Find the sum of all 3 digit numbers that leave a remainder of 4 when divided by 6

Question

Question

This question was previously asked in

UP Police SI (दरोगा) Official PYP (Held On: 14 Nov 2021 Shift 3)

Answer 1

Given:

3 digit numbers, remainder 4 when divided by 6.

First term (a) = 100

Last term (l) = 994

Common difference (d) = 6

Formula used:

Number of Terms (n) = \(\dfrac{l-a}{d} + 1\)

Sum = \(\dfrac{n}{2} \times (a + l)\)

Calculation:

Number of terms (n):

⇒ n = \(\dfrac{994-100}{6} + 1 = \dfrac{894}{6} + 1\) = 149 + 1 = 150

⇒ Sum = \(\dfrac{150}{2} \times (100 + 994) \)

⇒ Sum = \(75 \times 1094 = 82050\)

∴ Sum = 82050

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