2020 · Q41
The number of three digit numbers (all digits are different) which are divisible by 7 and also divisible by 7 on reversing the order of the digits, is
Elementary MathematicsNumber System
- ASix
- BFive
- CFour
- DThree
Explanation
Checking all 3-digit multiples of 7 with distinct digits, only four also have a multiple-of-7 reversal: 168 ↔ 861 and 259 ↔ 952 (168 = 7×24, 861 = 7×123; 259 = 7×37, 952 = 7×136). Hence there are 4 such numbers. They form the two reversal pairs 168 ↔ 861 and 259 ↔ 952.