Problem-Solving & Data Analysis practice questions
Rates, percentages, probability, and the centre and spread of a data set. The arithmetic is rarely hard; the work is deciding which quantity the question actually asks for.
Problem-Solving & Data Analysis questions
- 57PercentagesFoundation
A jacket priced at 80 pounds is reduced by 35 percent. What is the sale price?
- A52 pounds
- B45 pounds
- C28 pounds
- D58 pounds
Show the answer and explanationHide the explanation
Answer: 52 pounds
A 35 percent reduction leaves 65 percent, and 0.65 x 80 = 52 pounds. The choice 28 is the size of the discount rather than the price left after it.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 58MeanStandard
Rainfall at a weather station over five months was 42 mm, 55 mm, 38 mm, 61 mm and 44 mm. What is the mean monthly rainfall?
- A44 mm
- B48 mm
- C55 mm
- D46 mm
Show the answer and explanationHide the explanation
Answer: 48 mm
The five values total 240 mm, and 240 / 5 = 48 mm. The choice 44 is the middle value when the list is sorted, which is the median, and 55 is one reading rather than a summary of all five.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 59ProbabilityStandard
A box holds 5 red counters, 7 blue counters and 8 green counters. One counter is drawn at random. What is the probability that it is not green?
- A2/5
- B1/5
- C3/5
- D7/20
Show the answer and explanationHide the explanation
Answer: 3/5
There are 20 counters in all and 12 that are not green, so the probability is 12/20 = 3/5. The choice 2/5 is the probability that it is green, which is what you get by answering the question that was not asked.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 60Two-way frequenciesStandard
Of 120 students surveyed, 45 cycle to school and 75 do not. Among those who cycle, 18 play a team sport; among those who do not cycle, 42 play a team sport. If a student who plays a team sport is chosen at random, what is the probability that the student cycles?
- A2/5
- B3/20
- C1/2
- D3/10
Show the answer and explanationHide the explanation
Answer: 3/10
The group being chosen from is the 18 + 42 = 60 students who play a team sport, and 18 of them cycle, so the probability is 18/60 = 3/10. Dividing by 45 instead gives 2/5, which answers the reverse question: the chance a cyclist plays a sport.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 61MedianChallenge
A shop recorded umbrellas sold on nine days: 3, 7, 4, 12, 5, 7, 2, 9, 6. What is the median number sold?
- A6
- B7
- C5
- D6.1
Show the answer and explanationHide the explanation
Answer: 6
Sorted, the values are 2, 3, 4, 5, 6, 7, 7, 9, 12. With nine values the median is the fifth, which is 6. The choice 7 is the mode, and 6.1 is roughly the mean, which the single high value of 12 pulls upward.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 62RatesStandard
A printer produces 14 pages a minute. How many minutes does it take to print 630 pages?
- A35
- B45
- C50
- D44
Show the answer and explanationHide the explanation
Answer: 45
Dividing the total by the rate gives 630 / 14 = 45 minutes. Multiplying instead of dividing, or dividing by the wrong figure, produces the other choices.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 63Percent changeChallenge
A town grew from 12,500 people to 14,000 over one decade, then lost 8 percent of its population over the next. What was the population at the end of the second decade?
- A13,200
- B12,500
- C12,880
- D11,500
Show the answer and explanationHide the explanation
Answer: 12,880
The 8 percent loss applies to 14,000, not to the original figure: 14,000 x 0.92 = 12,880. Applying it to 12,500 gives 11,500, and subtracting 8 percent of the growth instead gives 13,200. Note that the town ends above where it started.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 64SamplingChallenge
A researcher wants to estimate the average commute time of the 2,000 staff at a company with six sites. She surveys the 90 people who arrive at the main site before 8 a.m. What is the strongest objection to her method?
- AThe sample of 90 is too small to support any estimate.
- BCommute times are not the sort of quantity that can be averaged.
- CThe survey should have asked about the cost of the journey as well.
- DStaff who arrive early at one site are unlikely to resemble staff across all six.
Show the answer and explanationHide the explanation
Answer: Staff who arrive early at one site are unlikely to resemble staff across all six.
