Multiple choice

The average of 5 numbers is 150. The largest number exceeds the smallest number by 100. If the five numbers are in arithmetic progression, find the smallest number.

  1. 100

  2. 150

  3. 170

  4. 135
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A Correct answer
Explanation

Let the 5 numbers be a-2d, a-d, a, a+d, a+2d. Sum = 5a = 5 * 150 = 750, so a = 150. Largest is a+2d, smallest is a-2d. Difference = 4d = 100, so d = 25. Smallest number = a - 2d = 150 - 50 = 100.

AI explanation

For an arithmetic progression of 5 numbers, the average equals the middle term, making the third term 150. The difference between the largest and smallest numbers is 100, meaning there are 4 gaps of 25 each between the consecutive terms. The smallest number is the middle term minus two gaps, calculated as 150 minus (2 times 25), resulting in 100.

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