Problem-Solving & Data Analysis practice questions

Problem-Solving & Data Analysis questions

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1. 1Percent changeFoundation

   A quantity increases from 48 to 60. What is the percent increase?A quantity increases from 48 to 60. What is the percent increase?

   • A125%125%
   • B30%30%
   • C20%20%
   • D25%25%
   Show the answer and explanationHide the explanation

   Answer: 25%25%

   The increase is 12. Divide by the original amount: 1248 = 0.25, or 25%.The increase is 12. Divide by the original amount: 12/48 = 0.25, or 25%.

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2. 2MeanFoundation

   What is the mean of 4, 6, 7, 9, and 14?What is the mean of 4, 6, 7, 9, and 14?

   • A88
   • B1010
   • C77
   • D99
   Show the answer and explanationHide the explanation

   Answer: 88

   Add the values and divide by how many there are: 405 = 8. The mean needs both numbers, and the count is the half that gets forgotten when the list is long.Add the values and divide by how many there are: 40/5 = 8. The mean needs both numbers, and the count is the half that gets forgotten when the list is long.

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3. 3ProbabilityFoundation

   A bag has 3 red, 5 blue, and 2 green counters. What is the probability of choosing a counter that is not blue?A bag has 3 red, 5 blue, and 2 green counters. What is the probability of choosing a counter that is not blue?

   • A151/5
   • B454/5
   • C353/5
   • D121/2
   Show the answer and explanationHide the explanation

   Answer: 121/2

   There are 5 counters that are not blue out of 10 total. That is 510, which simplifies to 12.There are 5 counters that are not blue out of 10 total. That is 5/10, which simplifies to 1/2.

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4. 4RatesFoundation

   A car travels 180 miles in 3 hours at a constant rate. Enter its speed in miles per hour.A car travels 180 miles in 3 hours at a constant rate. Enter its speed in miles per hour.

   Student-produced response: write your own answer rather than choosing one.

   Show the answer and explanationHide the explanation

   Answer: 6060

   Rate equals distance divided by time: 1803 = 60 miles per hour.Rate equals distance divided by time: 180/3 = 60 miles per hour.

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5. 5MedianFoundation

   What is the median of 2, 5, 6, 10, and 12?What is the median of 2, 5, 6, 10, and 12?

   • A55
   • B88
   • C66
   • D77
   Show the answer and explanationHide the explanation

   Answer: 66

   Order the values first, then take the middle one. These are already in order, so the median is the third of five: 6. Ordering is the step that decides the answer.Order the values first, then take the middle one. These are already in order, so the median is the third of five: 6. Ordering is the step that decides the answer.

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6. 6Percent decreaseStandard

   A jacket is discounted by 20% and then costs $72. What was its original price?A jacket is discounted by 20% and then costs $72. What was its original price?

   • A$86.40$86.40
   • B$92$92
   • C$80$80
   • D$90$90
   Show the answer and explanationHide the explanation

   Answer: $90$90

   After a 20% discount, the price is 80% of the original. 720.8 = 90.After a 20% discount, the price is 80% of the original. 72/0.8 = 90.

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7. 7PercentagesStandard

   In one group, 12 of 30 students joined a club. In another, 18 of 45 joined. Which statement is true?In one group, 12 of 30 students joined a club. In another, 18 of 45 joined. Which statement is true?

   • AThere is not enough information.There is not enough information.
   • BBoth groups have the same percentage.Both groups have the same percentage.
   • CThe second group has the greater percentage.The second group has the greater percentage.
   • DThe first group has the greater percentage.The first group has the greater percentage.
   Show the answer and explanationHide the explanation

   Answer: Both groups have the same percentage.Both groups have the same percentage.

   1230 = 0.4 and 1845 = 0.4, so both groups have 40% participation.12/30 = 0.4 and 18/45 = 0.4, so both groups have 40% participation.

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8. 8RangeFoundation

   What is the range of 4, 7, 7, 9, and 13?What is the range of 4, 7, 7, 9, and 13?

   • A77
   • B66
   • C99
   • D1313
   Show the answer and explanationHide the explanation

   Answer: 99

   Range is the largest minus the smallest: 13 - 4 = 9. Repeated values change nothing — only the two ends matter, so the second 7 is irrelevant.Range is the largest minus the smallest: 13 - 4 = 9. Repeated values change nothing — only the two ends matter, so the second 7 is irrelevant.

