SSAT Middle Level Quiz: Percent Of A Number
20 questions · exam conditions
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Percent Of A NumberQuestion 1 of 20

A tablet cost $250. A sale reduced the price by 18%. The discount was based on the original price. What was the new price?

$45 new price
$232 new price
$205 new price
$295 new price
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SSAT Middle Level Quiz

SSAT Middle Level Quiz: Percent Of A Number

Practice Percent Of A Number 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 Percent Of A Number, 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 tablet cost $250. A sale reduced the price by 18%. The discount was based on the original price. What was the new price?

  1. $45 new price
  2. $232 new price
  3. $205 new price (correct answer)
  4. $295 new price
Explanation: This question tests middle school mathematics skills in calculating a percentage of a number. Understanding percentages involves converting the percentage to a decimal and multiplying by the total to find the part. In this scenario, a specific real-world context is used to apply this concept, such as calculating a discount on a tablet. The correct answer is determined by accurately performing the multiplication of the percentage as a decimal with the given number. A common distractor might involve an error in decimal placement or misunderstanding the scenario's requirements, resulting in an incorrect calculation. Encourage students to practice converting percentages to decimals and multiplying, check work by estimating if the answer is reasonable. Be mindful of context clues that indicate the correct operation.

Question 2

At a school fundraiser, 35% of the students bought cookies, and 40% of those cookie buyers also bought lemonade. If 84 students bought both cookies and lemonade, how many total students participated in the fundraiser?

  1. 600 (correct answer)
  2. 700
  3. 540
  4. 420
  5. 480
Explanation: When you encounter percentage problems involving multiple groups, work backwards from the final number to find the total. This question tests your ability to handle "percentages of percentages." Let's set up the relationships step by step. If we call the total number of students xx, then 35% of students bought cookies, which equals 0.35x0.35x students. Of those cookie buyers, 40% also bought lemonade. So the number who bought both items is 0.40×0.35x=0.14x0.40 \times 0.35x = 0.14x. Since we know that 84 students bought both cookies and lemonade, we can write: 0.14x=840.14x = 84. Solving for xx: x=84÷0.14=600x = 84 ÷ 0.14 = 600. Let's verify: If 600 students participated, then 600×0.35=210600 \times 0.35 = 210 bought cookies, and 210×0.40=84210 \times 0.40 = 84 bought both items. ✓ Looking at the wrong answers: Choice B (700) would give us 700×0.14=98700 \times 0.14 = 98 students buying both items, not 84. Choice C (540) would result in 540×0.14=75.6540 \times 0.14 = 75.6 students, which is too low. Choice D (420) would give us 420×0.14=58.8420 \times 0.14 = 58.8 students, also too low. The correct answer is A (600). Strategy tip: In nested percentage problems, multiply the percentages together to find what fraction of the total the final group represents. Here, 35%×40%=14%35\% \times 40\% = 14\% of all students bought both items.

Question 3

In a survey, 24% of respondents preferred chocolate ice cream. If this represents 156 people, what was the total number of people surveyed?

  1. 650 (correct answer)
  2. 780
  3. 520
  4. 624
  5. 468
Explanation: This is a classic percentage problem where you know the percentage and the actual number, but need to find the total. When you see this type of question, set up the relationship: part = percentage × whole. Here, 24% of the total equals 156 people. Let's call the total number of people surveyed xx. So we have: 0.24x=1560.24x = 156 To solve for xx, divide both sides by 0.24: x=1560.24=650x = \frac{156}{0.24} = 650 You can verify this: 24% of 650 = 0.24 × 650 = 156 ✓ Now let's see why the other answers are wrong. Choice B (780) would mean 24% × 780 = 187.2 people, which is too many. Choice C (520) gives us 24% × 520 = 124.8 people, which is too few. Choice D (624) results in 24% × 624 = 149.76 people, also too few. The correct answer is A (650). Strategy tip: When solving "what is the total" percentage problems, remember the formula: Total = Part ÷ Percentage (as a decimal). Also, always check your answer by multiplying back: does your total × the given percentage equal the given part? This quick verification can catch calculation errors and boost your confidence.

Question 4

A recipe calls for 2.5 cups of flour to make 16 muffins. If Janet wants to make only 60% as many muffins, how many cups of flour should she use?

