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Sum

If 56 × 32y is divisible by 18, find the least value of y.

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#### Solution

It is given that, the number 56 × 32y is divisible by 18. Then, it is also divisible by each factor of 18.

Thus, it is divisible by 2 as well as 3.

Now, the number is divisible by – 2, its unit’s digit must be an even number that is 0, 2, 4, 6, Therefore, the least value of y is 0.

Again, the number is divisible by 3 also, sum of its digits is a multiple of 3. i.e. 5 + 6 + x + 3 + 2 + y is a multiple of 3

⇒ 16 + x + y = 0, 3, 6, 9,...

⇒ 16 + x = 18

⇒ x = 2, which is the least value of x.

Concept: Games with Numbers

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