SHSAT Math Quiz: Percent Of A Quantity

20 questions · exam conditions

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Percent Of A QuantityQuestion 1 of 20

Participation counts for $15\%$ of Carla's final grade. If her final grade is $92$ , how many points come from participation?

13.8

15.3

16.0

78.2

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SHSAT Math Quiz

SHSAT Math Quiz: Percent Of A Quantity

Practice Percent Of A Quantity in SHSAT Math 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 Quantity, giving you a quick way to practice the rules, question types, and explanations that matter most for SHSAT Math.

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

Participation counts for $15\%$ of Carla's final grade. If her final grade is $92$ , how many points come from participation?

$13.8$ (correct answer)
$15.3$
$16.0$
$78.2$

Explanation: When you encounter a percentage problem asking "how many points come from" a specific category, you're finding a part of a whole. The key is identifying what represents the total (Carla's final grade of 92) and what percentage of that total you need to calculate (15% for participation). To find how many points come from participation, multiply the final grade by the participation percentage:

92 \times 0.15 = 13.8

points. You convert 15% to its decimal form (0.15) and multiply directly by the total grade. Looking at the wrong answers: Choice B (15.3) likely comes from incorrectly adding the percentage to something or making a calculation error. Choice C (16.0) might result from rounding 15% up to a nice number and doing rough mental math, but precision matters on the SHSAT. Choice D (78.2) represents a common trap—this would be the points from everything except participation (85% of 92), which answers the opposite question of what's being asked. The trap in choice D is particularly important to recognize. When a problem asks for the percentage that does contribute to something, students sometimes accidentally calculate the percentage that doesn't contribute. Always double-check that you're finding the right piece of the whole. Strategy tip: On percentage problems, always identify the total first, convert the percentage to a decimal, then multiply. Also, do a quick reasonableness check—15% should be less than one-sixth of 92, which is about 15.3, so 13.8 makes sense.

Question 2

A $2.5$ -kilogram bag of rice is for sale. If a neighbor buys $40\%$ of the bag, how many kilograms of rice does the neighbor purchase?

$0.4\text{ kg}$
$1.0\text{ kg}$ (correct answer)
$1.4\text{ kg}$
$4.0\text{ kg}$

Explanation: This is a straightforward percentage calculation problem. When you need to find a percentage of a given quantity, you multiply the percentage (converted to decimal form) by the total amount. To find how much rice the neighbor purchases, you need to calculate 40% of 2.5 kilograms. First, convert the percentage to a decimal:

40\% = 0.40

. Then multiply:

0.40 \times 2.5 = 1.0

kilogram. Let's examine why each answer choice is correct or incorrect: Choice A (

0.4\text{ kg}

) represents a common error where students might confuse the decimal form of the percentage (0.40) with the final answer, forgetting to multiply by the total weight. Choice B (

1.0\text{ kg}

) is correct, as shown by our calculation above. Choice C (

1.4\text{ kg}

) might result from incorrectly adding the percentage to something, or from calculation errors in the multiplication. Choice D (

4.0\text{ kg}

) is impossible since it's greater than the original 2.5-kilogram bag. This could come from mistakenly multiplying 2.5 by 40 instead of by 0.40, or from other fundamental misunderstandings about percentage calculations. Remember this key strategy for percentage problems: always convert the percentage to a decimal first, then multiply by the total. Watch out for answer choices that represent the decimal form of the percentage itself—that's usually a trap designed to catch students who forget the multiplication step.

Question 3

A farmer harvested $7.2$ tons of apples; $37.5\%$ are Granny Smith apples. How many tons of Granny Smith apples were harvested?