  1. 1.5 (correct answer)
  2. 1.8
  3. 2.0
  4. 1.2
  5. 1.6
Explanation: This problem tests proportional reasoning and percentage calculations, which are fundamental skills in ratio and proportion problems. When you see a recipe problem asking for a different quantity, you need to scale all ingredients proportionally. First, determine how many muffins Janet wants to make: 60% of 16 muffins equals 0.60×16=9.60.60 \times 16 = 9.6 muffins. Since you can't make partial muffins in practice, this represents making 60% of the original batch. Now set up a proportion to find the flour needed. If 2.5 cups makes 16 muffins, then xx cups makes 9.6 muffins: 2.5 cups16 muffins=x cups9.6 muffins\frac{2.5 \text{ cups}}{16 \text{ muffins}} = \frac{x \text{ cups}}{9.6 \text{ muffins}} Cross multiply: 2.5×9.6=16x2.5 \times 9.6 = 16x, so 24=16x24 = 16x, which gives x=1.5x = 1.5 cups. Alternatively, since Janet is making 60% as many muffins, she needs 60% as much flour: 0.60×2.5=1.50.60 \times 2.5 = 1.5 cups. Looking at the wrong answers: Choice B (1.8) might result from incorrectly calculating 60% of something other than 2.5, or from computational errors. Choice C (2.0) could come from mistakenly thinking 60% means reducing by 0.5 cups. Choice D (1.2) might result from calculating 60% - 40% = 20% off the original, then subtracting incorrectly. Strategy tip: In proportion problems, always check if you can solve more directly. Here, "60% as many muffins" means you need "60% as much of each ingredient" – sometimes the shortcut is clearer than setting up the full proportion.

Question 5

In a parking lot, 45% of cars are sedans. Of the sedan owners, 20% have sunroofs. If there are 72 sedans with sunroofs, how many cars are in the parking lot?

  1. 800 (correct answer)
  2. 720
  3. 900
  4. 600
  5. 1000
Explanation: When you encounter percentage problems with multiple layers like this one, work backwards from the final known quantity to find the total. You know there are 72 sedans with sunroofs. Since 20% of sedan owners have sunroofs, these 72 cars represent 20% of all sedans. To find the total number of sedans: 72÷0.20=36072 ÷ 0.20 = 360 sedans total. Now you know sedans make up 45% of all cars in the parking lot, and there are 360 sedans. To find the total number of cars: 360÷0.45=800360 ÷ 0.45 = 800 cars. Looking at the wrong answers: Choice B (720) is what you'd get if you mistakenly thought the 72 sunroof sedans represented 10% of total cars instead of working through both percentage relationships properly. Choice C (900) results from incorrectly calculating 360 ÷ 0.40 instead of 0.45, mixing up the sedan percentage. Choice D (600) comes from errors in the backwards calculation, possibly confusing which percentages to divide by. The correct answer is A: 800 cars. Remember this strategy for layered percentage problems: identify your starting point (the concrete number you're given), then work backwards through each percentage relationship step by step. Always check that your percentages correspond to the right groups—here, 20% applies to sedans only, while 45% applies to all cars in the lot.

Question 6

A jacket originally costs $120. During a clearance sale, it was marked down 30%. The next week, the sale price was reduced by an additional 25%. What is the final price of the jacket?

  1. $63 (correct answer)
  2. $54
  3. $72
  4. $66
  5. $90
Explanation: When you see consecutive percentage discounts, remember that each discount applies to the current price, not the original price. You can't simply add the percentages together. Let's work through this step by step. The jacket starts at $120. The first discount is 30%, so you need to find what remains after removing 30%. Since 30% off means you pay 70% of the original price: $120×0.70=84120 \times 0.70 = 84 $. The sale price after the first markdown is $84. Now the second discount of 25% applies to this new price of $84, not the original $120. Again, 25% off means you pay 75% of the current price: $$84 \times 0.75 = 63$$. The final price is $63. Looking at the wrong answers: Choice B ($54) is what you'd get if you incorrectly added the percentages (30% + 25% = 55% total discount, leaving 45% of 120).ChoiceC(120). Choice C (72) might result from applying the discounts in reverse order or making calculation errors. Choice D ($66) could come from various computational mistakes in the two-step process. The correct answer is A ($63). Strategy tip: For consecutive percentage changes, always apply each percentage to the result of the previous calculation, never to the original amount. A quick way to check your work is to multiply the original price by both remaining percentages at once: $$120 \times 0.70 \times 0.75 = 63$$.

