Multiple choice

The average of ten consecutive numbers is n. If the next ten numbers are also included, the average increases by 50%. What is the value of n?

  1. 5

  2. 10

  3. 15

  4. 20

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the numbers be x, x+1, ..., x+9. Average n = x + 4.5. If 10 more numbers are added (x+10 to x+19), the new average is (sum of 20 numbers) / 20 = (20x + 190) / 20 = x + 9.5. Given x + 9.5 = 1.5 * n = 1.5 * (x + 4.5) = 1.5x + 6.75. So 0.5x = 2.75 => x = 5.5. n = 5.5 + 4.5 = 10.

AI explanation

Let the ten consecutive numbers be x, x+1, ..., x+9, so their average n is x+4.5. The sum of the next ten numbers from x+10 to x+19 is 100 more than the sum of the first ten. The combined average of all 20 numbers is x+9.5, which is 5 greater than the original average, meaning the average increases by 5. Since this increase is a 50 percent increase, 0.5 times n equals 5, making n equal to 10.

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