$2.16$
$2.7$ (correct answer)
$3.2$
$4.5$

Explanation: This is a percentage calculation problem where you need to find a part of a whole. When you see "X% of Y," you're looking for the product of the percentage (as a decimal) and the total amount. To find how many tons of Granny Smith apples were harvested, multiply the total harvest by the percentage that are Granny Smith apples. First, convert

37.5\%

to a decimal by dividing by 100:

37.5 ÷ 100 = 0.375

. Then multiply:

7.2 × 0.375 = 2.7

tons. Looking at the wrong answers: Choice A (

2.16

) likely comes from incorrectly converting the percentage—perhaps using

0.3

instead of

0.375

(

7.2 × 0.3 = 2.16

). Choice C (

3.2

) might result from rounding

37.5\%

40\%

and calculating

7.2 × 0.4 = 2.88

, then rounding to

3.2

. Choice D (

4.5

) could come from calculating

37.5\%

12

instead of

7.2

, or from another computational error involving the wrong base number. The correct answer is B (

2.7

). Strategy tip: When converting percentages to decimals, remember that

37.5\% = 37.5 ÷ 100 = 0.375

. Double-check your decimal conversion before multiplying, as this is where most errors occur in percentage problems.

Question 4

Out of $120$ eighth-grade students, $15\%$ were absent on Monday. How many students were absent?

$12$
$15$
$18$ (correct answer)
$20$

Explanation: This is a percentage calculation problem, which is fundamental to many math applications. When you see "15% of 120 students," you need to convert the percentage to a decimal and multiply. To find 15% of 120 students, convert 15% to decimal form by dividing by 100:

15\% = \frac{15}{100} = 0.15

. Then multiply:

0.15 \times 120 = 18

students were absent. You can also think of this as:

\frac{15}{100} \times 120 = \frac{15 \times 120}{100} = \frac{1800}{100} = 18

. Looking at the wrong answers: Choice A (12) might result from incorrectly calculating 10% of 120 instead of 15%. Choice B (15) is a common trap—students sometimes give the percentage value itself rather than calculating what that percentage represents of the total. This would be correct if the question asked "what percentage were absent," but it asks "how many students." Choice D (20) could come from mistakenly calculating

\frac{20}{100} \times 120

or confusing this with a different percentage. The correct answer is C (18). Study tip: For percentage problems, always identify what you're finding a percentage of (here, 120 students), convert the percentage to a decimal, then multiply. Watch out for the trap of giving the percentage number itself as your answer—always check that your final answer makes sense in context.

Question 5

At a school fundraiser, 60% of the money raised came from ticket sales, and 35% of the ticket sales revenue came from student tickets. If student tickets generated $840, what was the total amount raised at the fundraiser?

$3,500
$4,000 (correct answer)
$4,200
$4,800

Explanation: Student tickets ($840) represent 35% of ticket sales, so total ticket sales = $840 ÷ 0.35 = $2,400. Ticket sales represent 60% of total fundraising, so total raised = $2,400 ÷ 0.60 = $4,000. Choice A results from using $840 ÷ 0.35 × 0.60. Choice C comes from incorrectly adding percentages: $840 ÷ (0.35 + 0.60). Choice D results from $840 ÷ 0.35 × 2 instead of proper calculation.

Question 6

What is $35\%$ of $120$ ?

$36$
$42$ (correct answer)
$48$
$420$

Explanation: When you see a percentage problem asking "What is X% of Y?", you're being asked to convert a percentage to a decimal and multiply it by the given number. To find

35\%

120

, first convert the percentage to a decimal by dividing by 100:

35\% = 35 ÷ 100 = 0.35

. Then multiply:

0.35 × 120 = 42

. You can also think of this as

\frac{35}{100} × 120 = \frac{35 × 120}{100} = \frac{4200}{100} = 42

. Looking at the wrong answers: Choice A (

36

) likely comes from miscalculating

30\%

120

instead of

35\%

, since

0.30 × 120 = 36

. This could happen if you misread the percentage or made an arithmetic error. Choice C (

48

) represents

40\%

120

, since

0.40 × 120 = 48

. Again, this suggests misreading

35\%

40\%

. Choice D (

420

) is what you'd get if you forgot to convert the percentage to a decimal and simply multiplied

35 × 12 = 420

. This is a classic trap—always remember that percentages must be converted before multiplying. The correct answer is B (

42

). For percentage problems on the SHSAT, always double-check that you've converted the percentage correctly. A quick mental check:

35\%

should give you slightly more than one-third of the number, and one-third of

120

40

, so

42

makes perfect sense.

Question 7

Refer to the table to answer the question. The museum plans to offer a special tour to exactly $25\%$ of Wednesday's visitors. How many people will receive the tour?