Question 7

A store offers a loyalty program where customers earn 2.5% cashback on purchases. If Maria earned $18.75 in cashback last month, what was the total amount of her purchases?

  1. $750.00 (correct answer)
  2. $468.75
  3. $625.00
  4. $750.25
  5. $937.50
Explanation: When you encounter percentage problems involving cashback or earnings, you're working with the relationship between a part (the cashback) and the whole (total purchases). The key insight is that the cashback represents a percentage of the original purchase amount. To find Maria's total purchases, you need to work backwards from the cashback amount. Since she earned 2.5% of her purchases as cashback, you can set up the equation: 0.025×total purchases=$18.750.025 \times \text{total purchases} = \$18.75 To solve for the total purchases, divide both sides by 0.025: total purchases=$18.750.025=$750.00\text{total purchases} = \frac{\$18.75}{0.025} = \$750.00 You can verify this: $750.00×0.025=$18.75\$750.00 \times 0.025 = \$18.75 ✓ Looking at the wrong answers: Choice B ($468.75) would result from incorrectly multiplying 18.75by25insteadofdividingby0.025.ChoiceC(18.75 by 25 instead of dividing by 0.025. Choice C (625.00) might come from using 3% instead of 2.5% in your calculations. Choice D ($750.25) is close to the correct answer but includes an extra 25 cents, possibly from a decimal place error during calculation. The correct answer is A) $750.00. Study tip: When working with percentage problems, always identify whether you're finding the part or the whole. If you have the percentage and the part (like cashback), divide the part by the decimal form of the percentage to find the whole. Practice converting percentages to decimals quickly—2.5% becomes 0.025.

Question 8

A pizza restaurant charges $12 for a large pizza. On Tuesdays, they offer a 25% discount. If sales tax is 8%, what is the total cost of a large pizza on Tuesday?

  1. $9.72 (correct answer)
  2. $9.00
  3. $10.80
  4. $11.88
  5. $12.96
Explanation: This problem tests your ability to apply multiple percentage changes in sequence - a key skill for real-world shopping scenarios and standardized tests. When working with discounts and taxes, always apply them step by step in the correct order. Start with the original price, apply the discount first, then calculate tax on the discounted price. First, calculate the Tuesday discount: 25% of $12 = $0.25×12=30.25 \times 12 = 3 .Sothediscountedpriceis. So the discounted price is 12−3=912 - 3 = 9 $. Next, apply the 8% sales tax to the discounted price: 8% of $9 = $$0.08 \times 9 = 0.72.Thefinaltotalis. The final total is 9 + 0.72 = 9.72$$. Looking at the wrong answers: Choice B (9.00)representsthediscountedpricebeforeaddingtax−acommonmistakewhenstudentsforgetthattaxstillappliesafteradiscount.ChoiceC(9.00) represents the discounted price before adding tax - a common mistake when students forget that tax still applies after a discount. Choice C (10.80) occurs when you incorrectly apply the tax to the original $12 price (giving $12.96) then subtract the $3 discount, or when you calculate the net effect as 17% of 12plustheoriginalprice.ChoiceD(12 plus the original price. Choice D (11.88) happens when you apply the tax first ($12.96) then try to subtract the discount amount, forgetting that discounts should be calculated on the original price. Remember this sequence: discount first, then tax. Sales tax is always calculated on the amount the customer actually pays for the item, which is the post-discount price. This order matters because it affects your final answer.

Question 9

In a class election, candidate A received 45% of the votes, candidate B received 35% of the votes, and the remaining votes went to candidate C. If candidate C received 24 votes, how many students voted in total?

  1. 80 students
  2. 96 students
  3. 108 students
  4. 120 students (correct answer)
  5. 144 students
Explanation: This is a percentage problem where you need to work backwards from a known quantity to find the total. When you see a problem giving you percentages and one actual number, think about what portion that number represents. First, find what percentage of votes candidate C received. Since A got 45% and B got 35%, candidate C received the remainder: 100%−45%−35%=20%100\% - 45\% - 35\% = 20\% of the total votes. Now you know that 24 votes represents 20% of all votes cast. To find the total, set up the equation: 0.20×total votes=240.20 \times \text{total votes} = 24. Solving for the total: total votes=240.20=2415=24×5=120\text{total votes} = \frac{24}{0.20} = \frac{24}{\frac{1}{5}} = 24 \times 5 = 120 students. Let's check why the other answers are wrong. Answer A (80 students) would mean C received 2480=30%\frac{24}{80} = 30\% of votes, but we calculated C should have 20%. Answer B (96 students) gives C 2496=25%\frac{24}{96} = 25\% of votes, still incorrect. Answer C (108 students) would mean C received about 22% of votes, which is close but not the exact 20% we calculated. The correct answer is D (120 students), where C's 24 votes represent exactly 20% of the total. Remember this pattern: when you know a percentage and its corresponding value, divide the value by the decimal form of the percentage to find the whole. Always verify your percentages add up to 100% before solving.

