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If the average of the 3 digit numbers 335, 2x5, x35, 63x and 406 is 411, then what will be the average of x - 1, x - 3, x + 3 and  x + 5 ?

If the average of the 3 digit numbers 335, 2x5, x35, 63x and 406 is 411, then what will be the average of x - 1, x - 3, x + 3 and  x + 5 ? Correct Answer 5

Shortcut TrickSolve it by unit digit.

Unit digit of average is 1. The unit digit of the sum = 1 × 5 = 5

5 + 5 + 5 + x + 6 = 5

⇒ Unit digit of 21 + x = 5

⇒ 1 + x = 5

⇒ x = 4

Then,

Total sum of x - 1, x - 3, x + 3 and  x + 5 = (4 - 1) + (4 - 3) + (4 + 3) + (4 + 5) = 3 + 1 + 7 + 9 = 20

∴ Average of x - 1, x - 3, x + 3 and  x + 5 = 20/4 = 5

Traditional method:

Given:

Average of 335, 2x5, x35, 63x and 406 = 411

Formula:

Average = (Sum of terms)/(Number of terms)

Calculation:

Total of 335, 2x5, x35, 63x and 406 numbers = 411 × 5 = 2055

⇒ 335 + 2x5 + x35 + 63x + 406 = 2055

⇒ 300 + 30 + 5 + 200 + 10x + 5 + 100x + 30 + 5 + 600 + 30 + x + 400 + 0 + 6 = 2055

⇒ 1611 + 111x = 2055

⇒ x = 4

Then,

Total sum of x - 1, x - 3, x + 3 and  x + 5 = (4 - 1) + (4 - 3) + (4 + 3) + (4 + 5) = 3 + 1 + 7 + 9 = 20

∴ Average of x - 1, x - 3, x + 3 and  x + 5 = 20/4 = 5

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