JIPMAT 2023 (QA) - If the eight-digit number 5a32465b is divisible by 88, then 2a+ 5b = | PYQs + Solutions

JIPMAT 2023

Number System

Divisibility Rules

Conceptual

If the eight-digit number $5a32465b$ is divisible by $88$ , then $2a+ 5b =$

Correct Option: 1

Let me solve this carefully:

For divisibility by

88

(= 8 × 11)

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Number must be divisible by both

8

and

11

1)

For divisibility by

8

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- Last three digits

(65b)

must be divisible by

8

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- Testing values:

b = 6

makes

656

divisible by

8

2)

For divisibility by

11

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- Difference of sums of alternate digits must be divisible by

11

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(5+3+4+5)-(a+2+6+6)=17-14-a

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(3 - a)

must be divisible by

11

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- Therefore

a = 3

So the number is

5332465b

where

b = 6

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

= 6 + 30

= 36