Question 10

At a bookstore, 60% of customers buy fiction books, and 30% of all customers buy both fiction and non-fiction books. What percent of fiction buyers also buy non-fiction books?

  1. 18%
  2. 20%
  3. 30%
  4. 40%
  5. 50% (correct answer)
Explanation: This question tests conditional probability - specifically, finding what percentage of one group also belongs to another group. When you see overlapping categories like this, you need to distinguish between "percent of all customers" versus "percent of a specific subgroup." You're told that 60% of all customers buy fiction books, and 30% of all customers buy both fiction and non-fiction books. To find what percent of fiction buyers also buy non-fiction, you need to calculate: customers who buy bothcustomers who buy fiction×100%\frac{\text{customers who buy both}}{\text{customers who buy fiction}} \times 100\% This gives you: 30%60%=12=50%\frac{30\%}{60\%} = \frac{1}{2} = 50\% So 50% of fiction buyers also buy non-fiction books. Since this isn't among the choices A-D, the correct answer must be E. Let's examine why the other answers are wrong: A) 18% might come from incorrectly multiplying 60% × 30% = 18%, but this operation has no logical meaning here. B) 20% could result from mistakenly calculating 60% - 30% = 30%, then somehow getting 20%, but this doesn't address the conditional relationship. C) 30% is a trap - this is the percentage of all customers who buy both types, not the percentage of fiction buyers who also buy non-fiction. D) 40% doesn't correspond to any logical calculation from the given information. Remember: when dealing with overlapping groups, always check whether the question asks for a percentage of the whole population or a percentage of a subgroup. The denominator changes everything in conditional probability problems.

Question 11

In a survey of 250 people about their favorite beverages, 36% chose coffee, 28% chose tea, and 16% chose both coffee and tea. What percent of people chose neither coffee nor tea?

  1. 20%
  2. 36%
  3. 44%
  4. 48%
  5. 52% (correct answer)
Explanation: When you encounter overlapping sets problems like this one, you need to use the principle of inclusion-exclusion to avoid double-counting people who chose both beverages. Let's work through this systematically. Of the 250 people surveyed, 36% chose coffee and 28% chose tea. However, 16% chose both beverages, so simply adding 36% + 28% = 64% would count these overlap people twice. Using inclusion-exclusion: People who chose coffee OR tea = 36% + 28% - 16% = 48%. This means 48% of people chose at least one of these beverages, so 100% - 48% = 52% chose neither coffee nor tea. Since 52% isn't among the given options A through D, the correct answer must be E (which typically means "none of the above" or represents an unlisted percentage). Looking at the wrong answers: A) 20% severely underestimates by ignoring much of the data. B) 36% simply takes the coffee percentage, showing confusion about what the question asks. C) 44% might result from incorrectly calculating 100% - 36% - 20% (where 20% comes from 36% - 16%), demonstrating flawed logic about the overlap. D) 48% is actually the percentage who chose at least one beverage, representing the opposite of what we want. Strategy tip: In overlapping sets problems, always remember the inclusion-exclusion formula: Total = Group 1 + Group 2 - Overlap. Then subtract from 100% to find "neither." Watch for answer choices that represent common calculation errors or the opposite of what's asked.

Question 12

A concert hall has 1,200 seats. On Friday night, 85% of the seats were filled. On Saturday night, attendance increased by 20% compared to Friday. How many people attended the Saturday night concert?

