Multiple choice

The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?

  1. 8

  2. 5

  3. 2

  4. 4

  5. 3
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B Correct answer
Explanation

Let numbers be a, b, c, d. (a+b+c)/3 = 16 => a+b+c = 48. (b+c+d)/3 = 15 => b+c+d = 45. Subtracting: a-d = 3. Given a+d = 13. Adding: 2a = 16, a = 8. Then d = 13 - 8 = 5.

AI explanation

The sum of the first 3 numbers is 16 multiplied by 3, giving 48. The sum of the last 3 numbers is 15 multiplied by 3, giving 45. Adding these sums gives 93, which counts the middle two numbers twice along with the first and last numbers once. Subtracting the sum of the first and last numbers (13) from 93 gives 80, which is twice the sum of the middle two numbers. Therefore, the sum of all four numbers is 80 plus 13, which equals 93; subtracting the sum of the first three numbers (48) leaves the last number as 5.

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