A nine-digit number 9880x42y6 is divisible by 72 such that 1<y<9 then what is the value of 5x-3y.
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Step-by-step explanation:
As a nine-digit number is divisible by 72, it is divisible by 9. The number must pass divisiblity test of 9 first:
→
→
→ This number is a multiple of 9. So, is also a multiple of 9.
→ It is required that .
These followings are pairs of x, y:
(2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (7, 1)
Is the number divisible by 8?
Let's do the divisiblity test of 8.
Where x=2, y=6:
→ 266 is not divisible.
Where x=3, y=5:
→ 256 is divisible.
→ In other cases, only 216 will be divisible by 8 because 216=256-(8×5).
The solution pairs are (3, 5) and (7, 1).
Therefore the value of 5x-3y are:
→ Case 1. (3,5) → 15-15=0
→ Case 2. (7, 1) → 35-3=32
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