The number 79825x42y3 is divisible by 99. What is the geometric mean x and y

The number 79825x42y3 is divisible by 99. What is the geometric mean x and y?

1. 2
2. 3
3. 2√2
4. 2√3

Sol:

(24+y) – ( 16 + x ) → divisible by 11

(8 + y – x)

⇒ y – x = 3 or -8

(40 + x + y) → divisible by 9

⇒ x + y = 5 or 14

Taking y – x = 3 and x + y = 5

 Y = 4 and x = 1

⇒ Geometric mean =√xy=2