Multiple choice

The average of $8$ numbers is $20$. The average of first two numbers is $\displaystyle 15\frac{1}{2}$ and that of next three is $\displaystyle 21\frac{1}{3}$. If the sixth number be less than the seventh and eighth numbers by $4$ and $7$, respectively, then find the eighth number?

  1. $20$
  2. $22$
  3. $25$
  4. $27$
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C Correct answer
Explanation

Total sum of 8 numbers = 8 * 20 = 160. Sum of first two = 2 * 15.5 = 31. Sum of next three = 3 * 21.33 = 64. Sum of remaining three (6th, 7th, 8th) = 160 - 31 - 64 = 65. Let 6th number be x. Then 7th is x+4 and 8th is x+7. x + (x+4) + (x+7) = 65 => 3x + 11 = 65 => 3x = 54 => x = 18. The 8th number is x + 7 = 18 + 7 = 25.

AI explanation

The total sum of all 8 numbers is 20 times 8, which equals 160. The sum of the first two numbers is 15.5 times 2, equaling 31, and the sum of the next three is 21.33 times 3, equaling 64, making the sum of the first five numbers 95. Let the sixth number be x; the seventh number is x + 4 and the eighth number is x + 7, so their combined sum is 3x + 11. Setting the equation 95 + 3x + 11 = 160 yields 3x = 54, so x = 18; therefore, the eighth number is 18 + 7, which is 25.

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