A seven-digit number 489y5z6 is divisible by 72. Which of the options gives the highest possible product of y and z?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 42.
The number 489y5z6 is divisible by 72 which means it is also divisible by 8 and 9.
Divisibility by 8: The last three digits 5z6 must form a number divisible by 8.
Divisibility by 9: The sum of all the digits must be divisible by 9.
If z = 3, 536 is divisible by 8
If z = 7, 576 is also divisible by 8.
Thus, z = 3 or 7
Sum of the digits if z = 3
⇒ 35 + y.
For divisibility by 9, y = 1
Thus, product of y and z = 1 × 3 = 3
Sum of the digits if z = 3
⇒ 39 + y
For divisibility by 9, y = 6
Thus, product of y and z = 6 × 7 = 42
Hence, the highest possible product of y and z is 42.