  1. 1,020
  2. 1,080
  3. 1,200
  4. 1,224 (correct answer)
  5. 1,440
Explanation: This is a multi-step percentage problem that requires you to calculate percentages sequentially. When you see questions involving percentage increases based on previous amounts, work through each step methodically. First, find Friday night's attendance. With 1,200 total seats and 85% filled: 1,200×0.85=1,0201,200 \times 0.85 = 1,020 people attended Friday. Next, calculate Saturday's attendance. The key phrase is "attendance increased by 20% compared to Friday" — this means 20% more than Friday's 1,020 attendees, not 20% more than the hall's capacity. Saturday's attendance is: 1,020×1.20=1,2241,020 \times 1.20 = 1,224 people. Looking at the wrong answers: Choice (A) gives 1,020, which is only Friday's attendance — you'd get this if you stopped after the first calculation. Choice (B) shows 1,080, which you'd get if you incorrectly added 20% of the total capacity (240 seats) to Friday's attendance instead of 20% of Friday's actual attendance. Choice (C) gives 1,200, which is the hall's total capacity — you might choose this if you mistakenly thought Saturday was sold out. The correct answer is (D) 1,224. Strategy tip: In multi-step percentage problems, pay close attention to what each percentage refers to. The phrase "increased by X% compared to [previous amount]" means you multiply the previous amount by (1 + X%), not the original base number. Always identify your starting point for each calculation.

Question 13

Sarah scored 85% on a test with 60 questions. Later, she realized that 3 of her correct answers were actually marked wrong by mistake. What percent of the questions did she actually answer correctly?

  1. 90% (correct answer)
  2. 88%
  3. 87%
  4. 92%
  5. 89%
Explanation: When you encounter percentage problems involving corrections or adjustments, always work with the actual numbers first, then convert back to percentages at the end. Sarah initially scored 85% on 60 questions. To find how many she got right: 60×0.85=5160 \times 0.85 = 51 questions correct. However, 3 of her correct answers were mistakenly marked wrong, meaning she actually answered correctly on 51+3=5451 + 3 = 54 questions. Converting back to a percentage: 5460=0.90=90%\frac{54}{60} = 0.90 = 90\%. Looking at the wrong answers: Choice B (88%) represents a common calculation error where students might add the 3 questions but make an arithmetic mistake in the final conversion. Choice C (87%) could result from incorrectly adding only 2 questions instead of 3, giving 53 correct answers. Choice D (92%) might occur if students mistakenly think the original 85% was out of 57 questions (60 - 3) rather than understanding that the 3 questions were already counted in the original 60. The key strategy here is to always convert percentages to actual numbers when making adjustments, then convert back to percentages. Don't try to work directly with percentages when adding or subtracting specific quantities. Also, pay careful attention to what the percentage is "of" – in this case, Sarah's final percentage is still out of the original 60 questions, not a reduced number.

Question 14

What is 15% of 40% of 200?

  1. 12 (correct answer)
  2. 18
  3. 24
  4. 30
  5. 32
Explanation: When you encounter a problem asking for a percentage "of" another percentage "of" a number, you're dealing with successive percentage calculations. The key word "of" means multiplication, so you'll multiply the percentages together before applying them to the base number. To find 15% of 40% of 200, start by converting the percentages to decimals: 15% = 0.15 and 40% = 0.40. Then multiply them together: 0.15×0.40=0.060.15 \times 0.40 = 0.06, which equals 6%. Finally, take 6% of 200: 0.06×200=120.06 \times 200 = 12. Alternatively, you can work step by step: first find 40% of 200, which gives you 0.40×200=800.40 \times 200 = 80, then find 15% of that result: 0.15×80=120.15 \times 80 = 12. Looking at the wrong answers: Choice B (18) likely comes from incorrectly adding the percentages (15% + 40% = 55%, then finding 55% of some wrong base). Choice C (24) might result from finding 40% of 15% of 200 in the wrong order, or from calculation errors. Choice D (30) could come from finding 15% of 200 directly while ignoring the 40% step entirely. The correct answer is A) 12. Study tip: When you see "percentage of percentage" problems, remember that "of" means multiply. Convert both percentages to decimals, multiply them together to get your final percentage, then apply it to the base number. This approach prevents order-of-operations mistakes.

Question 15

During a clearance sale, all items are marked 40% off. Additionally, customers with a membership card get an extra 15% off the sale price. If a member pays $35.70 for an item, what was the original price?

