If x and y are two digits of the number 653xy such that this number is…

2023

If x and y are two digits of the number 653xy such that this number is divisible by 80, then x + y = ?

  1. A.

    2

  2. B.

    3

  3. C.

    4

  4. D.

    5

Attempted by 7 students.

Show answer & explanation

Correct answer: A

Step-by-Step Solution

To determine if the number 653xy is divisible by 80, we must apply the rules of divisibility. Since 80 = 8 * 10, the number must be divisible by both 8 and 10.

  1. Divisibility by 10: For a number to be divisible by 10, its units digit must be 0. Therefore, y = 0.

  2. Divisibility by 8: For a number to be divisible by 8, its last three digits must be divisible by 8. With y = 0, the last three digits are 3x0. We test values for x:

    • If x = 0: 300 / 8 = 37.5 (No)

    • If x = 1: 310 / 8 = 38.75 (No)

    • If x = 2: 320 / 8 = 40 (Yes)

  3. Conclusion: Since the number 320 is divisible by 8, x must be 2. Given y = 0 and x = 2, we calculate x + y: x + y = 2 + 0 = 2

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