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9. 9Linear relationshipsStandard

   A table has pairs (1, 5), (2, 8), and (3, 11). By how much does y change when x increases by 1?A table has pairs (1, 5), (2, 8), and (3, 11). By how much does y change when x increases by 1?

   x	1	2	3
   y	5	8	11

   • A55
   • B22
   • C33
   • D11
   Show the answer and explanationHide the explanation

   Answer: 33

   Each step of 1 in x raises y by 3: 5 to 8 to 11. That constant step is the slope, and a constant step is what makes the relationship linear in the first place.Each step of 1 in x raises y by 3: 5 to 8 to 11. That constant step is the slope, and a constant step is what makes the relationship linear in the first place.

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10. 10PercentagesFoundation

    A class has 20 students and 5 are absent. What percent of the class is present?A class has 20 students and 5 are absent. What percent of the class is present?

    • A80%80%
    • B50%50%
    • C25%25%
    • D75%75%
    Show the answer and explanationHide the explanation

    Answer: 75%75%

    The question asks for present, not absent: 20 - 5 = 15 present, and 1520 = 0.75, or 75%. Reading which group is being asked for is the whole question; 25% is waiting.The question asks for present, not absent: 20 - 5 = 15 present, and 15/20 = 0.75, or 75%. Reading which group is being asked for is the whole question; 25% is waiting.

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11. 11MedianStandard

    What is the median of 3, 4, 6, 8, 10, and 13?What is the median of 3, 4, 6, 8, 10, and 13?

    • A66
    • B99
    • C88
    • D77
    Show the answer and explanationHide the explanation

    Answer: 77

    With six values, take the mean of the two middle values: 6 + 82 = 7.With six values, take the mean of the two middle values: (6 + 8)/2 = 7.

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12. 12RatesFoundation

    A printer produces 45 pages in 3 minutes at a constant rate. Enter the number of pages it produces in 8 minutes.A printer produces 45 pages in 3 minutes at a constant rate. Enter the number of pages it produces in 8 minutes.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 120120

    The rate is 453 = 15 pages per minute, and 15 × 8 = 120 pages.The rate is 45/3 = 15 pages per minute, and 15 × 8 = 120 pages.

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13. 13Percent changeChallenge

    A store raises a $50 price by 10 percent and then lowers the new price by 10 percent. What is the final price?A store raises a $50 price by 10 percent and then lowers the new price by 10 percent. What is the final price?

    • A$49.50$49.50
    • B$45.00$45.00
    • C$50.50$50.50
    • D$50.00$50.00
    Show the answer and explanationHide the explanation

    Answer: $49.50$49.50

    The increase gives 50 × 1.10 = $55. The decrease is taken from $55, not $50: 55 × 0.90 = $49.50. The two percentages apply to different amounts, so they do not cancel.The increase gives 50 × 1.10 = $55. The decrease is taken from $55, not $50: 55 × 0.90 = $49.50. The two percentages apply to different amounts, so they do not cancel.

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14. 14MeanFoundation

    Five numbers have a mean of 12. Enter their sum.Five numbers have a mean of 12. Enter their sum.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 6060

    The mean is the sum divided by the count, so the sum is 12 × 5 = 60.The mean is the sum divided by the count, so the sum is 12 × 5 = 60.

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15. 15ProbabilityFoundation

    A spinner has 8 equal sections, 3 of which are shaded. What is the probability of landing on an unshaded section?A spinner has 8 equal sections, 3 of which are shaded. What is the probability of landing on an unshaded section?

    • A535/3
    • B383/8
    • C585/8
    • D181/8
    Show the answer and explanationHide the explanation

    Answer: 585/8

    There are 8 - 3 = 5 unshaded sections out of 8 equally likely outcomes, so the probability is 58.There are 8 - 3 = 5 unshaded sections out of 8 equally likely outcomes, so the probability is 5/8.

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16. 16Two-way frequenciesStandard

    Of 40 surveyed students, 24 ride the bus, and 10 of those bus riders also sometimes walk. What fraction of the bus riders sometimes walk?Of 40 surveyed students, 24 ride the bus, and 10 of those bus riders also sometimes walk. What fraction of the bus riders sometimes walk?

    • A141/4
    • B5245/24
    • C5125/12
    • D353/5
    Show the answer and explanationHide the explanation

    Answer: 5125/12

    The question asks for a fraction of bus riders, not of all students: 1024, which reduces to 512.The question asks for a fraction of bus riders, not of all students: 10/24, which reduces to 5/12.

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17. 17MeanChallenge

    The list 4, 8, 9, 11, 13 gains a sixth number, which raises the mean of the list to 10. Enter the sixth number.The list 4, 8, 9, 11, 13 gains a sixth number, which raises the mean of the list to 10. Enter the sixth number.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 1515

    The five numbers sum to 45. Six numbers with a mean of 10 sum to 60, so the new number is 60 - 45 = 15.The five numbers sum to 45. Six numbers with a mean of 10 sum to 60, so the new number is 60 - 45 = 15.

