Medium is where most scores are actually won and lost. These questions are not tricky for the sake of it, but every one of them has a wrong answer built to catch a specific shortcut.
Every question below is a real item from the SAT Climb bank, tagged medium by the same difficulty model the app uses to build your practice. Pick an answer before you open the explanation.
Math · Problem-Solving and Data Analysis~2 per testMedium tier
None of these repeat the 25 hard Percentages questions, so the two pages together are 45 different questions on this one skill.
Question 1Medium
The number of members in a club increased by 15% from Month 1 to Month 2. If the number of members in Month 2 is n times the number of members in Month 1, what is the value of n?
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Why C is right
Let x be the number of members in Month 1. A 15% increase means the Month 2 membership is x+0.15x=1.15x. Therefore, the Month 2 membership is 1.15 times the Month 1 membership, so n=1.15.
Why the others are wrong
AThis represents only the increase portion (15%) rather than the total multiplier including the original amount.
BThis incorrectly treats the increase as a decrease, using 1 - 0.15 instead of 1 + 0.15.
DThis results from adding 1 + 0.15 + 1 instead of just 1 + 0.15, representing an additive error in combining the base and increase.
Question 2Medium
A store sold 240 items in January. If 240 represents 60% of the total number of items the store had in stock at the beginning of January, how many items did the store have in stock at the beginning of January?
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Why C is right
It's given that 240 items represents 60% of the total stock. This can be written as 240=0.60x, where x is the total number of items in stock. Dividing both sides by 0.60 gives x=400.
Why the others are wrong
AThis is 60% of 240, which incorrectly uses the sold items as the base instead of recognizing that 240 is already 60% of the total.
BThis results from adding 60 to 240 instead of recognizing the multiplicative relationship required for percentage problems.
DThis results from multiplying 240 by 60 instead of dividing by 0.60, representing a sign error in the operation.
Question 3Medium
In a school, 35% of the students play sports. Of all the students who play sports, 40% also participate in music programs. What percentage of all students in the school both play sports and participate in music programs?
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Why B is right
Let x be the total number of students. Then 0.35x play sports. Of these, 40% also participate in music, which is 0.40(0.35x)=0.14x. Therefore, 14% of all students both play sports and participate in music.
Why the others are wrong
AThis results from subtracting 40 - 35 instead of multiplying the percentages.
CThis results from adding 35% and 40% instead of finding the percentage of a percentage through multiplication.
DThis incorrectly uses the sports students as the base for the entire calculation, computing 40% of 35 (treating 35 as if it were 100% of students) and then adding.
Question 4Medium
A store's revenue increased by 15% from January to February. If the February revenue was $9200, what was the January revenue, in dollars?
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Why C is right
Let x be the January revenue. Since revenue increased by 15%, the February revenue equals 1.15x. Setting 1.15x=9200 and solving gives x=9200 ÷ 1.15 = 8000.
Why the others are wrong
AThis is 15% of 9200, not the original revenue.
BThis results from subtracting 15% of February revenue instead of properly reversing the percentage increase.
DThis incorrectly adds 15% to February revenue instead of finding the base before the increase.
Question 5Medium
A quantity decreased by 12% and then increased by 12%. If the final quantity is d times the original quantity, what is the value of d?
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Why A is right
After a 12% decrease, the quantity is 0.88 times the original. After a 12% increase from that point, the quantity is 1.12 times 0.88, which equals 0.88 × 1.12 = 0.9856. Therefore, d=0.9856.
Why the others are wrong
BThis incorrectly assumes the decrease and increase cancel out by adding -12% + 12% = 0%.
CThis incorrectly applies both changes as increases, calculating 1.12 × 0.88 with wrong signs, or treating decrease as increase.
DThis gives only the result after the first decrease (0.88) without applying the second increase.
Question 6Medium
A company's expenses decreased by 12% from the first quarter to the second quarter. If the second quarter expenses were $22000, what were the first quarter expenses, in dollars?
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Why D is right
Let x be the first quarter expenses. After a 12% decrease, the second quarter expenses are 0.88x=22000. Dividing both sides by 0.88 gives x=25000. Therefore, the first quarter expenses were $25000.
Why the others are wrong
AThis incorrectly decreases 22000 by 12% again instead of recognizing that 22000 is already the result after the decrease.
BThis incorrectly subtracts 12 from 22000 instead of calculating 12% of the original value.
CThis incorrectly adds 12% of 22000 to 22000, using 22000 as the base instead of the unknown original value.
Question 7Medium
In a school, 45% of the students play sports. Of the students who play sports, 60% also participate in music programs. What percentage of all students in the school both play sports and participate in music programs?
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Why B is right
Let x represent the total number of students. The number who play sports is 0.45x. Of those, 60% also participate in music, which is 0.60(0.45x)=0.27x. Therefore, 27% of all students both play sports and participate in music programs.
