF of the differences of the given numbers.
\(4627-2871=1756\)
\(7700-4627=3073\)
\(7700-2871=4829\)
\(1756=4\times439\), \(3073=7\times439\), \(4829=11\times439\)
4, 7 and 11 have no common factor, so \(X=439\)
\(2871=439\times6+237\), so \(Y=237\)
Check: \(4627=439\times10+237\) and \(7700=439\times17+237\)
\(X-Y=439-237=202\)
So \(X-Y=\) 202.