Question 61

If a 10-digit number 5 4 3 2 y 1 7 4 9 x is divisible by 72, then what is the value of (5x - 4y)?

Solution

For divisibility by 72, number should be divisible by 8 and 9.
For divisibility by 8,
49x should be divisible by 8.
So, value of x = 6
For divisibility by 9,
The sum of the number will be divided by 9.
So, 5 + 4 + 3 + 2 + y + 1 + 7 + 4 + 9 + x = 5 + 4 + 3 + 2 + y + 1 + 7 + 4 + 9 + 6 = 41 + y
Value of y = 4
($$\because$$ 45 is divided by 9)
Now,
5x - 4y = $$5 \times 6 + 4 \times 4$$
30 - 14 = 14


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