Question

If the 9-digit number 83x93678y is divisible by 72, then what is the value of (3x - 2y)?

• A. 8
• B. 10
• C. 12
• D. 15

Answer 1

Answer:

B. 10

Solution: Given: The 9-digit number 83x93678y is divisible by 72. Concept used: If the last three digits of a number are divisible by 8, then the number is completely divisible by 8. If the sum of digits of the number is divisible by 9, then the number itself is divisible by 9. Calculation: If the 9-digit number 83x93678y is divisible by 72, then it must be divisible by 8 and 9 simultaneously. The last three digits of 83x93678y are 78y. Hence, In order to be divisible by 8, y must be 4. The number becomes = 83x936784 Now, in order to be divisible by 9, 8 + 3 + x + 9 + 3 + 6 + 7 + 8 + 4 = Multiple of 9 ⇒ 48 + x = Multiple of 9 In order to be a multiple of 9, x must be 6. That makes (48 + 6) i.e. 54 a multiple of 9. Hence, ⇒ 3x - 2y ⇒ 3 × 6 - 2 × 4 ⇒ 10 ∴ The value of (3x - 2y) is 10.