The problem is how the sample was chosen, not how large it is: early arrivals at one site may well live nearer, and five sites are missing entirely. A sample of 90 can support an estimate when it is drawn at random from the whole group.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 65Unit conversionFoundation
A tank holds 4.5 cubic metres of water. Given that 1 cubic metre is 1,000 litres, how many litres does it hold?
- A4,500
- B450
- C45,000
- D4.5
Show the answer and explanationHide the explanation
Answer: 4,500
Multiplying by 1,000 moves the decimal point three places: 4.5 x 1,000 = 4,500 litres. Moving it two places or four gives the other choices, which is why it is worth naming the factor before converting.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 66Percent decreaseStandard
A subscription fell from 48 pounds a year to 36 pounds. What was the percentage decrease?
- A33 percent
- B25 percent
- C12 percent
- D75 percent
Show the answer and explanationHide the explanation
Answer: 25 percent
The fall is 12 pounds, and a percentage decrease is measured against the starting figure: 12 / 48 = 0.25, so 25 percent. Dividing by 36 gives about 33 percent, which would be the increase needed to go back.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 67RangeStandard
Daily high temperatures for a week, in degrees Celsius, were 14, 19, 11, 22, 17, 13 and 20. What is the range?
- A22 degrees
- B16.6 degrees
- C11 degrees
- D9 degrees
Show the answer and explanationHide the explanation
Answer: 11 degrees
The range is the highest value minus the lowest: 22 - 11 = 11 degrees. The choice 22 is the maximum on its own and 16.6 is roughly the mean, neither of which measures spread.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 68Weighted averagesChallenge
A class of 30 students averaged 72 on a test and a class of 20 averaged 82. What is the average score across both classes?
- A77
- B75
- C78
- D76
Show the answer and explanationHide the explanation
Answer: 76
Totals must be combined before dividing: (30 x 72) + (20 x 82) = 2,160 + 1,640 = 3,800, and 3,800 / 50 = 76. Averaging 72 and 82 directly gives 77, which would only be right if the classes were the same size.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 69Linear relationshipsStandard
A candle burns at a constant rate. Two hours after it is lit it is 21 cm tall, and five hours after it is lit it is 15 cm tall. How tall was it when it was lit?
- A25 cm
- B23 cm
- C27 cm
- D24 cm
Show the answer and explanationHide the explanation
Answer: 25 cm
The height falls 6 cm over 3 hours, so the rate is 2 cm an hour. Working back two hours from 21 cm gives 21 + 4 = 25 cm. Working back only one hour, or forgetting to work back at all, produces the other choices.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 70ProbabilityStandard
Two fair six-sided dice are rolled. What is the probability that the two numbers total 9?
- A1/6
- B1/9
- C4/12
- D1/12
Show the answer and explanationHide the explanation
Answer: 1/9
There are 36 equally likely outcomes and four give a total of 9: 3 and 6, 4 and 5, 5 and 4, 6 and 3. So the probability is 4/36 = 1/9. Counting 3 and 6 as the same outcome as 6 and 3 loses two of the four.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 71PercentagesChallenge
A price rises by 20 percent and then falls by 20 percent. Compared with the original price, the final price is
- Athe same.
- B4 percent higher.
- C4 percent lower.
- D20 percent lower.
Show the answer and explanationHide the explanation
Answer: 4 percent lower.
The two changes are percentages of different amounts. Multiplying gives 1.20 x 0.80 = 0.96, so the final price is 96 percent of the original, 4 percent lower. The fall is larger in money terms because it is taken from the raised price.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 72Two-way frequenciesChallenge
In a survey of 200 people, 120 own a bicycle and 90 own a car. If 40 own both, how many own neither?
- A10
- B50
- C70
- D30
Show the answer and explanationHide the explanation
Answer: 30
Adding 120 and 90 counts the 40 who own both twice, so the number owning at least one is 120 + 90 - 40 = 170. That leaves 200 - 170 = 30 owning neither. Forgetting to subtract the overlap gives 210, which is more people than were surveyed — a useful sign that a step is missing.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 73Proportional relationshipsFoundation
A car uses 6 litres of fuel for every 100 km driven. How much fuel does it use for 250 km?
