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If the eight-digit number 5a32465b5a32465b is divisible by 8888, then 2a+5b=2a+ 5b =

Solution

✅ Correct Option: 1

Let me solve this carefully:

For divisibility by 8888 (=8×11)(= 8 × 11):

Number must be divisible by both 88 and 1111

1)1) For divisibility by 88:

  • Last three digits (65b)(65b) must be divisible by 88
    • Testing values: b=6b = 6 makes 656656 divisible by 88

2)2) For divisibility by 1111:

  • Difference of sums of alternate digits must be divisible by 1111
    • (5+3+4+5)−(a+2+6+6)=17−14−a(5+3+4+5)-(a+2+6+6)=17-14-a
    • (3−a)(3 - a) must be divisible by 1111
    • Therefore a=3a = 3

So the number is 5332465b5332465b where b=6b = 6

2a+5b=2(3)+5(6)2a + 5b = 2(3) + 5(6)

=6+30= 6 + 30

=36= 36

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