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18. 18Proportional relationshipsStandard

    A map uses 1 inch to represent 25 miles. Enter the number of miles represented by 3.5 inches.A map uses 1 inch to represent 25 miles. Enter the number of miles represented by 3.5 inches.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 87.587.5

    Multiply the scale by the measured length: 25 × 3.5 = 87.5 miles.Multiply the scale by the measured length: 25 × 3.5 = 87.5 miles.

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19. 19Percent changeStandard

    After a 25 percent increase, a membership costs $80. What was the original price?After a 25 percent increase, a membership costs $80. What was the original price?

    • A$100$100
    • B$64$64
    • C$60$60
    • D$65$65
    Show the answer and explanationHide the explanation

    Answer: $64$64

    The new price is 1.25 times the original, so the original is 801.25 = $64. Subtracting 25 percent of $80 would be a different, incorrect calculation.The new price is 1.25 times the original, so the original is 80/1.25 = $64. Subtracting 25 percent of $80 would be a different, incorrect calculation.

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20. 20Center and spreadStandard

    A data set of home prices in one area includes a few homes that sold for far more than the rest. Which measure best represents a typical price in that area?A data set of home prices in one area includes a few homes that sold for far more than the rest. Which measure best represents a typical price in that area?

    • AThe meanThe mean
    • BThe medianThe median
    • CThe maximumThe maximum
    • DThe rangeThe range
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    Answer: The medianThe median

    A few very large values pull the mean upward, while the median depends on position rather than size and is not moved much by extreme values.A few very large values pull the mean upward, while the median depends on position rather than size and is not moved much by extreme values.

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21. 21RatesChallenge

    One tap fills a tank in 6 minutes and a second tap fills the same tank in 12 minutes. Enter the number of minutes the two taps take to fill it together.One tap fills a tank in 6 minutes and a second tap fills the same tank in 12 minutes. Enter the number of minutes the two taps take to fill it together.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 44

    In one minute the taps fill 16 and 112 of the tank, so together they fill 16 + 112 = 312 = 14 of the tank per minute. Filling the whole tank takes 4 minutes.In one minute the taps fill 1/6 and 1/12 of the tank, so together they fill 1/6 + 1/12 = 3/12 = 1/4 of the tank per minute. Filling the whole tank takes 4 minutes.

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22. 22PercentagesFoundation

    Of 250 survey responses, 60 selected the first of four listed choices. What percent selected it?Of 250 survey responses, 60 selected the first of four listed choices. What percent selected it?

    • A24%24%
    • B40%40%
    • C20%20%
    • D30%30%
    Show the answer and explanationHide the explanation

    Answer: 24%24%

    Divide the part by the whole, then convert: 60250 = 0.24, which is 24 percent. The number of listed choices is not used — it is there to invite dividing by 4.Divide the part by the whole, then convert: 60/250 = 0.24, which is 24 percent. The number of listed choices is not used — it is there to invite dividing by 4.

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23. 23Weighted averagesChallenge

    A class of 10 students averaged 80 on a test and a class of 15 students averaged 90. Enter the average for all 25 students.A class of 10 students averaged 80 on a test and a class of 15 students averaged 90. Enter the average for all 25 students.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 8686

    Averages cannot simply be averaged when the groups differ in size. Total points are 10 × 80 + 15 × 90 = 800 + 1350 = 2150, and 215025 = 86.Averages cannot simply be averaged when the groups differ in size. Total points are 10 × 80 + 15 × 90 = 800 + 1350 = 2150, and 2150/25 = 86.

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24. 24SpreadStandard

    Two data sets have the same mean. Set A is 48, 49, 50, 51, 52 and Set B is 30, 40, 50, 60, 70. Which statement is true?Two data sets have the same mean. Set A is 48, 49, 50, 51, 52 and Set B is 30, 40, 50, 60, 70. Which statement is true?

    • ASet B has the greater standard deviation.Set B has the greater standard deviation.
    • BSet A has the greater standard deviation.Set A has the greater standard deviation.
    • CThe two have equal standard deviations.The two have equal standard deviations.
    • DStandard deviation cannot be compared without more information.Standard deviation cannot be compared without more information.
    Show the answer and explanationHide the explanation

    Answer: Set B has the greater standard deviation.Set B has the greater standard deviation.

    Standard deviation measures spread around the mean. Both sets center on 50, but Set B's values sit much further from it, so its standard deviation is larger. No calculation is needed to see this.Standard deviation measures spread around the mean. Both sets center on 50, but Set B's values sit much further from it, so its standard deviation is larger. No calculation is needed to see this.

