If the 8-digit number 2074x4y2 is divisible by 88, then the value of (4x + 3y) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 45
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Concept |
Understanding |
Application |
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For divisibility by 88, number should be divisible by 11 and 8 both. |
2074x4y2 is divisible by 88 |
For divisible by 8 last 3 digits of the number (4y2) must be divisible by 8. So, the value of y can be 3 or 7. For divisibility by 11, the difference of the sum of digits at the odd place and the sum of digits at even place must be zero or divisible by 11. So, (2 + 4 + 4 + 0) - (y + x + 7 + 2) = 0 or 11 Now, x + y – 1 = 0 (for y = 3) x + 3 – 1 = 0 x = -2 ……digit cannot be negative And, x + y – 1 = 0 (for y = 7) x = -6 ……digit cannot be negative So, x + y – 1 = 11 x = 5 for y = 7 4x + 3y = 20 + 21 = 41 (not in options) x = 9 for y = 3 We have x = 9 and y = 3 4x + 3y = 36 + 9 = 45 |