When 3336, 4188 and 5679 are divided by a 2-digit number p, the remainder in each case is q. What is the value of (p – q)?

Explanation

The differences 4188 − 3336 = 852 and 5679 − 4188 = 1491 are divisible by p. HCF(852, 1491) = 213 = 3 × 71, so the 2-digit number is p = 71. Remainder q = 3336 mod 71 = 70. So p − q = 71 − 70 = 1.