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25. 25Unit conversionFoundation

    A tank holds 3.5 liters. If 1 liter is about 1000 milliliters, enter the capacity in milliliters.A tank holds 3.5 liters. If 1 liter is about 1000 milliliters, enter the capacity in milliliters.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 35003500

    Multiply by the conversion factor: 3.5 × 1000 = 3500 milliliters.Multiply by the conversion factor: 3.5 × 1000 = 3500 milliliters.

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26. 26Line of best fitStandard

    A scatterplot of study hours against test score has a line of best fit with a positive slope of 4. What does the slope indicate?A scatterplot of study hours against test score has a line of best fit with a positive slope of 4. What does the slope indicate?

    • AStudents who study score 4 points in total.Students who study score 4 points in total.
    • BEach additional hour of study is associated with about 4 more points.Each additional hour of study is associated with about 4 more points.
    • CFour students studied for the test.Four students studied for the test.
    • DStudy time causes scores to rise by exactly 4 points.Study time causes scores to rise by exactly 4 points.
    Show the answer and explanationHide the explanation

    Answer: Each additional hour of study is associated with about 4 more points.Each additional hour of study is associated with about 4 more points.

    The slope of a line of best fit gives the average change in the predicted y-value per unit increase in x. It describes an association, not a guaranteed or causal effect.The slope of a line of best fit gives the average change in the predicted y-value per unit increase in x. It describes an association, not a guaranteed or causal effect.

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27. 27ProbabilityStandard

    A drawer holds 4 blue socks and 6 gray socks. One sock is taken out and kept. What is the probability that the first two socks taken are both gray?A drawer holds 4 blue socks and 6 gray socks. One sock is taken out and kept. What is the probability that the first two socks taken are both gray?

    • A9259/25
    • B353/5
    • C131/3
    • D252/5
    Show the answer and explanationHide the explanation

    Answer: 131/3

    The first gray sock has probability 610. With that sock removed, 5 of the remaining 9 are gray, so the second has probability 59. Multiplying gives 3090 = 13.The first gray sock has probability 6/10. With that sock removed, 5 of the remaining 9 are gray, so the second has probability 5/9. Multiplying gives 30/90 = 1/3.

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28. 28PercentagesStandard

    A shop's takings rose from $2,400 to $2,760. What was the percent increase?A shop's takings rose from $2,400 to $2,760. What was the percent increase?

    • A13%13%
    • B36%36%
    • C15%15%
    • D8.7%8.7%
    Show the answer and explanationHide the explanation

    Answer: 15%15%

    The increase is 360. Divide by the original amount, not the new one: 3602400 = 0.15, which is 15 percent.The increase is 360. Divide by the original amount, not the new one: 360/2400 = 0.15, which is 15 percent.

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29. 29RatesChallenge

    A cyclist rides 12 kilometers at 24 km/h and then 12 kilometers at 12 km/h. What is the average speed for the whole ride?A cyclist rides 12 kilometers at 24 km/h and then 12 kilometers at 12 km/h. What is the average speed for the whole ride?

    • A20 km/h20 km/h
    • B16 km/h16 km/h
    • C15 km/h15 km/h
    • D18 km/h18 km/h
    Show the answer and explanationHide the explanation

    Answer: 16 km/h16 km/h

    Average speed is total distance over total time, not the average of the speeds. The legs take 0.5 and 1 hour, so 24 kilometers in 1.5 hours gives 16 km/h. The tempting 18 km/h is the average of the two speeds.Average speed is total distance over total time, not the average of the speeds. The legs take 0.5 and 1 hour, so 24 kilometers in 1.5 hours gives 16 km/h. The tempting 18 km/h is the average of the two speeds.

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30. 30MedianFoundation

    Enter the median of 7, 3, 11, 5, and 9.Enter the median of 7, 3, 11, 5, and 9.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 77

    Order the values first: 3, 5, 7, 9, 11. With five values the median is the third, which is 7.Order the values first: 3, 5, 7, 9, 11. With five values the median is the third, which is 7.

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31. 31SamplingStandard

    A researcher surveys shoppers leaving one supermarket on a Tuesday morning and concludes that most people in the city shop mid-week. What is the main problem with this conclusion?A researcher surveys shoppers leaving one supermarket on a Tuesday morning and concludes that most people in the city shop mid-week. What is the main problem with this conclusion?

