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If the seven digit number 3x6349y is divisible by 88, then what will be the value of (2x + 3y)?
28
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35
To determine the divisibility of 3x6349y by 88, follow these steps:
- Divisibility by 88: A number is divisible by 88 if it's divisible by both 8 and 11.
- Check divisibility by 8: The last three digits, 49y, must be divisible by 8.
- Try y = 6: 496 is divisible by 8 (since 496 ÷ 8 = 62).
- Check divisibility by 11: The alternating sum of the digits (3 - x + 6 - 3 + 4 - 9 + 6) must be divisible by 11.
- Simplify to (7 - x). For 7 - x to be divisible by 11:
- x = 6, because (7 - 6 = 1), and (1 - 11 = -10), the absolute difference should be divisible by 11, suggesting to test further for valid combinations.
- Validate: Verify x = 6 and y = 8 makes both divisible checks true: 7 - 6 = 1, and 49y forms divisible by 8.
- Calculate (2x + 3y): Substitute x = 6 and y = 8.
- 2×6+3×8=12+24=36.
Here's the correct statement:
- Correct Answer: None of the provided options match as 36. Current valid answer based on conditions is 36.
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