Quantitative Aptitude

Averages

1,527 Questions
All Basic average and reverse calculation 405 Adding or removing an observation 342 Weighted and combined averages 320 Replacement and correction of a recorded value 233 Ratio shortcut for two-group mixtures 111 Equal-distance average speed 59 Age, score, weight, and spending applications 32 Consecutive terms and arithmetic progressions 25

Averages Questions

Multiple choice

The average weight of $14$ students was calculated as $71$. But it was later found that the weight of one student had been wrongly entered as $42$ instead of $56$ and of another as $74$ instead of $32$. The correct average is
  1. $75$
  2. $80$
  3. $68$
  4. $69$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The initial sum was 14 * 71 = 994. The errors were: 42 was written instead of 56 (add 14) and 74 was written instead of 32 (subtract 42). The net change is 14 - 42 = -28. The correct sum is 994 - 28 = 966. The correct average is 966 / 14 = 69.

Multiple choice

A total of $22$ men and $26$ women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly $35$ years. If the average age of the men was exactly $38$ years, which of the following was closest to the average age, in years of the women?
  1. $31$
  2. $31.5$
  3. $32$
  4. $32.5$
  5. $33$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total adults = 22 + 26 = 48. Total age = 48 * 35 = 1680. Men's total age = 22 * 38 = 836. Women's total age = 1680 - 836 = 844. Women's average = 844 / 26 = 32.46, which is closest to 32.5.

Multiple choice

In a class of 20 students, 10 boys brought 11 books each and 6 girls brought 13 books each. Remaining students brought at least one book each and no two students brought the same number of books. If the average number of books brought in the class is a positive integer then what could be the total number of books brought by the remaining students?

  1. 12

  2. 16

  3. 14

  4. 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total students = 20. 10 boys brought 110 books. 6 girls brought 78 books. Total = 188. Remaining 4 students brought at least one book each, all distinct. Let the number of books be x1, x2, x3, x4. Sum = S. Total books = 188 + S. Average = (188 + S) / 20. For this to be an integer, 188 + S must be a multiple of 20. S must be 12, 32, 52... Since x1, x2, x3, x4 are distinct and >= 1, the minimum sum is 1+2+3+4 = 10. 12 is a possible sum.

Multiple choice

Working for $10$ months as a teacher in High School, David earned $\$3,200$ per month from September to June. He then undertook a job as a barista at a cafe, where he earned $\$2,000$ per month during July and August. Find the average monthly pay of David for the $12$ months.
  1. $\$2400$
  2. $\$2500$
  3. $\$2600$
  4. $\$2800$
  5. $\$3000$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Total earnings = (10 months * 3200) + (2 months * 2000) = 32000 + 4000 = 36000. Average monthly pay = 36000 / 12 = 3000.