Find the sum of the numbers between 400 and 500 such that when 8, 12, and 16 divides them, it leaves 5 as remainder in each case.
Solution:
Numbers are 8, 12 and 16 that must divide numbers between 400 and 500 and give 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 = 48k + 5
Putting the values of k possible numbers between 400 and 500 are
Number = 48 × 9 + 5 = 437
Number = 48 × 10 + 5 = 485
Now,
Sum of numbers = 437 + 485
=> 922
Therefore, option (b) is the correct answer.
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