Sum of four consecutive multiples of 3 is 78. The largest of these number is:

Question

Question

This question was previously asked in

NTPC CBT-I (Held On: 9 Jan 2021 Shift 1)

Answer 1

Given:

Sum of four consecutive multiples of 3 = 78

Calculation:

Let the first multiple of 3 be = 3a

Likewise, second multiple of 3 be = 3(a + 1)

⇒ Third multiple of 3 be = 3(a + 2)

⇒ Fourth multiple of 3 be = 3(a + 3)

3a +3(a + 1) + 3(a + 2) + 3(a + 3) = 78

⇒ 3a + 3a + 3 + 3a + 6 + 3a + 9 = 78

⇒ 12a + 18 = 78

⇒ 12a = 78 - 18 = 60

⇒ a = 60/12 = 5

∴ The largest multiple of 3 = 3(a + 3) = 3 × (5 + 3) = 24

Shortcut Trick Calculation:

Average of 4 consecutive multiples of 3 = 78/4 = 19.5

So, the number should be 18 and 21.

So, the Series will be

15, 18, 21, 24

∴ The largest multiple is 24.

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