SSAT Middle Level Quiz: Average Problems
20 questions · exam conditions
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Average ProblemsQuestion 1 of 20

A student tracks allowance for four weeks: $10, $15, $12, and $13. The student adds them as 10+10+15+12+12+13 to get the total. Next, the student divides by 4 because there are four weeks. The result is the average allowance each week. Find the average allowance received.

The average allowance is $12.5
The average allowance is $12.4
The average allowance is $15
The average allowance is $10
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SSAT Middle Level Quiz

SSAT Middle Level Quiz: Average Problems

Practice Average Problems in SSAT Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Average Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for SSAT Middle Level.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A student tracks allowance for four weeks: $10, $15, $12, and $13. The student adds them as 10+10+15+12+12+13 to get the total. Next, the student divides by 4 because there are four weeks. The result is the average allowance each week. Find the average allowance received.

  1. The average allowance is $12.5 (correct answer)
  2. The average allowance is $12.4
  3. The average allowance is $15
  4. The average allowance is $10
Explanation: This question tests middle school math skills in solving average problems using sums and counts. To find the average, add all the numbers together and divide the sum by the number of items. In this problem, you are given the numbers $10, $15, $12, and $13 and need to calculate their average. The correct answer is choice A because it accurately reflects the sum of 50 divided by 4 which equals 12.5. Choice B is incorrect because it involves a common error of rounding down incorrectly. To help students master this skill, encourage them to carefully count the number of items, double-check their sums, and ensure they divide by the correct count. Practice with varied scenarios to build confidence in identifying and calculating averages.

Question 2

A teacher lists five quiz scores for a small group: 78, 85, 92, 88, and 81. The teacher finds the sum of all five scores. Next, the teacher divides the sum by 5 to get the mean. The students want the single number that represents their average. What is the average of the given numbers?

  1. The average is 84.8 (correct answer)
  2. The average is 85.6
  3. The average is 85
  4. The average is 88
Explanation: This question tests middle school math skills in solving average problems using sums and counts. To find the average, add all the numbers together and divide the sum by the number of items. In this problem, you are given the numbers 78, 85, 92, 88, and 81 and need to calculate their average. The correct answer is choice A because it accurately reflects the sum of 424 divided by 5 which equals 84.8. Choice C is incorrect because it involves a common error of rounding to the nearest whole number. To help students master this skill, encourage them to carefully count the number of items, double-check their sums, and ensure they divide by the correct count. Practice with varied scenarios to build confidence in identifying and calculating averages.

Question 3

A coach tracks five practice scores: 78, 85, 92, 88, and 81. The coach adds all five scores to find the total points. Then the coach divides by 5 because there are five scores. The team uses this number as the average performance score. What is the average of the given numbers?

  1. The average is 84.8 (correct answer)
  2. The average is 86
  3. The average is 85
  4. The average is 88
Explanation: This question tests middle school math skills in solving average problems using sums and counts. To find the average, add all the numbers together and divide the sum by the number of items. In this problem, you are given the numbers 78, 85, 92, 88, and 81 and need to calculate their average. The correct answer is choice A because it accurately reflects the sum of 424 divided by 5 which equals 84.8. Choice B is incorrect because it involves a common error of misadding the numbers or dividing by the wrong count. To help students master this skill, encourage them to carefully count the number of items, double-check their sums, and ensure they divide by the correct count. Practice with varied scenarios to build confidence in identifying and calculating averages.

Question 4

A family drives during four parts of a trip at speeds of 60 mph, 55 mph, 70 mph, and 65 mph. They add the four speeds to find the total of the recorded values. Then they divide by 4 because there are four parts listed. This gives the average of the speeds they recorded. What is the average speed over the entire trip?

  1. The average speed is 62.5 mph (correct answer)
  2. The average speed is 65 mph
  3. The average speed is 250 mph
  4. The average speed is 60 mph
Explanation: This question tests middle school math skills in solving average problems using sums and counts. To find the average, add all the numbers together and divide the sum by the number of items. In this problem, you are given the numbers 60 mph, 55 mph, 70 mph, and 65 mph and need to calculate their average. The correct answer is choice A because it accurately reflects the sum of 250 divided by 4 which equals 62.5. Choice C is incorrect because it involves a common error of using the sum instead of dividing by the count. To help students master this skill, encourage them to carefully count the number of items, double-check their sums, and ensure they divide by the correct count. Practice with varied scenarios to build confidence in identifying and calculating averages.

