Question : Find the sum of the numbers between 550 and 700 such that when they are divided by 12, 16, and 24, leave the remainder of 5 in each case.
Option 1: 1980
Option 2: 1887
Option 3: 1860
Option 4: 1867
Correct Answer: 1887
Solution :
LCM of 12, 16, and 24 = 48
Multiples of 48 which are between 550 and 700 such that they leave a remainder of 5 are:
48 × 12 + 5 = 581
48 × 13 + 5 = 629
48 × 14 + 5 = 677
$\therefore$ The sum of these numbers = 581 + 629 + 677 = 1887
Hence, the correct answer is 1887.
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