    • AThe researcher should have surveyed on more than one Tuesday.The researcher should have surveyed on more than one Tuesday.
    • BSupermarkets are not a valid place to conduct surveys.Supermarkets are not a valid place to conduct surveys.
    • CThe sample size is too small to calculate a percentage.The sample size is too small to calculate a percentage.
    • DThe sample only includes people who already shop at that time.The sample only includes people who already shop at that time.
    Show the answer and explanationHide the explanation

    Answer: The sample only includes people who already shop at that time.The sample only includes people who already shop at that time.

    Everyone surveyed was, by construction, shopping mid-week, so the sample cannot say anything about people who shop at other times. This is a selection problem, not a size problem.Everyone surveyed was, by construction, shopping mid-week, so the sample cannot say anything about people who shop at other times. This is a selection problem, not a size problem.

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32. 32Two-way frequenciesStandard

    Of 120 respondents, 45 own a bicycle and 18 of those also own a car. What percent of bicycle owners also own a car?Of 120 respondents, 45 own a bicycle and 18 of those also own a car. What percent of bicycle owners also own a car?

    • A15%15%
    • B26.7%26.7%
    • C40%40%
    • D37.5%37.5%
    Show the answer and explanationHide the explanation

    Answer: 40%40%

    The denominator is bicycle owners, not all respondents: 1845 = 0.40, which is 40 percent. Dividing by 120 answers a different question.The denominator is bicycle owners, not all respondents: 18/45 = 0.40, which is 40 percent. Dividing by 120 answers a different question.

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33. 33Percent changeChallenge

    A population falls by 20 percent and then rises by 25 percent. What is the net change?A population falls by 20 percent and then rises by 25 percent. What is the net change?

    • AA 5 percent fallA 5 percent fall
    • BA 45 percent riseA 45 percent rise
    • CA 5 percent riseA 5 percent rise
    • DNo net changeNo net change
    Show the answer and explanationHide the explanation

    Answer: No net changeNo net change

    Multiply rather than add: 0.80 × 1.25 = 1.00, so the population returns to its starting value. The percentages apply to different amounts, which is why they do not simply combine.Multiply rather than add: 0.80 × 1.25 = 1.00, so the population returns to its starting value. The percentages apply to different amounts, which is why they do not simply combine.

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34. 34ProbabilityStandard

    A box holds 5 red, 3 green and 2 blue tokens. What is the probability that a token drawn at random is not red?A box holds 5 red, 3 green and 2 blue tokens. What is the probability that a token drawn at random is not red?

    • A121/2
    • B252/5
    • C3103/10
    • D5105/10
    Show the answer and explanationHide the explanation

    Answer: 121/2

    Five of the ten tokens are not red, so the probability is 510 = 12. Working with the complement is quicker than adding the green and blue cases separately, though both give the same answer.Five of the ten tokens are not red, so the probability is 5/10 = 1/2. Working with the complement is quicker than adding the green and blue cases separately, though both give the same answer.

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35. 35RatesStandard

    A pump moves 4,200 liters in 3.5 hours. Enter its rate in liters per hour.A pump moves 4,200 liters in 3.5 hours. Enter its rate in liters per hour.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 12001200

    Divide the volume by the time: 42003.5 = 1200 liters per hour.Divide the volume by the time: 4200/3.5 = 1200 liters per hour.

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36. 36MeanChallenge

    Six numbers have a mean of 14. If the largest number is removed, the mean of the remaining five is 12. What was the largest number?Six numbers have a mean of 14. If the largest number is removed, the mean of the remaining five is 12. What was the largest number?

    • A2424
    • B1818
    • C2626
    • D2020
    Show the answer and explanationHide the explanation

    Answer: 2424

    Six numbers at a mean of 14 sum to 84; five at a mean of 12 sum to 60. The removed value is the difference, 84 - 60 = 24.Six numbers at a mean of 14 sum to 84; five at a mean of 12 sum to 60. The removed value is the difference, 84 - 60 = 24.

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37. 37Proportional relationshipsFoundation

    A recipe for 6 servings uses 300 grams of rice. How much rice is needed for 9 servings?A recipe for 6 servings uses 300 grams of rice. How much rice is needed for 9 servings?

    • A450 grams450 grams
    • B350 grams350 grams
    • C400 grams400 grams
    • D500 grams500 grams
    Show the answer and explanationHide the explanation

    Answer: 450 grams450 grams

    Find the unit rate first: 3006 = 50 grams a serving, so 9 servings need 50 × 9 = 450 grams. Scaling the original by 96 gives the same answer in one step.Find the unit rate first: 300/6 = 50 grams a serving, so 9 servings need 50 × 9 = 450 grams. Scaling the original by 9/6 gives the same answer in one step.