Question 5

A student lists four travel speeds: 60 mph, 55 mph, 70 mph, and 65 mph. The student adds them to get a total of 250 mph. Then the student divides by 4 to find the mean of the listed speeds. This mean is the average speed for those parts. What is the average speed over the entire trip?

  1. The average speed is 62.5 mph (correct answer)
  2. The average speed is 62 mph
  3. The average speed is 55 mph
  4. The average speed is 65 mph
Explanation: This question tests middle school math skills in solving average problems using sums and counts. To find the average, add all the numbers together and divide the sum by the number of items. In this problem, you are given the numbers 60 mph, 55 mph, 70 mph, and 65 mph and need to calculate their average. The correct answer is choice A because it accurately reflects the sum of 250 divided by 4 which equals 62.5. Choice B is incorrect because it involves a common error of rounding down to the nearest whole number. To help students master this skill, encourage them to carefully count the number of items, double-check their sums, and ensure they divide by the correct count. Practice with varied scenarios to build confidence in identifying and calculating averages.

Question 6

A weather app records daily temperatures for seven days: 70°F, 72°F, 68°F, 75°F, 73°F, 71°F, and 69°F. A student adds all seven temperatures to find the total. Then the student divides by 7 because there are seven days. This gives the average temperature for the week. Determine the average temperature for the week.

  1. The average temperature is 71°F
  2. The average temperature is 72°F
  3. The average temperature is 71.1°F (correct answer)
  4. The average temperature is 498°F
Explanation: This question tests middle school math skills in solving average problems using sums and counts. To find the average, add all the numbers together and divide the sum by the number of items. In this problem, you are given the numbers 70°F, 72°F, 68°F, 75°F, 73°F, 71°F, and 69°F and need to calculate their average. The correct answer is choice C because it accurately reflects the sum of 498 divided by 7 which equals 71.1. Choice D is incorrect because it involves a common error of using the sum instead of dividing by the count. To help students master this skill, encourage them to carefully count the number of items, double-check their sums, and ensure they divide by the correct count. Practice with varied scenarios to build confidence in identifying and calculating averages.

Question 7

Five students earn these scores on a science test: 78, 85, 92, 88, and 81. Their teacher adds the scores to get a total of points. The teacher divides by 5 to share the total equally across students. This gives the class average for the test. Based on the information provided, calculate the average score.

  1. The average score is 85
  2. The average score is 84.8 (correct answer)
  3. The average score is 81
  4. The average score is 424
Explanation: This question tests middle school math skills in solving average problems using sums and counts. To find the average, add all the numbers together and divide the sum by the number of items. In this problem, you are given the numbers 78, 85, 92, 88, and 81 and need to calculate their average. The correct answer is choice B because it accurately reflects the sum of 424 divided by 5 which equals 84.8. Choice D is incorrect because it involves a common error of using the sum instead of dividing by the count. To help students master this skill, encourage them to carefully count the number of items, double-check their sums, and ensure they divide by the correct count. Practice with varied scenarios to build confidence in identifying and calculating averages.

Question 8

Over four weeks, a student earns allowance amounts of $10, $15, $12, and $13. The student adds all four numbers to get the total allowance. Then the student divides the total by 4 to find the average per week. The student writes the average in dollars and cents. Find the average allowance received.

  1. The average allowance is $12.5 (correct answer)
  2. The average allowance is $12.0
  3. The average allowance is $13
  4. The average allowance is $50
Explanation: This question tests middle school math skills in solving average problems using sums and counts. To find the average, add all the numbers together and divide the sum by the number of items. In this problem, you are given the numbers $10, $15, $12, and $13 and need to calculate their average. The correct answer is choice A because it accurately reflects the sum of 50 divided by 4 which equals 12.5. Choice D is incorrect because it involves a common error of using the sum instead of dividing by the count. To help students master this skill, encourage them to carefully count the number of items, double-check their sums, and ensure they divide by the correct count. Practice with varied scenarios to build confidence in identifying and calculating averages.

Question 9

Jake's average score on his first 4 tests is 88. His average score on his first 6 tests is 85. What is his average score on just the 5th and 6th tests?

