A 10 digit number 7x584805y6 is divisible by 72, then maximum value of √(xy) = ?

M4maths Previous Puzzles

06 Jun 2022 Number System

A 10 digit number 7x584805y6 is divisible by 72, then maximum value of √(xy) = ?

OPtion

1) 2√5
2) 2√6
3) 2√3
4) 2√14
5) 3√6
6) 2√7
7) 3√2
8) 4√2
9) √21
10) None of these

Solution

To be divisible by 72 the number must be divisible by 8 and 9 as 8 x 9 = 72
Divisibility rule by 8: The last three digits i.e. unit's, ten's and hundredth digit must be divisible by 8.
Divisibility rule by 9: Sum of digits of number must be divisible by 9 completely.
Let us apply divisibility rule of 8 in a number for last three digits 5y6
5y6 is completely divisible by 8 only when y = 3, 7
Let us put first y=3, then apply the divisibility rule by 9
Sum of the digits = 7+ x + 5 + 8 + 4 + 8 + 0 + 5 + 3 + 6 = x + 46
For the number to be divisible by 9, x=8
Similarly for y=7, checking divisibility rule by 9
Sum of the digits = 7+ x + 5 + 8 + 4 + 8 + 0 + 5 + 7 + 6 = x + 50
For the number to be divisible by 9, x=4
Thus, we have two sets of x,y i.e x=8, y=3 and x=4, y=7
Hence maximum value of √(xy) = √(4*7) = 2√7

Correct Option: 6 Best Solution (0)