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38. 38Center and spreadStandard

    Adding the value 12 to the data set 10, 11, 12, 13, 14 will change which of the following?Adding the value 12 to the data set 10, 11, 12, 13, 14 will change which of the following?

    • ABoth the mean and the medianBoth the mean and the median
    • BNeither the mean nor the medianNeither the mean nor the median
    • CThe mean onlyThe mean only
    • DThe median onlyThe median only
    Show the answer and explanationHide the explanation

    Answer: Neither the mean nor the medianNeither the mean nor the median

    The set already has mean and median 12, and adding another 12 leaves both at 12. Adding a value equal to the center moves neither measure.The set already has mean and median 12, and adding another 12 leaves both at 12. Adding a value equal to the center moves neither measure.

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39. 39PercentagesStandard

    After a 15 percent discount, a coat costs $102. What was the price before the discount?After a 15 percent discount, a coat costs $102. What was the price before the discount?

    • A$117$117
    • B$120$120
    • C$125$125
    • D$115$115
    Show the answer and explanationHide the explanation

    Answer: $120$120

    The discounted price is 85 percent of the original, so the original is 1020.85 = $120. Adding 15 percent to $102 gives $117.30, which answers a different question.The discounted price is 85 percent of the original, so the original is 102/0.85 = $120. Adding 15 percent to $102 gives $117.30, which answers a different question.

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40. 40SamplingChallenge

    A council emails a survey about a proposed cycle lane to everyone on its cycling newsletter list. What is the main limitation of the result?A council emails a survey about a proposed cycle lane to everyone on its cycling newsletter list. What is the main limitation of the result?

    • AThe sample is too small to reach a conclusion.The sample is too small to reach a conclusion.
    • BEmail surveys always have low response rates.Email surveys always have low response rates.
    • CThe council should have used a paper survey instead.The council should have used a paper survey instead.
    • DThe people surveyed are more likely than the general public to favor the lane.The people surveyed are more likely than the general public to favor the lane.
    Show the answer and explanationHide the explanation

    Answer: The people surveyed are more likely than the general public to favor the lane.The people surveyed are more likely than the general public to favor the lane.

    Everyone asked has already signalled an interest in cycling, so the sample is not representative of the population the decision affects. That is a selection problem, and no response rate or sample size fixes it.Everyone asked has already signalled an interest in cycling, so the sample is not representative of the population the decision affects. That is a selection problem, and no response rate or sample size fixes it.

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41. 41PercentagesStandard

    A test has 45 questions. A student answers 36 correctly. What percentage did they answer correctly?A test has 45 questions. A student answers 36 correctly. What percentage did they answer correctly?

    • A75%75%
    • B85%85%
    • C90%90%
    • D80%80%
    Show the answer and explanationHide the explanation

    Answer: 80%80%

    Divide the part by the whole, then convert: 3645 = 0.80, which is 80 percent. The number correct goes on top; putting the total on top gives 1.25 and no percentage above 100 is possible here.Divide the part by the whole, then convert: 36/45 = 0.80, which is 80 percent. The number correct goes on top; putting the total on top gives 1.25 and no percentage above 100 is possible here.

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42. 42ProbabilityChallenge

    Two fair coins are tossed. What is the probability that at least one shows heads?Two fair coins are tossed. What is the probability that at least one shows heads?

    • A343/4
    • B232/3
    • C121/2
    • D141/4
    Show the answer and explanationHide the explanation

    Answer: 343/4

    The four equally likely outcomes are HH, HT, TH, TT. Three contain at least one head. Working with the complement is faster: the only outcome without a head is TT, so 1 - 14 = 34.The four equally likely outcomes are HH, HT, TH, TT. Three contain at least one head. Working with the complement is faster: the only outcome without a head is TT, so 1 - 1/4 = 3/4.

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43. 43RatesStandard

    A train travels 210 kilometers in 2 hours 30 minutes. Enter its average speed in kilometers per hour.A train travels 210 kilometers in 2 hours 30 minutes. Enter its average speed in kilometers per hour.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 8484

    Convert the time to hours first: 2 hours 30 minutes is 2.5 hours. Then 2102.5 = 84 kilometers per hour.Convert the time to hours first: 2 hours 30 minutes is 2.5 hours. Then 210/2.5 = 84 kilometers per hour.

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44. 44MeanStandard

    A student's four test scores average 78. What score on a fifth test would raise the average to 80?A student's four test scores average 78. What score on a fifth test would raise the average to 80?

