Multiple choice

The average of fifteen observations is 20. The average of first five observations is 16 and it is 22 for the next seven observations. The thirteenth observation is 2 more than the fourteenth observation, which is 2 more than the fifteenth observation. What is the value of the fifteenth observation?

  1. 7

  2. 15

  3. 20

  4. 25

  5. 45
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C Correct answer
Explanation

Total sum = 15 * 20 = 300. First 5 sum = 5 * 16 = 80. Next 7 sum = 7 * 22 = 154. Sum of last 3 = 300 - 80 - 154 = 66. Let 15th = x, 14th = x+2, 13th = x+4. x + x+2 + x+4 = 66 => 3x + 6 = 66 => 3x = 60 => x = 20.

AI explanation

Using the basic average formula, the sum of all fifteen observations is 15 times 20, which equals 300. The sum of the first twelve observations is 5 times 16 plus 7 times 22, equaling 234. This leaves 66 for the last three observations, and subtracting 66 from 300 confirms this. Let the fifteenth observation be x, making the fourteenth x plus 2 and the thirteenth x plus 4. Their combined sum is 3x plus 6, so setting 3x plus 6 equal to 66 gives 3x equals 60. Therefore, x is 20, which is the value of the fifteenth observation.

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