  1. $42.00
  2. $51.00
  3. $59.50
  4. $65.00
  5. $70.00 (correct answer)
Explanation: When you encounter multi-step discount problems, you need to work backwards from the final price through each discount layer to find the original amount. Let's trace through the discounts systematically. First, the item gets marked 40% off, meaning customers pay 60% of the original price. Then members get an additional 15% off the already-reduced sale price, so they pay 85% of the sale price. If we call the original price xx, then:
  • After 40% off: Price becomes 0.60x0.60x
  • After additional 15% off: Final price = 0.85×0.60x=0.51x0.85 × 0.60x = 0.51x
Since the member paid $35.70, we have: 0.51x=35.700.51x = 35.70 Solving for xx: x=35.70÷0.51=70x = 35.70 ÷ 0.51 = 70 So the original price was $70.00, which corresponds to answer choice E. Let's check why the other options are wrong:
  • Choice A ($42.00): This would result in a final price of $21.42, far too low
  • Choice B ($51.00): This gives a final price of $26.01, still too low
  • Choice C ($59.50): This yields a final price of $30.35, closer but still incorrect
  • Choice D ($65.00): This produces a final price of $33.15, close but not exact
The key strategy here is recognizing that sequential percentage discounts multiply together (60% × 85% = 51% of original), not add. Always work backwards from the final amount when given multiple discounts, and remember that "15% off the sale price" means you pay 85% of that reduced amount.

Question 16

A savings account earns 3% annual interest. If the account balance after one year is $1,236, what was the original principal amount?

  1. $1,165.50
  2. $1,180.00
  3. $1,199.07
  4. $1,200.00 (correct answer)
  5. $1,272.48
Explanation: When you encounter interest problems where you know the final amount but need to find the original principal, you're working backwards from compound growth. The key relationship is: Final Amount = Principal × (1 + interest rate). To find the original principal, you need to set up the equation: $1,236 = Principal × (1 + 0.03). This simplifies to $1,236 = Principal × 1.03. Dividing both sides by 1.03: Principal = $1,236 ÷ 1.03 = $1,200. Let's verify: $1,200 × 1.03 = $1,236 ✓ Now examine why the other answers are wrong. Choice A ($1,165.50) represents a common error where students subtract 3% from the final amount instead of dividing by 1.03. This gives $1,236 × 0.97 = 1,199.07,butthenstudentsmightroundincorrectly.ChoiceB(1,199.07, but then students might round incorrectly. Choice B (1,180.00) likely comes from incorrectly calculating 1,236−(1,236 - (1,236 × 0.03), which shows confusion about what the 3% applies to. Choice C ($1,199.07) is exactly what you get when you mistakenly subtract 3% from the final amount: $1,236 × 0.97 = $1,199.07. The correct answer is D ($1,200.00). Strategy tip: For "working backwards" interest problems, always divide the final amount by (1 + interest rate) rather than subtracting the interest percentage. The trap answers typically come from subtraction methods, so division is your reliable path to the correct answer.

Question 17

A basketball team won 65% of their games in the first half of the season and 75% of their games in the second half. If they played 20 games in each half, what percent of all their games did they win?

  1. 65%
  2. 68%
  3. 70% (correct answer)
  4. 72%
  5. 75%
Explanation: When you encounter percentage problems involving different groups or time periods, you need to find the actual numbers first, then calculate the overall percentage from the combined results. Let's work through this step by step. In the first half, the team won 65% of 20 games: 0.65×20=130.65 \times 20 = 13 games. In the second half, they won 75% of 20 games: 0.75×20=150.75 \times 20 = 15 games. Total games won: 13+15=2813 + 15 = 28 games Total games played: 20+20=4020 + 20 = 40 games Overall winning percentage: 2840=0.70=70%\frac{28}{40} = 0.70 = 70\% The correct answer is C) 70%. Now let's see why the other choices are wrong. Choice A) 65% simply uses the first half's percentage, ignoring the second half entirely. Choice B) 68% might result from incorrectly weighting the percentages or making calculation errors. Choice D) 72% is close but could come from rounding errors or mixing up the calculation steps. The most tempting wrong approach is to average the two percentages: 65%+75%2=70%\frac{65\% + 75\%}{2} = 70\%. While this happens to give the right answer here, it only works because both halves had equal numbers of games. If the halves had different numbers of games, simply averaging percentages would be incorrect. Strategy tip: Always convert percentages to actual numbers first, then recalculate the overall percentage from the totals. Never just average percentages unless you're certain the groups are equal in size.

Question 18

A school's enrollment increased by 15% this year to 1,380 students. What was the enrollment last year?