    • A8686
    • B9090
    • C8888
    • D8282
    Show the answer and explanationHide the explanation

    Answer: 8888

    Four scores at 78 total 312. Five scores at 80 total 400. The fifth score must be 400 - 312 = 88.Four scores at 78 total 312. Five scores at 80 total 400. The fifth score must be 400 - 312 = 88.

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45. 45Two-way frequenciesStandard

    Of 80 members, 50 attend the evening session and 30 of those also attend the morning one. What fraction of evening attendees also attend in the morning?Of 80 members, 50 attend the evening session and 30 of those also attend the morning one. What fraction of evening attendees also attend in the morning?

    • A353/5
    • B383/8
    • C3103/10
    • D585/8
    Show the answer and explanationHide the explanation

    Answer: 353/5

    The denominator is evening attendees: 3050 = 35. Dividing by all 80 members answers a different question.The denominator is evening attendees: 30/50 = 3/5. Dividing by all 80 members answers a different question.

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46. 46Center and spreadChallenge

    A data set has mean 50 and every value is increased by 10. What happens to the mean and the standard deviation?A data set has mean 50 and every value is increased by 10. What happens to the mean and the standard deviation?

    • AThe mean is unchanged; the standard deviation rises by 10.The mean is unchanged; the standard deviation rises by 10.
    • BThe mean rises to 60; the standard deviation falls.The mean rises to 60; the standard deviation falls.
    • CBoth rise by 10.Both rise by 10.
    • DThe mean rises to 60; the standard deviation is unchanged.The mean rises to 60; the standard deviation is unchanged.
    Show the answer and explanationHide the explanation

    Answer: The mean rises to 60; the standard deviation is unchanged.The mean rises to 60; the standard deviation is unchanged.

    Adding a constant shifts every value equally, so the center moves but the distances between values do not change. Standard deviation measures spread, which a shift leaves alone.Adding a constant shifts every value equally, so the center moves but the distances between values do not change. Standard deviation measures spread, which a shift leaves alone.

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47. 47Percent changeStandard

    A subscription rises from $12 to $15 a month. What is the percent increase?A subscription rises from $12 to $15 a month. What is the percent increase?

    • A25%25%
    • B3%3%
    • C20%20%
    • D30%30%
    Show the answer and explanationHide the explanation

    Answer: 25%25%

    The increase is $3. Divide by the original price, not the new one: 312 = 0.25, which is 25 percent.The increase is $3. Divide by the original price, not the new one: 3/12 = 0.25, which is 25 percent.

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48. 48Line of best fitStandard

    A scatterplot of rainfall against crop yield has a line of best fit with a negative slope. What does that indicate?A scatterplot of rainfall against crop yield has a line of best fit with a negative slope. What does that indicate?

    • AThere is no relationship between rainfall and yield.There is no relationship between rainfall and yield.
    • BRainfall causes crop yield to fall.Rainfall causes crop yield to fall.
    • CHigher rainfall is associated with lower yield in this data.Higher rainfall is associated with lower yield in this data.
    • DThe data contains an error.The data contains an error.
    Show the answer and explanationHide the explanation

    Answer: Higher rainfall is associated with lower yield in this data.Higher rainfall is associated with lower yield in this data.

    A negative slope describes the direction of an association within the data shown. It does not establish a cause, and a real association is not an error.A negative slope describes the direction of an association within the data shown. It does not establish a cause, and a real association is not an error.

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49. 49PercentagesStandard

    A jacket costs $84 after a 30 percent discount. What was the original price?A jacket costs $84 after a 30 percent discount. What was the original price?

    • A$120$120
    • B$114$114
    • C$112$112
    • D$109.20$109.20
    Show the answer and explanationHide the explanation

    Answer: $120$120

    The sale price is 70 percent of the original, so the original is 840.70 = $120. Adding 30 percent to $84 gives $109.20, which answers a different question.The sale price is 70 percent of the original, so the original is 84/0.70 = $120. Adding 30 percent to $84 gives $109.20, which answers a different question.

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50. 50ProbabilityChallenge

    A bag holds 4 white and 6 black marbles. Two are drawn without replacement. What is the probability both are white?A bag holds 4 white and 6 black marbles. Two are drawn without replacement. What is the probability both are white?

    • A151/5
    • B2152/15
    • C8458/45
    • D4254/25
    Show the answer and explanationHide the explanation

    Answer: 2152/15

    The first is white with probability 410. With it removed, 3 of the remaining 9 are white, so the second is 39. Multiplying gives 1290 = 215.The first is white with probability 4/10. With it removed, 3 of the remaining 9 are white, so the second is 3/9. Multiplying gives 12/90 = 2/15.

