Question
Download Solution PDFFind 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculations:
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.
Last updated on Jul 10, 2025
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