  1. 80
  2. 82
  3. 79 (correct answer)
  4. 81
  5. 78
Explanation: When you encounter average problems involving different groups of tests or scores, think systematically about what information you have and what you need to find. The key is working with totals rather than just averages. Start by finding the total points from the given averages. Jake's average on his first 4 tests is 88, so his total points for those tests is 4×88=3524 \times 88 = 352. His average on all 6 tests is 85, so his total for all 6 tests is 6×85=5106 \times 85 = 510. To find the combined score on just the 5th and 6th tests, subtract the first four tests' total from the six tests' total: 510−352=158510 - 352 = 158. Since this represents the sum of two test scores, the average is 158÷2=79158 \div 2 = 79. Looking at the wrong answers: Choice A (80) is close but represents a common calculation error where students might round incorrectly or make an arithmetic mistake. Choice B (82) could result from incorrectly calculating the difference between the two given averages (88 - 85 = 3, then perhaps adding this to 79). Choice D (81) might come from averaging the two given averages incorrectly: (88+85)÷2=86.5(88 + 85) \div 2 = 86.5, then making further errors. The correct answer is C (79). Strategy tip: Always convert averages to totals first in multi-group problems. This makes the arithmetic clearer and helps you avoid the trap of trying to work directly with averages, which often leads to incorrect shortcuts.

Question 10

A store sells 3 items on Monday with an average price of $15, and 5 items on Tuesday with an average price of $12. What is the average price of all items sold over the two days?

  1. $13.50
  2. $12.75
  3. $13.00
  4. $13.25
  5. $13.13 (correct answer)
Explanation: When you encounter weighted average problems, remember that you can't simply average the averages when the groups have different sizes. You need to find the total value and divide by the total number of items. To find the correct average price, start by calculating the total revenue from each day. On Monday, 3 items at $15 average means $3 \times 15 = \45 total. On Tuesday, 5 items at $12 average means $5 \times 12 = \60total.Thecombinedrevenueistotal. The combined revenue is$45 + $60 = $105forfor3 + 5 = 8totalitems.Therefore,theaveragepriceistotal items. Therefore, the average price is\frac{$105}{8} = $13.125$$, which rounds to $13.13. However, since the correct answer is listed as E, there appears to be an error in the provided options. Looking at the given choices: Choice A (13.50)incorrectlyweightsMonday′ssalestooheavily.ChoiceB(13.50) incorrectly weights Monday's sales too heavily. Choice B (12.75) falls closer to Tuesday's average, suggesting an error in calculation or improper weighting. Choice C (13.00)isclosebutrepresentsroundedthinkingratherthanprecisecalculation.ChoiceD(13.00) is close but represents rounded thinking rather than precise calculation. Choice D (13.25) overestimates the average, possibly from computational errors. None of these match the calculated $13.125, which is why E must be correct—it likely represents "none of the above" or the actual calculated value not shown in the visible options. Remember: with weighted averages, always multiply each average by its frequency, sum those products, then divide by the total frequency. Don't just average the given averages unless the groups are equal in size.

Question 11

In a group of 12 people, 4 people are 25 years old, 6 people are 30 years old, and 2 people are 40 years old. If 2 more people join the group, both aged 35, what is the new average age?

  1. 30.0 years
  2. 31.4 years
  3. 30.7 years (correct answer)
  4. 29.6 years
  5. 32.1 years
Explanation: When you encounter average problems where new data points are added to a group, you need to recalculate using all the data, not adjust the existing average. First, find the total age of the original 12 people. You have 4 people at 25 years old (4 × 25 = 100), 6 people at 30 years old (6 × 30 = 180), and 2 people at 40 years old (2 × 40 = 80). The total age is 100 + 180 + 80 = 360 years. When 2 more people join, both aged 35, you add 2 × 35 = 70 years to your total. The new total age becomes 360 + 70 = 430 years, and you now have 12 + 2 = 14 people total. The new average age is 43014=30.714...\frac{430}{14} = 30.714... years, which rounds to 30.7 years. Choice (A) 30.0 years is the original average age of the initial group (360 ÷ 12 = 30), but this ignores the two new people entirely. Choice (B) 31.4 years might result from incorrectly calculating the weighted contributions or making an arithmetic error. Choice (D) 29.6 years is too low and could come from miscalculating the original total or the final division. Remember that when new data points are added to find a new average, always recalculate from scratch using the total of all values divided by the new count. Don't try to "adjust" the existing average—this often leads to errors on SSAT problems.

Question 12

Sarah bowled 4 games with scores of 120, 135, 110, and 115. In her 5th game, she wants her overall average to be at least 125. What is the minimum score she needs in the 5th game?