  1. 1,200 students (correct answer)
  2. 1,173 students
  3. 1,265 students
  4. 1,323 students
  5. 1,150 students
Explanation: When you see a problem where something "increased by a percent to reach a final value," you're working backwards from the result to find the original amount. This is a reverse percentage problem. Let's call last year's enrollment xx. If enrollment increased by 15%, then this year's enrollment equals last year's enrollment plus 15% of last year's enrollment. In equation form: x+0.15x=1.15x=1,380x + 0.15x = 1.15x = 1,380. To find xx, divide both sides by 1.15: x=1,3801.15=1,200x = \frac{1,380}{1.15} = 1,200. You can verify this: 15% of 1,200 is 180, and 1,200 + 180 = 1,380 ✓ Looking at the wrong answers: Choice B (1,173) likely comes from incorrectly subtracting 15% of 1,380 from 1,380. This gives 1,380−(0.15×1,380)=1,380−207=1,1731,380 - (0.15 \times 1,380) = 1,380 - 207 = 1,173, but this logic is backwards. Choice C (1,265) might result from calculation errors or confusion about the percentage relationship. Choice D (1,323) appears to come from subtracting a smaller percentage, perhaps mixing up the 15% increase with a different calculation. The key insight is recognizing that if something increases by 15%, the final amount represents 115% of the original. Always set up your equation as: (original amount) × (1 + percentage as decimal) = final amount. This framework works for any "increased by" percentage problem and helps you avoid the common trap of working with the final amount incorrectly.

Question 19

A store sells apples for $2.40 per pound. During a promotion, customers get 25% more apples for the same price. What is the effective price per pound during the promotion?

  1. $1.92 (correct answer)
  2. $1.80
  3. $2.00
  4. $2.10
  5. $3.00
Explanation: When you see a promotion offering "more for the same price," you need to determine the new effective rate by figuring out how much you're actually getting per dollar spent. Let's work through this step-by-step. Normally, you pay $2.40 for 1 pound of apples. During the promotion, you pay the same $2.40 but receive 25% more apples. So you get $1+0.25=1.251 + 0.25 = 1.25 $ pounds for $2.40. To find the effective price per pound, divide the total cost by the actual amount received: $\frac{\2.40}{1.25 \text{ pounds}} = $1.92 \text{ per pound}$$ This makes (A) $1.92 the correct answer. Let's examine why the other choices are wrong. Choice (B) $1.80 would result from incorrectly calculating 25% of 2.40(2.40 (0.60) and subtracting it from the original price—this confuses a percentage discount with getting more product. Choice (C) $2.00 might come from rough mental math that doesn't properly account for the 25% increase in quantity. Choice (D) $2.10 could result from subtracting a smaller percentage (like 12.5%) from the original price, showing incomplete calculation. Remember this key strategy: when promotions give you "more for the same price," always calculate the new effective rate by dividing the price by the increased quantity you receive. Don't fall into the trap of simply applying the percentage to the price—focus on what you're actually getting per unit.

Question 20

A company's stock price decreased by 20% on Monday, then increased by 25% on Tuesday. If the stock price was $80 at the end of Tuesday, what was the original price before Monday?

  1. $64.00
  2. $76.80
  3. $80.00 (correct answer)
  4. $84.00
  5. $96.00
Explanation: When you see percentage changes applied sequentially, you need to work backwards from the final value to find the original amount. The key insight is that percentage changes are multiplicative, not additive. Let's call the original price xx and track the changes step by step. After Monday's 20% decrease, the stock was worth 0.80x0.80x (since losing 20% means keeping 80%). After Tuesday's 25% increase, the price became 0.80x×1.25=x0.80x \times 1.25 = x. Notice that 0.80×1.25=1.000.80 \times 1.25 = 1.00, which means the stock returned to its original price. Since we know the final price was $80, and this equals the original price, the answer is $x=80x = 80 $. Let's verify: Starting at $80, a 20% decrease gives us 80×0.80=6480 \times 0.80 = 64. Then a 25% increase gives us 64×1.25=8064 \times 1.25 = 80. Perfect! Now for the wrong answers: Choice (A) $64.00 represents the price after Monday's decrease, not the original price. Choice (B) $76.80 might tempt you if you incorrectly calculated the percentage changes or made an arithmetic error in the backwards calculation. Choice (D) $84.00 could result from misunderstanding the direction of the percentage changes or making calculation mistakes. Study tip: When dealing with sequential percentage changes, always multiply the decimal forms rather than trying to combine the percentages directly. Also, get comfortable working backwards from a final result—this skill appears frequently on standardized tests in various contexts beyond just stock prices.