Find the sum of the numbers between 550 and 700 such that when they are divided by 12 16 and 24 leav...........

Quantitative Aptitude (CPO) LCM, HCF

Find the sum of the numbers between 550 and 700 such that when they are divided by 12, 16 and 24, leave remainder 5 in each

case.

This questions was previously asked in

SSC CPO 9th Nov 2022 Shift 2

1980

1887

1860

1867

To solve this problem, we need to find numbers that give a remainder of 5 when divided by 12, 16, and 24:

- For such numbers, consider `x = 12k + 5 = 16m + 5 = 24n + 5`.

- Simplifying, `x - 5` should be a common multiple of 12, 16, and 24.

- The Least Common Multiple (LCM) of 12, 16, and 24 is 48.

- So, `x - 5 = 48p`, giving `x = 48p + 5`.

Now, we find `x` values in the range 550 to 700:

- `48p + 5 = 550` gives `p = 11.375`, thus `p = 12`.

- `48p + 5 = 700` gives `p = 14.479`, thus `p = 14`.

The numbers are `48*12 + 5 = 581`, `48*13 + 5 = 629`, and `48*14 + 5 = 677`.

Calculate the sum:

$$ 581 + 629 + 677 = 1887 $$

- Option 1: 1980

- Option 2: 1887

- Option 3: 1860

- Option 4: 1867

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