An 8 - digit number 4985x76y is divisible by 45. Find the difference b

1.	An 8 - digit number 4985x76y is divisible by 45. Find the difference between the minimum and maximum values of (3x + y).1. 112. 103. 154. 14
Answer» Correct Answer - Option 2 : 10 Given - 8 - digit number 4985x76y is divisible by 45 Concept used - For divisibility of 5, unit digit must be either 0 or 5 For divisibility of 9, sum of the digits divisible by 9 Solution - 8 - digit number 4985x76y If y = 0 the number divisible by 5 For divisibility of 9, ⇒ 4 + 9 + 8 + 5 + x + 7 + 6 + 0 = 39 + x, so x = 6 Value of (3x + y) = 3 × 6 + 0 = 18 If y = 5 the number divisible by 5. For divisibility of 9, ⇒ 4 + 9 + 8 + 5 + x + 7 + 6 + 5 = 44 + x, so, x = 1 Value of (3x + y) = 3 × 1 + 5 = 8 Difference between minimum and maximum value = (18 - 8) = 10. ∴ Difference between the minimum and maximum value = 10.

An 8 - digit number 4985x76y is divisible by 45. Find the difference between the minimum and maximum values of (3x + y).1. 112. 103. 154. 14

Answer» Correct Answer - Option 2 : 10

Given -

8 - digit number 4985x76y is divisible by 45

Concept used -

For divisibility of 5, unit digit must be either 0 or 5

For divisibility of 9, sum of the digits divisible by 9

Solution -

8 - digit number 4985x76y

If y = 0 the number divisible by 5

For divisibility of 9,

⇒ 4 + 9 + 8 + 5 + x + 7 + 6 + 0 = 39 + x, so x = 6

Value of (3x + y) = 3 × 6 + 0 = 18

If y = 5 the number divisible by 5.

For divisibility of 9,

⇒ 4 + 9 + 8 + 5 + x + 7 + 6 + 5 = 44 + x, so, x = 1

Value of (3x + y) = 3 × 1 + 5 = 8

Difference between minimum and maximum value = (18 - 8) = 10.

∴ Difference between the minimum and maximum value = 10.

Discussion

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