- A15 litres
- B24 litres
- C12 litres
- D41.7 litres
Show the answer and explanationHide the explanation
Answer: 15 litres
250 km is 2.5 lots of 100 km, so the fuel used is 2.5 x 6 = 15 litres. Dividing 250 by 6 gives 41.7, which answers how many 6-km stretches there are rather than how much fuel is burned.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 74Percent decreaseStandard
A machine that produced 480 units an hour was reconfigured and now produces 408. What was the percentage decrease?
- A17.6 percent
- B15 percent
- C72 percent
- D12 percent
Show the answer and explanationHide the explanation
Answer: 15 percent
The fall of 72 is measured against the original 480: 72 / 480 = 0.15. Dividing by the new figure of 408 gives 17.6 percent, which is the rise needed to get back rather than the fall that happened.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 75SpreadStandard
Class A scored 68, 70, 71, 72 and 74 on a test. Class B scored 55, 64, 71, 79 and 86. Both classes have a mean of 71. Which statement is true?
- AClass A's scores are more spread out than Class B's.
- BThe two classes have the same range.
- CClass B's scores are more spread out than Class A's.
- DSpread cannot be compared when two sets have the same mean.
Show the answer and explanationHide the explanation
Answer: Class B's scores are more spread out than Class A's.
The means are identical and say nothing about spread. Class A runs from 68 to 74, a range of 6; class B runs from 55 to 86, a range of 31. Equal means with different spreads is the ordinary case, not a special one.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 76RangeStandard
Six parcels had masses, in kg, of 2.4, 5.1, 3.8, 7.2, 4.0 and 6.5. What is the range of these masses?
- A7.2 kg
- B4.9 kg
- C2.4 kg
- D4.8 kg
Show the answer and explanationHide the explanation
Answer: 4.8 kg
The range is the largest value minus the smallest: 7.2 - 2.4 = 4.8 kg. The choices 7.2 and 2.4 are those two values on their own, neither of which describes how far apart the masses are.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 77Linear relationshipsStandard
A tank is filled at a constant rate. Three minutes after filling starts it holds 26 litres, and eight minutes after it starts it holds 66 litres. How much was in the tank when filling began?
- A2 litres
- B0 litres
- C8 litres
- D10 litres
Show the answer and explanationHide the explanation
Answer: 2 litres
The tank gains 40 litres in 5 minutes, a rate of 8 litres a minute. Working back three minutes from 26 litres gives 26 - 24 = 2 litres. Assuming it started empty ignores the figures given.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 78ProbabilityChallenge
A bag holds 4 white marbles and 6 black ones. Two marbles are drawn without replacement. What is the probability that both are white?
- A4/25
- B2/15
- C1/5
- D2/5
Show the answer and explanationHide the explanation
Answer: 2/15
The first draw is white with probability 4/10. The second is then drawn from 9 marbles of which 3 are white, so 3/9. Multiplying gives 12/90 = 2/15. Using 4/10 twice gives 4/25 and quietly puts the first marble back.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 79PercentagesStandard
A jacket costs 64 pounds after a 20 percent discount. Enter its original price in pounds.
Student-produced response: write your own answer rather than choosing one.
Show the answer and explanationHide the explanation
Answer: 80
The sale price is 80 percent of the original, so the original is 64 / 0.8 = 80 pounds. Adding 20 percent to 64 gives 76.80, which is a different quantity: 20 percent of the smaller number.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 80RatesStandard
A tap fills a 240-litre tank in 16 minutes. Enter the number of litres it delivers per minute.
Student-produced response: write your own answer rather than choosing one.
Show the answer and explanationHide the explanation
Answer: 15
Dividing the volume by the time gives 240 / 16 = 15 litres a minute.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 81PercentagesFoundation
What is 15 percent of 240?
- A36
- B16
- C24
- D360
Show the answer and explanationHide the explanation
Answer: 36
15 percent is 0.15, and 0.15 x 240 = 36. A useful check: 10 percent is 24 and 5 percent is 12, and 24 + 12 = 36.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 82MeanStandard
Six readings were 12, 15, 11, 18, 14 and 20. What is their mean?
