If the seven-digit number 94x29y6 is divisible by 72, then what is the value of (2x + 3y) for x ≠ y?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e 37.
Here it is given that 94x29y6 is divisible by 72.
Co - prime factors of 72 = 9 and 8.
It means that 94x29y6 must be divisible by 9 and 8.
If 94x29y6 is divisible by 8 then the last three digits of the number must be divisible by 8 which implies that 9y6 must be divisible by 8.
The possible values of 'y' at which 9y6 becomes divisible by 8 are 3 and 7 (936 and 976).
If 94x29y6 is divisible by 9 then the sum of the digits must be divisible by 9.
Sum of digits of 94x29y6 = (30 + x + y)
At y = 3 possible value of x by which 30 + x + y become divisible by 9 is 3.
It is given that x ≠ y. So x = 3 and y = 3 is not possible.
At y = 7 possible value of x by which 30 + x + y become divisible by 9 is 8.
Required value of 2x + 3y = 2 × 8 + 3 × 7 = 37.