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51. 51RatesChallenge

    A cyclist covers 45 kilometers at 15 km/h and returns along the same road at 30 km/h. Enter the average speed for the whole journey in km/h.A cyclist covers 45 kilometers at 15 km/h and returns along the same road at 30 km/h. Enter the average speed for the whole journey in km/h.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 2020

    Average speed is total distance over total time. The legs take 3 hours and 1.5 hours, so 90 kilometers in 4.5 hours gives 20 km/h. Averaging the two speeds would give 22.5, which is wrong because more time is spent at the slower speed.Average speed is total distance over total time. The legs take 3 hours and 1.5 hours, so 90 kilometers in 4.5 hours gives 20 km/h. Averaging the two speeds would give 22.5, which is wrong because more time is spent at the slower speed.

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52. 52MeanStandard

    The mean of five numbers is 20. Two of them are 14 and 26. What is the mean of the other three?The mean of five numbers is 20. Two of them are 14 and 26. What is the mean of the other three?

    • A1818
    • B2020
    • C2424
    • D2222
    Show the answer and explanationHide the explanation

    Answer: 2020

    The five total 100, and 14 + 26 = 40, so the other three total 60 and average 20. The two removed happen to average 20 themselves, which is why the rest are unaffected.The five total 100, and 14 + 26 = 40, so the other three total 60 and average 20. The two removed happen to average 20 themselves, which is why the rest are unaffected.

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53. 53Two-way frequenciesStandard

    Of 200 respondents, 120 own a pet and 42 of those own more than one. What percentage of pet owners own more than one?Of 200 respondents, 120 own a pet and 42 of those own more than one. What percentage of pet owners own more than one?

    • A60%60%
    • B35%35%
    • C58%58%
    • D21%21%
    Show the answer and explanationHide the explanation

    Answer: 35%35%

    The denominator is pet owners: 42120 = 0.35, which is 35 percent. Dividing by all 200 gives 21 percent.The denominator is pet owners: 42/120 = 0.35, which is 35 percent. Dividing by all 200 gives 21 percent.

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54. 54Center and spreadChallenge

    Every value in a data set is multiplied by 3. What happens to the mean and the standard deviation?Every value in a data set is multiplied by 3. What happens to the mean and the standard deviation?

    • AThe mean is unchanged; the standard deviation is multiplied by 3.The mean is unchanged; the standard deviation is multiplied by 3.
    • BThe mean is multiplied by 3; the standard deviation is unchanged.The mean is multiplied by 3; the standard deviation is unchanged.
    • CBoth are multiplied by 9.Both are multiplied by 9.
    • DBoth are multiplied by 3.Both are multiplied by 3.
    Show the answer and explanationHide the explanation

    Answer: Both are multiplied by 3.Both are multiplied by 3.

    Multiplying scales the values and the distances between them equally, so both the center and the spread are multiplied by 3. Adding a constant would move only the mean.Multiplying scales the values and the distances between them equally, so both the center and the spread are multiplied by 3. Adding a constant would move only the mean.

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55. 55Percent changeStandard

    Attendance fell from 250 to 200. What was the percent decrease?Attendance fell from 250 to 200. What was the percent decrease?

    • A80%80%
    • B20%20%
    • C25%25%
    • D50%50%
    Show the answer and explanationHide the explanation

    Answer: 20%20%

    The decrease is 50. Divide by the original figure: 50250 = 0.20, which is 20 percent. Dividing by 200 gives 25 percent, which measures the wrong thing.The decrease is 50. Divide by the original figure: 50/250 = 0.20, which is 20 percent. Dividing by 200 gives 25 percent, which measures the wrong thing.

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56. 56SamplingStandard

    A researcher wants to estimate the average commute time in a city and surveys people waiting at a train station at 8 a.m. What is the main limitation?A researcher wants to estimate the average commute time in a city and surveys people waiting at a train station at 8 a.m. What is the main limitation?

    • ACommute times cannot be averaged.Commute times cannot be averaged.
    • BTrain stations are too noisy for accurate surveys.Train stations are too noisy for accurate surveys.
    • CPeople who commute by other means, or at other times, are excluded.People who commute by other means, or at other times, are excluded.
    • DThe sample size will inevitably be too small.The sample size will inevitably be too small.
    Show the answer and explanationHide the explanation

    Answer: People who commute by other means, or at other times, are excluded.People who commute by other means, or at other times, are excluded.

    Everyone surveyed commutes by train at peak time, so the sample cannot represent drivers, cyclists or off-peak travelers. That is a coverage problem no sample size fixes.Everyone surveyed commutes by train at peak time, so the sample cannot represent drivers, cyclists or off-peak travelers. That is a coverage problem no sample size fixes.

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