- A14
- B15
- C16
- D14.5
Show the answer and explanationHide the explanation
Answer: 15
The six values total 90, and 90 / 6 = 15. The choice 14.5 is the median — the average of the third and fourth values once sorted — which happens to differ here.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 83RatesStandard
A cyclist covers 54 km in 2 hours and 15 minutes. What is the average speed in kilometres per hour?
- A27
- B21.6
- C24
- D36
Show the answer and explanationHide the explanation
Answer: 24
2 hours 15 minutes is 2.25 hours, and 54 / 2.25 = 24 km/h. Dividing by 2 instead gives 27, which treats the extra quarter-hour as free.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 84ProbabilityStandard
A spinner has 8 equal sectors numbered 1 to 8. What is the probability of landing on a prime number?
- A3/8
- B5/8
- C1/4
- D1/2
Show the answer and explanationHide the explanation
Answer: 1/2
The primes from 1 to 8 are 2, 3, 5 and 7 — four of the eight, so the probability is 1/2. Counting 1 as prime gives 5/8; it is not, because a prime has exactly two distinct factors.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 85Two-way frequenciesStandard
Of 250 people surveyed, 140 are under 40. Of those under 40, 98 use public transport daily. What proportion of the under-40s use public transport daily?
- A39.2 percent
- B56 percent
- C70 percent
- D43 percent
Show the answer and explanationHide the explanation
Answer: 70 percent
The group being asked about is the 140 under-40s, so the calculation is 98 / 140 = 0.70. Dividing by the whole 250 gives 39.2 percent, which answers a question about the survey rather than about the under-40s.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 86Percent changeChallenge
A quantity falls by 25 percent and then rises by 40 percent. What is the overall change?
- A15 percent rise
- B5 percent fall
- CNo change
- D5 percent rise
Show the answer and explanationHide the explanation
Answer: 5 percent rise
Percentage changes multiply rather than add: 0.75 x 1.40 = 1.05, a 5 percent rise. Adding -25 and +40 gives 15, which would only be right if both percentages were of the same starting amount.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 87MedianStandard
Enter the median of the values 8, 3, 11, 6, 9 and 4.
Student-produced response: write your own answer rather than choosing one.
Show the answer and explanationHide the explanation
Answer: 7
Sorted, the values are 3, 4, 6, 8, 9, 11. With six values the median is the average of the third and fourth: (6 + 8) / 2 = 7. Note that 7 is not one of the values, which is normal for an even-sized set.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 88Unit conversionStandard
A recipe calls for 1.5 kg of flour. Enter that quantity in grams.
Student-produced response: write your own answer rather than choosing one.
Show the answer and explanationHide the explanation
Answer: 1500
One kilogram is 1,000 grams, so 1.5 kg is 1,500 g.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 89Proportional relationshipsFoundation
Two lengths are in the ratio 3 : 5, and together they measure 96 cm. What is the shorter length?
- A60 cm
- B36 cm
- C32 cm
- D48 cm
Show the answer and explanationHide the explanation
Answer: 36 cm
The ratio has 3 + 5 = 8 parts, so each part is 96 / 8 = 12 cm and the shorter length is 3 x 12 = 36 cm. The choice 60 is the longer length and 48 is half the total.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 90RatesChallenge
A driver covers 60 km at 60 km/h and the next 60 km at 40 km/h. What is the average speed for the whole journey?
- A50 km/h
- B52 km/h
- C48 km/h
- D45 km/h
Show the answer and explanationHide the explanation
Answer: 48 km/h
Average speed is total distance over total time. The two legs take 1 hour and 1.5 hours, so 120 km in 2.5 hours is 48 km/h. Averaging the two speeds gives 50, which would only be right if equal time were spent at each.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 91ProbabilityStandard
Two fair coins are tossed. What is the probability of getting at least one head?
- A1/2
- B1/4
- C2/3
- D3/4
Show the answer and explanationHide the explanation
Answer: 3/4
The four equally likely outcomes are HH, HT, TH and TT, and three of them contain a head, so the probability is 3/4. It is quicker as 1 minus the probability of no heads: 1 - 1/4.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 92PercentagesChallenge
An account holds 2,000 pounds and earns 5 percent interest each year, added to the balance. What is the balance after two years?