$40$
$45$
$50$ (correct answer)
$65$

Explanation: Wednesday shows

200

visitors;

0.25\times200=50

. Choices A and B result from using Monday or averaging two days, while D mistakenly applies

25\%

to Friday's count.

Question 8

Based on the graph shown, $30\%$ of the science fiction books sold were hardcover. How many hardcover science fiction books were sold?

$36$
$40$
$45$ (correct answer)
$60$

Explanation: The graph shows

150

science fiction books sold;

0.30\times150=45

. Choices A and B misread the bar as

120

135

, while D multiplies by

40\%

instead of

30\%

Question 9

A recipe calls for ingredients in the following ratios: 40% flour, 25% sugar, 20% butter, and 15% other ingredients. If you need 450 grams of flour for a large batch, how many grams of sugar do you need?

281.25 grams (correct answer)
315.50 grams
327.75 grams
360.00 grams

Explanation: If 450g represents 40% of the total, then the total batch is 450 ÷ 0.40 = 1,125g. Sugar is 25% of the total: 1,125 × 0.25 = 281.25g. Choice B results from incorrectly calculating 450 × 25 ÷ 40 + 15. Choice C comes from using 450 × 0.25 ÷ 40 × 100. Choice D results from simply calculating 450 × 0.80 without proper ratio conversion.

Question 10

During a clearance sale, all items are marked down 40%. Additionally, customers with a membership card receive an extra 15% off the already discounted price. If a member pays $76.50 for an item, what was the original price before any discounts?

$147.50
$150.00 (correct answer)
$155.25
$162.75

Explanation: Let P be the original price. After 40% off: P × 0.60. After additional 15% off: P × 0.60 × 0.85 = P × 0.51 = $76.50. Therefore P = $76.50 ÷ 0.51 = $150. Choice A results from incorrectly calculating the compound discount. Choice C comes from adding the percentages (55%) instead of multiplying. Choice D results from applying discounts in wrong order or miscalculating the final multiplier.

Question 11

A company's quarterly profits were distributed as follows: 45% to shareholders, 30% reinvested in the company, and 25% set aside for taxes. If $180,000 was reinvested, how much was set aside for taxes?

$135,000
$145,000
$150,000 (correct answer)
$162,000

Explanation: If $180,000 represents 30% of total profits, then total profits = $180,000 ÷ 0.30 = $600,000. Taxes are 25% of total: $600,000 × 0.25 = $150,000. Choice A results from calculating $180,000 × 25 ÷ 30 incorrectly. Choice B comes from estimation errors in the division. Choice D results from using the ratio 30:25 incorrectly as $180,000 × 0.90.

Question 12

Maria's savings account earns 3% interest annually. After one year, she withdraws 15% of her total balance. If she ends up with $2,125.50 after the withdrawal, what was her original principal?

$2,050
$2,125
$2,250
$2,500 (correct answer)

Explanation: Let P be the original principal. After earning 3% interest: P × 1.03. After withdrawing 15%: P × 1.03 × 0.85 = 2,125.50. Solving: P × 0.8755 = 2,125.50, so P = $2,500. Choice A results from dividing by 1.03 instead of the full calculation. Choice B comes from ignoring the interest. Choice C results from only accounting for the withdrawal but not the interest properly.

Question 13

A laboratory solution contains $2{,}500$ milliliters of liquid. What volume is $0.4\%$ of the solution?

$1\text{ mL}$
$4\text{ mL}$
$10\text{ mL}$ (correct answer)
$100\text{ mL}$

Explanation: When you see a percentage problem, you're converting a percent to a decimal and multiplying by the total amount. To find

0.4\%

2{,}500

milliliters, first convert the percentage:

0.4\% = \frac{0.4}{100} = 0.004

. Now multiply:

0.004 \times 2{,}500 = 10

milliliters. You can think of this as

\frac{4}{1000} \times 2{,}500 = \frac{4 \times 2{,}500}{1000} = \frac{10{,}000}{1000} = 10

. Choice A (

1\text{ mL}

) represents a common error where students might calculate

0.04\%

instead of

0.4\%

, or miscalculate the decimal conversion. Choice B (

4\text{ mL}

) likely comes from forgetting to convert the percentage properly and just using

4 \times 2{,}500 \div 1000

incorrectly. Choice D (

100\text{ mL}

) suggests the student calculated

4\%

instead of

0.4\%

— this is what you'd get if you used

0.04

instead of

0.004

as your decimal. Choice C (

10\text{ mL}

) is correct because

0.004 \times 2{,}500 = 10

. Strategy tip: When working with small percentages like

0.4\%

, double-check your decimal conversion. Remember that

0.4\% = 0.004

, not

0.04

. A quick reasonableness check helps too:

0.4\%

is less than half a percent, so your answer should be much smaller than

1\%

of the solution (which would be

25

mL).

