Find the sum of the numbers between 400 and 500 such that when 8, 12, and 16 divide them, it leaves 5 as remainder in each case.

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NTPC CBT-I (Held On: 4 Jan 2021 Shift 2)

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Answer 1

Calculations:

Numbers are 8, 12 and 16 that must divide numbers between 400 & 500 & get remainder 5

To find the multiple of different numbers, we need to find out the LCM

LCM of 8, 12, 16

8 = 2³, 12 = 2² × 3, 16 = 2⁴

LCM = 2⁴ × 3 = 48

Number pattern = 48k + 5 (Remainder)

Number between 400 & 500

Smallest number = 48 × 9 + 5 = 437

Largest number = 48 × 10 + 5 = 485

So,

Sum of numbers = 437 + 485

⇒ 922

∴ The correct choice is option 1.

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