  1. 145 (correct answer)
  2. 140
  3. 150
  4. 155
  5. 135
Explanation: When you encounter average problems like this, you're working with the relationship between sum, count, and average. The key insight is that if you know the desired average and the number of values, you can find the required total sum. To find the minimum score Sarah needs, start by calculating what her total points must be across all 5 games. If she wants an average of at least 125 over 5 games, her total points must be at least 125×5=625125 \times 5 = 625 points. Next, find her current total from the first 4 games: 120+135+110+115=480120 + 135 + 110 + 115 = 480 points. Therefore, her 5th game score must be at least 625−480=145625 - 480 = 145 points to achieve her goal. Looking at the wrong answers: Choice B (140) falls short because 480+140=620480 + 140 = 620 total points, giving an average of 620÷5=124620 ÷ 5 = 124, which doesn't meet her minimum requirement of 125. Choices C (150) and D (155) would certainly work since they exceed the minimum, but the question asks for the minimum score needed, making these unnecessarily high. The answer is A) 145. Strategy tip: In minimum/maximum average problems, always set up the equation using the target average times the number of values to find the required total, then subtract what you already have. This systematic approach prevents calculation errors and ensures you find the exact minimum rather than just any score that works.

Question 13

A restaurant's lunch sales for one week were: Monday $240, Tuesday $180, Wednesday $220, Thursday $200, Friday $280, Saturday $350, and Sunday $290. What was the average daily sales amount?

  1. $251.43 (correct answer)
  2. $245.71
  3. $252.86
  4. $248.57
  5. $250.00
Explanation: When you encounter an "average" question, you're being tested on your ability to find the mean of a data set. To find the average, you need to add up all the values and divide by the number of items. Let's work through this step by step. First, add up all seven days of sales: $240 + $180 + $220 + $200 + $280 + $350 + $290 = $1,760. Then divide this total by the number of days: $17607=251.428...\frac{1760}{7} = 251.428... $ Rounding to two decimal places gives us $251.43, which is answer choice A. Now let's see why the other answers are wrong. Choice B ($245.71) would result from a calculation error, likely from adding the numbers incorrectly and getting a sum of $1,720 instead of 1,760.ChoiceC(1,760. Choice C (252.86) represents another addition error, probably getting 1,770asthesum.ChoiceD(1,770 as the sum. Choice D (248.57) could come from miscounting the number of days or making an error in the division process. The key trap on average problems is arithmetic mistakes under time pressure. Always double-check your addition, especially when dealing with multiple numbers. A quick way to verify: your answer should fall somewhere within the range of the given values, and it should be closer to the middle values than the extremes. Here, $251.43 makes sense because most daily sales were in the $200-$290 range. Remember to organize your work clearly and add numbers systematically to avoid careless errors.

Question 14

In a math class, 15 students scored an average of 85 on a test, and 10 students scored an average of 92 on the same test. What is the overall average score for all 25 students?

  1. 88.5
  2. 87.8 (correct answer)
  3. 88.0
  4. 87.4
  5. 89.2
Explanation: When you encounter weighted average problems, you're dealing with groups of different sizes that each have their own average. The key insight is that larger groups have more influence on the overall average than smaller groups. To find the overall average, you need to calculate the total points earned by all students, then divide by the total number of students. Start by finding the total points for each group: the 15 students averaging 85 earned 15×85=1,27515 \times 85 = 1,275 total points, while the 10 students averaging 92 earned 10×92=92010 \times 92 = 920 total points. The combined total is 1,275+920=2,1951,275 + 920 = 2,195 points earned by all 25 students. Therefore, the overall average is 2,19525=87.8\frac{2,195}{25} = 87.8. Choice A (88.5) represents the trap of simply averaging the two given averages: 85+922=88.5\frac{85 + 92}{2} = 88.5. This ignores the fact that the groups have different sizes. Choice C (88.0) might result from rounding errors or similar miscalculations. Choice D (87.4) could come from computational mistakes when handling the weighted calculation. Strategy tip: On weighted average problems, never just average the averages unless the groups are the same size. Always calculate total points (or total whatever is being measured) for each group first, then find the overall average. Remember that the final answer should be closer to the average of the larger group—here, 87.8 is closer to 85 than to 92, which makes sense since the group of 15 students is larger.

Question 15

Tom's quiz scores are 78, 82, 85, and 91. If he drops his lowest score, what is his new average?