- A2,205 pounds
- B2,200 pounds
- C2,100 pounds
- D2,050 pounds
Show the answer and explanationHide the explanation
Answer: 2,205 pounds
Each year multiplies the balance by 1.05: 2,000 x 1.05 x 1.05 = 2,205 pounds. Taking 5 percent of the original twice gives 2,200 and misses the interest earned on the first year's interest.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 93Percent changeStandard
A shop's weekly takings rose from 3,400 pounds to 3,825 pounds. What was the percentage increase?
- A11.1 percent
- B12.5 percent
- C14.3 percent
- D8.5 percent
Show the answer and explanationHide the explanation
Answer: 12.5 percent
The rise is 425 pounds, measured against the original 3,400: 425 / 3,400 = 0.125, so 12.5 percent. Dividing by the new figure gives 11.1 percent, which is the fall needed to go back.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 94Two-way frequenciesStandard
In a club of 80 members, 52 play chess and 45 play bridge. If 30 play both, how many play neither?
- A17
- B22
- C13
- D8
Show the answer and explanationHide the explanation
Answer: 13
The number playing at least one is 52 + 45 - 30 = 67, so 80 - 67 = 13 play neither. Adding 52 and 45 without removing the overlap gives 97, more members than the club has.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 95MeanStandard
Five numbers have a mean of 18. Four of them are 12, 20, 15 and 22. Enter the fifth number.
Student-produced response: write your own answer rather than choosing one.
Show the answer and explanationHide the explanation
Answer: 21
The five must total 5 x 18 = 90. The four given add to 69, so the fifth is 90 - 69 = 21. Working from the total rather than from the mean is what makes this straightforward.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 96Unit conversionStandard
A journey takes 2 hours and 40 minutes. Enter its length in minutes.
Student-produced response: write your own answer rather than choosing one.
Show the answer and explanationHide the explanation
Answer: 160
Two hours is 120 minutes, and 120 + 40 = 160 minutes.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 97PercentagesFoundation
What is 18 percent of 350?
- A53
- B70
- C18
- D63
Show the answer and explanationHide the explanation
Answer: 63
0.18 x 350 = 63. As a check, 10 percent is 35 and 8 percent is 28, and 35 + 28 = 63.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 98Proportional relationshipsStandard
Two amounts are in the ratio 2 : 7 and total 108. What is the larger amount?
- A84
- B96
- C24
- D54
Show the answer and explanationHide the explanation
Answer: 84
The ratio has 9 parts, so each part is 108 / 9 = 12 and the larger amount is 7 x 12 = 84. The smaller is 24, and the two sum to 108 as a check.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 99ProbabilityStandard
Two fair six-sided dice are rolled. What is the probability that the total is 7?
- A1/12
- B1/6
- C7/36
- D1/9
Show the answer and explanationHide the explanation
Answer: 1/6
Six of the 36 outcomes total 7 — (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — so the probability is 6/36 = 1/6. Seven is the likeliest total, which is worth remembering.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 100Percent decreaseStandard
A weekly figure fell from 250 to 200. What was the percentage decrease?
- A20 percent
- B25 percent
- C50 percent
- D80 percent
Show the answer and explanationHide the explanation
Answer: 20 percent
The fall of 50 is measured against the starting figure: 50 / 250 = 0.20. Dividing by 200 gives 25 percent, which is the rise needed to return.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 101MeanStandard
Six numbers have a mean of 14. Five of them are 9, 17, 12, 20 and 11. Enter the sixth.
Student-produced response: write your own answer rather than choosing one.
Show the answer and explanationHide the explanation
Answer: 15
The six must total 6 x 14 = 84. The five given add to 69, so the sixth is 84 - 69 = 15.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 102RatesStandard
A train covers 45 km in 36 minutes. What is its average speed in kilometres per hour?
