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Average questions with answers

Average questions are almost always about the total in disguise. Once you write the total as average times count, the replacement, inclusion and correction types all become one subtraction. Every walkthrough below goes through the total, which is why none of them needs a formula beyond that one.

Download the PDF — 15 questions with answers

Free, ungated, no email. This is the average questions with answers PDF — the same 15 questions as below, with every worked solution at the back, ready to print.

How to use this set

The 15 questions below are ordered the way an exam block is rather than easiest-first: two gentle openers, then a run of medium, and a hard one every sixth question — 2 of the 15 sit in the hard band. Every question is a averages.

Work each question on paper before you open its solution. The walkthrough is the method itself, step for step, so reading it first turns a practice set into a reading exercise and teaches nothing. If you are stuck on the method rather than on one question, the method guide is a better place to start than the next question: Averages: work through the total.

15 average questions with answers

Every question below was generated by the same engine that mints the ComputePrep daily timed drill, and machine-checked before it reached this page — a multiple-choice question validates its own answer against its own options at generation, and ships only with a walkthrough attached. The walkthrough is the engine's own.

Question 1

Averages — total and mean, no paper.

The average of 4 numbers is 36. What is their total?

  1. 108
  2. 144
  3. 134
  4. 36
  5. 40
Show the worked solution
  1. Total = count × average — the definition, read backwards.
  2. 4 × 36 = 144. Total: 144.

Question 2

Averages — total and mean, no paper.

The average of 7 numbers is 43. What is their total?

  1. 310
  2. 43
  3. 311
  4. 301
  5. 344
Show the worked solution
  1. Total = count × average — the definition, read backwards.
  2. 7 × 43 = 301. Total: 301.

Question 3

Averages — total and mean, no paper.

The average of 8 numbers is 56. The other 7 of them add up to 384. What is the remaining number?

  1. 56
  2. 54
  3. 63
  4. 448
  5. 64
Show the worked solution
  1. All 8 together: 8 × 56 = 448.
  2. Subtract the 7 you were given: 448 − 384 = 64. The remaining number is 64.

Question 4

Averages — total and mean, no paper.

The average of 7 numbers is 16. The other 6 of them add up to 103. What is the remaining number?

  1. 103
  2. 16
  3. 9
  4. 19
  5. 96
Show the worked solution
  1. All 7 together: 7 × 16 = 112.
  2. Subtract the 6 you were given: 112 − 103 = 9. The remaining number is 9.

Question 5

Averages — total and mean, no paper.

The average of 6 numbers is 39. The other 5 of them add up to 192. What is the remaining number?

  1. 39
  2. 192
  3. 42
  4. 234
  5. 32
Show the worked solution
  1. All 6 together: 6 × 39 = 234.
  2. Subtract the 5 you were given: 234 − 192 = 42. The remaining number is 42.

Question 6

Averages — total and mean, no paper.

The average of 6 numbers is 39. When two more numbers are included, the average becomes 41. What is the average of the two new numbers?

  1. 46
  2. 94
  3. 53
  4. 41
  5. 47
Show the worked solution
  1. Total before: 6 × 39 = 234. Total after: 8 × 41 = 328.
  2. The two new numbers add up to 328 − 234 = 94.
  3. Their average: 94 ÷ 2 = 47.

Question 7

Averages — total and mean, no paper.

The average of 4 numbers is 30. What is their total?

  1. 90
  2. 34
  3. 30
  4. 110
  5. 120
Show the worked solution
  1. Total = count × average — the definition, read backwards.
  2. 4 × 30 = 120. Total: 120.

Question 8

Averages — total and mean, no paper.

The average of 8 numbers is 49. What is their total?

  1. 392
  2. 343
  3. 49
  4. 402
  5. 441
Show the worked solution
  1. Total = count × average — the definition, read backwards.
  2. 8 × 49 = 392. Total: 392.

Question 9

Averages — total and mean, no paper.

The average of 6 numbers is 34. The other 5 of them add up to 180. What is the remaining number?

  1. 34
  2. 180
  3. 204
  4. 24
  5. 14
Show the worked solution
  1. All 6 together: 6 × 34 = 204.
  2. Subtract the 5 you were given: 204 − 180 = 24. The remaining number is 24.

Question 10

Averages — total and mean, no paper.

The average of 5 numbers is 38. The other 4 of them add up to 170. What is the remaining number?

  1. 38
  2. 20
  3. 190
  4. 12
  5. 10
Show the worked solution
  1. All 5 together: 5 × 38 = 190.
  2. Subtract the 4 you were given: 190 − 170 = 20. The remaining number is 20.

Question 11

Averages — total and mean, no paper.

The average of 8 numbers is 55. The other 7 of them add up to 375. What is the remaining number?

  1. 57
  2. 55
  3. 50
  4. 56
  5. 65
Show the worked solution
  1. All 8 together: 8 × 55 = 440.
  2. Subtract the 7 you were given: 440 − 375 = 65. The remaining number is 65.

Question 12

Averages — total and mean, no paper.

The average age of 24 students in a class is 12 years. When the teacher's age is included, the average rises by 2 years. What is the teacher's age?

  1. 62
  2. 63
  3. 72
  4. 60
  5. 14
Show the worked solution
  1. Students' total: 24 × 12 = 288.
  2. With the teacher: 25 × 14 = 350.
  3. Teacher's age: 350 − 288 = 62.

Question 13

Averages — total and mean, no paper.

The average of 6 numbers is 21. What is their total?

  1. 136
  2. 126
  3. 21
  4. 130
  5. 147
Show the worked solution
  1. Total = count × average — the definition, read backwards.
  2. 6 × 21 = 126. Total: 126.

Question 14

Averages — total and mean, no paper.

The average of 4 numbers is 24. What is their total?

  1. 97
  2. 120
  3. 106
  4. 24
  5. 96
Show the worked solution
  1. Total = count × average — the definition, read backwards.
  2. 4 × 24 = 96. Total: 96.

Question 15

Averages — total and mean, no paper.

The average of 9 numbers is 25. The other 8 of them add up to 188. What is the remaining number?

  1. 25
  2. 28
  3. 27
  4. 33
  5. 37
Show the worked solution
  1. All 9 together: 9 × 25 = 225.
  2. Subtract the 8 you were given: 225 − 188 = 37. The remaining number is 37.
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Where these questions come from

Most free practice for this topic is a scanned upload or a blog quiz, and neither can tell you a question has exactly one answer. That is the one thing this set can promise: it is minted, not typed. The engine behind it serves ComputePrep's daily timed drill, so the questions here are the same shape as the ones a live round would give you — and there is an unlimited supply of them, which is why this page can be regenerated rather than padded.

If you want the method rather than more questions, Averages: work through the total covers the approach, the traps and a worked table. This page and that one deliberately answer different questions: that one is how do I solve these, this one is give me average questions with the answers.

FAQ

What is the fastest way to handle a replacement question?

Use the change in total. If the average of eleven players rises by two when one is replaced, the total rose by twenty-two, so the new player scores twenty-two more than the one who left. No individual score is ever needed.

How do I find a wrongly-recorded value?

The difference in totals is the difference in that one value. If a corrected average shifts by 0.5 across twenty entries, the total shifted by ten, so the misrecorded figure was ten away from the true one — in whichever direction the average moved.

What is weighted average and when does it appear?

When two groups of unequal size combine, the overall average leans towards the larger group: (n₁a₁ + n₂a₂)/(n₁ + n₂). It appears constantly in data interpretation, where averaging two column averages directly is one of the most common errors on the paper.

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