  1. 86 (correct answer)
  2. 84.7
  3. 85.3
  4. 86.7
  5. 85.0
Explanation: When you see a question asking about a "new average" after dropping scores, you're dealing with mean calculations where the dataset changes. To find Tom's new average, first identify his scores and determine which one to drop. His scores are 78, 82, 85, and 91. The lowest score is 78, so you'll remove that from consideration. The remaining scores are 82, 85, and 91. To calculate the average, add these three scores and divide by 3: 82+85+913=2583=86\frac{82 + 85 + 91}{3} = \frac{258}{3} = 86 This confirms that choice A) 86 is correct. Let's examine why the other answers are wrong. Choice B) 84.7 would result from incorrectly averaging all four original scores: 78+82+85+914=84\frac{78 + 82 + 85 + 91}{4} = 84, but this doesn't account for dropping the lowest score. Choice C) 85.3 appears to be a calculation error, possibly from adding incorrectly or using the wrong divisor. Choice D) 86.7 is close to the correct answer but represents a computational mistake—perhaps adding an extra point somewhere in the calculation. Remember that "dropping the lowest score" problems require two steps: identify what to remove, then recalculate with the remaining values. Always double-check that you're dividing by the correct number of remaining scores, not the original count. This type of question tests both your ability to follow directions and perform accurate arithmetic under time pressure.

Question 16

The average weight of 8 packages is 12.5 pounds. If 3 packages weighing 10 pounds each are removed, what is the average weight of the remaining packages?

  1. 14.0 pounds (correct answer)
  2. 13.5 pounds
  3. 15.0 pounds
  4. 14.8 pounds
  5. 13.8 pounds
Explanation: When you encounter average problems involving changes to a group, you need to work with total weights rather than jumping straight to the new average. Start by finding the total weight of all 8 packages: 8×12.5=1008 \times 12.5 = 100 pounds. Now you're removing 3 packages that weigh 10 pounds each, so you're taking away 3×10=303 \times 10 = 30 pounds. This leaves you with 100−30=70100 - 30 = 70 pounds remaining, distributed among 8−3=58 - 3 = 5 packages. The new average is 70÷5=14.070 \div 5 = 14.0 pounds. Looking at the wrong answers: Choice B (13.5 pounds) likely comes from incorrectly averaging the original average with the weight of removed packages: 12.5+102=11.25\frac{12.5 + 10}{2} = 11.25, though this doesn't match exactly—it represents muddled thinking about combining averages. Choice C (15.0 pounds) might result from simply adding something to the original average without proper calculation. Choice D (14.8 pounds) could come from miscalculating the remaining total or number of packages, perhaps using 4 packages instead of 5 in the denominator. The key insight is that removing lighter packages (10 pounds each) from a group with a higher average (12.5 pounds) will increase the remaining average, since you're left with the heavier packages. Strategy tip: Always convert averages to totals first, then adjust the total and count separately before calculating the new average. This prevents the common mistake of trying to manipulate averages directly.

Question 17

During basketball practice, Alex made 12 free throws out of 20 attempts on Monday, 8 out of 15 attempts on Tuesday, and 15 out of 18 attempts on Wednesday. What was his overall free throw percentage for the three days?

  1. 66.0% (correct answer)
  2. 65.1%
  3. 68.2%
  4. 67.5%
  5. 64.8%
Explanation: When you encounter percentage problems involving multiple events, remember that you need to find the overall rate, not the average of individual rates. This means combining all successes and all attempts first. To find Alex's overall free throw percentage, add up all his successful shots and all his attempts across the three days. On Monday: 12 out of 20. On Tuesday: 8 out of 15. On Wednesday: 15 out of 18. Total successful free throws: 12+8+15=3512 + 8 + 15 = 35 Total attempts: 20+15+18=5320 + 15 + 18 = 53 Overall percentage: 3553=0.660...=66.0%\frac{35}{53} = 0.660... = 66.0\% This confirms that A) 66.0% is correct. Now let's see why the other answers are wrong. B) 65.1% likely comes from a calculation error, perhaps misadding the totals. C) 68.2% and D) 67.5% represent common traps where students incorrectly average the daily percentages instead of using the total shots and attempts. If you calculated the daily percentages (60%, 53.3%, 83.3%) and averaged them, you'd get about 65.5%, which is close to some wrong answers but not the correct approach. This method fails because it doesn't account for the different number of attempts each day. Strategy tip: For combined percentage problems, always use total successes divided by total attempts. Never average individual percentages unless each group has the same size—the varying number of attempts on each day makes simple averaging incorrect.

Question 18

Jenny's science test scores are 88, 92, 85, 90, and 95. If her teacher drops the lowest score and counts the remaining four scores equally, what is Jenny's new average?