Why the others are wrong
AThis incorrectly subtracts the percentages (45% - 30%) instead of multiplying them.
CThis incorrectly uses 60% of all students as the base instead of 60% of the students who play sports.
DThis adds the two percentages (45% + 60%) instead of finding the compound percentage.
Question 8Medium
A number is increased by 40%, and then the result is decreased by 40%. The final result is what percent of the original number?
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Why A is right
Let the original number be x. After a 40% increase, the result is 1.4x. Decreasing 1.4x by 40% gives 1.4x×0.6=0.84x. Therefore, the final result is 84% of the original number.
Why the others are wrong
BThis incorrectly uses the original number as the base for the second decrease instead of using the increased value.
CThis incorrectly assumes the two percent changes cancel out by adding -40% + 40% = 0%.
DThis incorrectly adds 40% instead of decreasing by 40% in the second step.
Question 9Medium
A town's water usage decreased by 18% from June to July. If the July water usage was 32800 gallons, what was the June water usage, in gallons?
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Why D is right
Let x be the June water usage. After an 18% decrease, the July water usage is 0.82x=32800. Dividing both sides by 0.82 gives x=40000. Therefore, the June water usage was 40000 gallons.
Why the others are wrong
AThis incorrectly decreases 32800 by 18% again instead of recognizing that 32800 is already the result after the decrease.
BThis incorrectly subtracts 18 from 32800 instead of calculating 18% of the original value.
CThis incorrectly adds 18% of 32800 to 32800, using 32800 as the base instead of the unknown original value.
Question 10Medium
The price of a product decreased by 20% and then the new price increased by 25%. The final price is k times the original price. What is the value of k?
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Why B is right
Let x be the original price. After a 20% decrease, the price becomes 0.80x. After a 25% increase from this new price, the price becomes 1.25(0.80x)=1.00x. Therefore, k=1.00.
Why the others are wrong
AThis incorrectly calculates 1.25(0.80) but then subtracts an additional amount, using the wrong base for one of the percentage changes.
CThis incorrectly adds -20% + 25% = 5% to get 1.05 instead of compounding the percentage changes multiplicatively.
DThis incorrectly multiplies by adding the percentages: 0.20 + 1.25 = 1.45 instead of properly compounding.
Question 11Medium
A store decreased the price of a jacket by 20%. If the new price is $96, what was the original price, in dollars?
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Why C is right
Let x be the original price. A 20% decrease means the new price is 80% of the original, so 0.8x=96. Dividing both sides by 0.8 gives x=120. The original price was $120.
Why the others are wrong
AThis results from subtracting 20 from 96 instead of accounting for the percentage decrease properly.
BThis incorrectly applies the 20% to the new price ($96) instead of recognizing that $96 represents 80% of the original.
DThis results from adding 20% of the new price to the new price, treating the decrease base incorrectly.
Question 12Medium
The enrollment at a university increased by 8% from 2018 to 2019 and then decreased by 8% from 2019 to 2020. The 2020 enrollment is k times the 2018 enrollment. What is the value of k?
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Why A is right
Let x be the 2018 enrollment. After an 8% increase, the 2019 enrollment is 1.08x. After an 8% decrease from 2019, the 2020 enrollment is 0.92(1.08x)=0.9936x. Therefore, k=0.9936.
Why the others are wrong
BThis incorrectly adds +8% + (-8%) = 0% to conclude the enrollment is unchanged, instead of compounding the percentage changes multiplicatively.
CThis incorrectly reverses the order of operations or applies the wrong sign, treating both changes as increases.
DThis incorrectly multiplies 1.08 by 8% treated as an additive factor instead of 0.92.
Question 13Medium
A store's revenue in January was $18000. If this represents 60% of the store's revenue in February, what was the store's revenue, in dollars, in February?
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Why C is right
It's given that $18000 represents 60% of February's revenue. This means 0.60x=18000, where x is February's revenue. Dividing both sides by 0.60 gives x=30000.
Why the others are wrong
AThis incorrectly calculates 60% of January's revenue instead of finding the value for which January is 60%.
BThis incorrectly adds 60% of January's revenue to January's revenue instead of recognizing that January is already 60% of the target.
DThis incorrectly divides by 0.60 in the wrong direction, computing 18000/0.006 instead of 18000/0.60.
Question 14Medium
The population of a town increased by 20% from 2020 to 2021 and then decreased by 10% from 2021 to 2022. If the 2022 population is t times the 2020 population, what is the value of t?
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Why B is right
After a 20% increase, the 2021 population is 1.20 times the 2020 population. After a 10% decrease from 2021 to 2022, the population is 0.90 times the 2021 population. Therefore, t=1.20×0.90=1.08.