- A60
- B75
- C80
- D54
Show the answer and explanationHide the explanation
Answer: 75
36 minutes is 0.6 hours, and 45 / 0.6 = 75 km/h. Dividing by 36 rather than converting to hours first gives a figure per minute, not per hour.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 103PercentagesChallenge
An account of 4,000 pounds earns 3 percent interest a year, added to the balance. What is the balance after two years?
- A4,240 pounds
- B4,120 pounds
- C4,243.60 pounds
- D4,360 pounds
Show the answer and explanationHide the explanation
Answer: 4,243.60 pounds
Each year multiplies by 1.03: 4,000 x 1.03 x 1.03 = 4,243.60. Taking 3 percent of 4,000 twice gives 4,240 and misses the interest earned on the first year's interest.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 104Unit conversionStandard
A plank measures 3.2 metres. Enter its length in centimetres.
Student-produced response: write your own answer rather than choosing one.
Show the answer and explanationHide the explanation
Answer: 320
One metre is 100 centimetres, so 3.2 m is 320 cm.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 105PercentagesFoundation
What is 24 percent of 425?
- A98
- B106
- C120
- D102
Show the answer and explanationHide the explanation
Answer: 102
0.24 x 425 = 102. As a check, 25 percent of 425 is 106.25, so the answer must be slightly below that.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 106Proportional relationshipsStandard
Two amounts are in the ratio 4 : 5 and total 153. What is the larger amount?
- A85
- B68
- C76.5
- D92
Show the answer and explanationHide the explanation
Answer: 85
The ratio has 9 parts, so each part is 153 / 9 = 17 and the larger amount is 5 x 17 = 85. The smaller is 68, and the two sum to 153 as a check.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 107ProbabilityStandard
Two fair six-sided dice are rolled. What is the probability that the total is 5?
- A1/12
- B1/9
- C5/36
- D1/6
Show the answer and explanationHide the explanation
Answer: 1/9
Four of the 36 outcomes total 5 — (1,4), (2,3), (3,2) and (4,1) — so the probability is 4/36 = 1/9. Counting (1,4) and (4,1) as one outcome would halve it wrongly.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 108Percent decreaseStandard
A weekly figure fell from 640 to 544. What was the percentage decrease?
- A17.6 percent
- B96 percent
- C15 percent
- D12 percent
Show the answer and explanationHide the explanation
Answer: 15 percent
The fall of 96 is measured against the starting figure: 96 / 640 = 0.15. Dividing by 544 gives 17.6 percent, which is the rise needed to return.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 109MeanStandard
Seven numbers have a mean of 22. Six of them are 19, 25, 18, 27, 21 and 20. Enter the seventh.
Student-produced response: write your own answer rather than choosing one.
Show the answer and explanationHide the explanation
Answer: 24
The seven must total 7 x 22 = 154. The six given add to 130, so the seventh is 154 - 130 = 24.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 110RatesStandard
A coach covers 84 km in 1 hour and 12 minutes. What is its average speed in kilometres per hour?
- A62
- B75
- C84
- D70
Show the answer and explanationHide the explanation
Answer: 70
1 hour 12 minutes is 1.2 hours, and 84 / 1.2 = 70 km/h. Treating the 12 minutes as 0.12 of an hour gives about 75, which is the commonest conversion slip.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 111PercentagesChallenge
An account of 5,000 pounds earns 4 percent interest a year, added to the balance. What is the balance after two years?
- A5,408 pounds
- B5,400 pounds
- C5,200 pounds
- D5,416 pounds
Show the answer and explanationHide the explanation
Answer: 5,408 pounds
Each year multiplies by 1.04: 5,000 x 1.04 x 1.04 = 5,408. Taking 4 percent of 5,000 twice gives 5,400 and misses the interest earned on the first year's interest.
How did you do?Saved in this browser. Weak Skills will replay this skill. - 112Unit conversionStandard
A bag of flour weighs 2.75 kg. Enter its mass in grams.
Student-produced response: write your own answer rather than choosing one.
Show the answer and explanationHide the explanation
Answer: 2750
One kilogram is 1,000 grams, so 2.75 kg is 2,750 g.
How did you do?Saved in this browser. Weak Skills will replay this skill.
SAT® is a registered trademark of the College Board, which does not endorse this study guide.