  1. 91.3 (correct answer)
  2. 91.0
  3. 90.8
  4. 91.8
  5. 90.5
Explanation: When you encounter a problem about dropping scores and calculating a new average, you need to systematically identify which scores to keep and then apply the average formula. First, identify Jenny's scores: 88, 92, 85, 90, and 95. Since the teacher drops the lowest score, you need to find which score is smallest. Arranging them in order: 85, 88, 90, 92, 95. The lowest score is 85, so this gets dropped. The remaining four scores are: 88, 92, 90, and 95. To find the new average, add these scores and divide by 4: Average=88+92+90+954=3654=91.25\text{Average} = \frac{88 + 92 + 90 + 95}{4} = \frac{365}{4} = 91.25 Since 91.25 rounds to 91.3, the answer is A) 91.3. Looking at the wrong answers: B) 91.0 might result from rounding 91.25 down incorrectly or making an arithmetic error in addition. C) 90.8 could come from including the dropped score of 85 in your calculation by mistake, giving you 4505=90\frac{450}{5} = 90, then making a small error. D) 91.8 might result from calculation errors when adding the four remaining scores. Strategy tip: Always double-check that you've correctly identified which score to drop, and verify your arithmetic when calculating the sum. When dealing with averages after dropping scores, make sure you're dividing by the correct number of remaining items, not the original count.

Question 19

Marcus saved money over 6 months with the following amounts: January $45, February $62, March $38, April $71, May $55, and June $49. He wants to save the same total amount over the next 6 months, but spread it evenly. How much should he save each month?

  1. $53.33 (correct answer)
  2. $50.00
  3. $55.00
  4. $48.00
  5. $60.00
Explanation: This question tests your ability to work with averages and equal distribution of amounts. When you see a problem asking to "spread evenly" or distribute equally, you need to find the total first, then divide by the number of parts. To find how much Marcus should save each month, you first need to calculate his total savings from the six months: $45 + $62 + $38 + $71 + $55 + $49 = $320. Since he wants to save this same total amount over the next 6 months but spread it evenly, you divide the total by 6: $3206=53.33\frac{320}{6} = 53.33 $ Let's examine why the other answers are incorrect. Answer B ($50.00) is tempting because it's a round number, but it would only give Marcus 300totalover6months(300 total over 6 months (50 × 6 = $300), which is 20shortofhisgoal.AnswerC(20 short of his goal. Answer C (55.00) might seem reasonable since it's close to some of his monthly amounts, but $55 × 6 = $330, which exceeds his target by 10.AnswerD(10. Answer D (48.00) would only total 288over6months(288 over 6 months (48 × 6 = $288), falling $32 short of his $320 goal. Remember that average problems often involve two steps: find the total, then divide by the number of items. Don't let round numbers like $50 or $55 distract you from doing the actual calculation. Always verify your answer by multiplying back—the monthly amount times 6 should equal the original total of $320.

Question 20

In a class of 24 students, the average score on a quiz was 82. If 8 students scored 90 and the remaining students all scored the same, what did each of the remaining students score?

  1. 78 (correct answer)
  2. 76
  3. 74
  4. 80
  5. 75
Explanation: When you encounter average problems involving groups with different scores, you need to use the total points to work backwards and find unknown values. Start by finding the total points for all students: 24 students×82 average=1,968 total points24 \text{ students} \times 82 \text{ average} = 1,968 \text{ total points} Next, calculate the points from the high-scoring group: 8 students×90 points each=720 points8 \text{ students} \times 90 \text{ points each} = 720 \text{ points} The remaining students contributed: 1,968−720=1,248 points1,968 - 720 = 1,248 \text{ points} Since there are 24−8=1624 - 8 = 16 remaining students who all scored the same, each scored: 1,248÷16=781,248 ÷ 16 = 78 This confirms answer A is correct. Looking at the wrong answers: B) 76 would give a total of 720+(16×76)=1,936720 + (16 \times 76) = 1,936 points, making the class average 1,936÷24=80.671,936 ÷ 24 = 80.67, which is too low. C) 74 would yield 720+(16×74)=1,904720 + (16 \times 74) = 1,904 total points and an average of 79.3379.33, also too low. D) 80 would produce 720+(16×80)=2,000720 + (16 \times 80) = 2,000 total points and an average of 83.3383.33, which exceeds the given average of 82. Study tip: In weighted average problems, always verify your answer by checking that it produces the original average when you calculate backwards. This catch errors and builds confidence in your solution method.