Why the others are wrong
AThis incorrectly gives the net additive change, 20% - 10% = 10%, as 0.10 instead of computing the compound multiplier.
CThis incorrectly adds the percentage changes instead of compounding: 1 + 0.20 - 0.10.
DThis incorrectly treats the decrease as based on the original population, calculating 1.20 + 0.10.
Question 15Medium
The value of an investment increased by 15% in the first year and then increased by 10% in the second year. If the value at the end of the second year is k times the original value, what is the value of k?
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Why B is right
After a 15% increase, the value becomes 1.15 times the original. After an additional 10% increase, the value becomes 1.10 times that amount. Therefore, k=1.15×1.10=1.265.
Why the others are wrong
AThis incorrectly adds the percentages (15% + 10% = 25%) instead of compounding them multiplicatively.
CThis results from adding the percentages and then treating the result as a decrease or miscalculating the multiplicative factor.
DThis represents only the first year's percentage increase without accounting for the second year or the base multiplier.
Question 16Medium
A company's revenue increased by 15% from Year 1 to Year 2, then increased by 20% from Year 2 to Year 3. If the Year 3 revenue is k times the Year 1 revenue, what is the value of k?
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Why C is right
After a 15% increase, the Year 2 revenue is 1.15 times the Year 1 revenue. After another 20% increase, the Year 3 revenue is 1.20 times the Year 2 revenue. Therefore, k=1.15×1.20=1.38.
Why the others are wrong
AThis incorrectly treats the percent increases as decreases and multiplies 0.85 by 0.80.
BThis incorrectly adds the two percentages (15% + 20% = 35%) rather than compounding them.
DThis incorrectly applies the 20% increase to the original amount (1.15 + 0.20 × 1.15 = 1.38, but this was miscalculated as 1.42).
Question 17Medium
In a survey, 55% of respondents preferred Brand A. Of those who preferred Brand A, 36% also preferred Product X. What percentage of all respondents preferred both Brand A and Product X?
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Why B is right
Let x represent the total number of respondents. The number who preferred Brand A is 0.55x. Of those, 36% also preferred Product X, which is 0.36(0.55x)=0.198x. Therefore, 19.8% of all respondents preferred both.
Why the others are wrong
AThis incorrectly subtracts the percentages (55% - 36%) instead of multiplying them.
CThis incorrectly uses all respondents as the base for the 36%, calculating 0.55x + 0.36(0.55x).
DThis adds the two percentages (55% + 36%) instead of finding the compound percentage.
Question 18Medium
A warehouse's inventory increased by 25% from Month 1 to Month 2, then decreased by 10% from Month 2 to Month 3. If the Month 3 inventory is p times the Month 1 inventory, what is the value of p?
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Why B is right
After a 25% increase, the Month 2 inventory is 1.25 times the Month 1 inventory. After a 10% decrease, the Month 3 inventory is 0.90 times the Month 2 inventory. Therefore, p=1.25×0.90=1.125.
Why the others are wrong
AThis incorrectly treats the 25% increase as a decrease, calculating 0.75 × 0.90.
CThis incorrectly adds the two percentages (25% - 10% = 15%) and treats the result as 1.15.
DThis incorrectly treats the 10% decrease as an increase and calculates 1.25 × 1.10, but arrives at the wrong value.
Question 19Medium
In a school, 45% of the students play sports. Of all the students who play sports, 60% also play a musical instrument. What percentage of the students in the school play sports and also play a musical instrument?
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Why B is right
Let x represent the total number of students. The number who play sports is 0.45x. Of those, 60% also play an instrument, which is 0.60(0.45x)=0.27x. Therefore, 27% of all students play sports and a musical instrument.
Why the others are wrong
AThis incorrectly subtracts 45% - 60% instead of multiplying the percentages.
CThis incorrectly calculates 60% of 45 as if 45 were the total population rather than 45% of the population.
DThis incorrectly adds 45% + 60% instead of finding 60% of 45%.
Question 20Medium
The value of an investment increased by 20% in year 1 and then decreased by 20% in year 2. If the value at the end of year 2 is $9600, what was the original value, in dollars?
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Why B is right
If x is the original value, after a 20% increase it becomes 1.2x, then after a 20% decrease it becomes 1.2x×0.8=0.96x. Setting 0.96x=9600 gives x=10000.
Why the others are wrong
AThis results from incorrectly assuming the 20% increase and 20% decrease cancel out exactly.
CThis results from computing 9600/0.8, treating the final value as if it only underwent the 20% decrease.
DThis results from computing 9600/1.2, treating the final value as if it only underwent the 20% increase.
What to do after medium
Medium is the tier that decides most scores. If these are landing, the hard set is where the remaining points are.
Questions are written by SAT Climb and drawn from its own item bank. SAT® is a registered trademark of College Board, which is not affiliated with and does not endorse SAT Climb.