Question 14

A car's gas tank holds $16$ gallons when full. If the gauge shows the tank is $62.5\%$ full, how many gallons of gasoline are in the tank?

$6.25$
$8$
$10$ (correct answer)
$12.5$

Explanation: This is a percentage calculation problem where you need to find a part of a whole. When you see "percent of" language, you're looking for: percentage × total amount = part. To find how many gallons are in the tank, multiply the total capacity by the percentage that's full. Convert

62.5\%

to a decimal by dividing by 100:

62.5\% = 0.625

. Then calculate:

16 \text{ gallons} \times 0.625 = 10 \text{ gallons}

. You can verify this makes sense:

62.5\% = \frac{5}{8}

, so the tank is five-eighths full. Since

\frac{5}{8} \times 16 = \frac{80}{8} = 10

, this confirms our answer. Looking at the wrong choices: Choice A (

6.25

) likely comes from incorrectly calculating

16 \times 0.0625

instead of

16 \times 0.625

— a decimal place error when converting the percentage. Choice B (

8

) represents half the tank (

50\%

), which students might choose if they misread

62.5\%

50\%

or confused the percentage. Choice D (

12.5

) could result from calculating

16 \times 0.78125

(which is

78.125\%

), possibly from misreading the percentage or making an arithmetic error. Strategy tip: When working with percentages, always double-check your decimal conversion. Also, do a quick reasonableness check —

62.5\%

is more than half but less than three-quarters, so your answer should be between

8

and

12

gallons.

Question 15

A sauce recipe calls for $12$ teaspoons of liquid, $30\%$ of which should be lemon juice. How many teaspoons of lemon juice are needed?

$2.4$
$3.0$
$3.6$ (correct answer)
$4.8$

Explanation: When you encounter percentage problems, you're finding a part of a whole. Here, you need to determine what

30\%

12

teaspoons equals. To find

30\%

12

, convert the percentage to a decimal by dividing by

100

30\% = 0.30

. Then multiply:

0.30 \times 12 = 3.6

teaspoons of lemon juice. Let's examine why the other answers are incorrect. Choice A (

2.4

) results from calculating

20\%

12

instead of

30\%

. This is a common error when you misread the percentage in the problem. Choice B (

3.0

) comes from calculating

25\%

12

, which might happen if you round

30\%

25\%

for easier mental math. Choice D (

4.8

) is what you'd get if you calculated

40\%

12

, another misreading error. You can verify the answer by checking if

3.6

teaspoons represents

30\%

of the total:

\frac{3.6}{12} = 0.30 = 30\%

✓ The correct answer is C. Strategy tip: Always double-check percentage problems by working backwards. Take your answer, divide it by the total, and see if you get the original percentage. This catches calculation errors and ensures you used the right percentage from the problem.

Question 16

On an $80$ -question test, a student must answer at least $65\%$ correctly to pass. What is the minimum number of questions the student must answer correctly?

$50$
$51$
$52$ (correct answer)
$53$

Explanation: When you encounter percentage problems involving minimum requirements, you need to calculate the exact percentage first, then determine whether rounding is appropriate based on the context. To find the minimum number of correct answers needed, calculate

65\%

80

questions:

0.65 \times 80 = 52

questions exactly. Since this calculation yields a whole number, the student must answer exactly

52

questions correctly to achieve the

65\%

passing threshold. Let's verify why the other options don't work. Choice A (

50

) represents

\frac{50}{80} = 0.625 = 62.5\%

, which falls short of the required

65\%

. Choice B (

51

) gives

\frac{51}{80} = 0.6375 = 63.75\%

, still below the passing threshold. Choice D (

53

) would give

\frac{53}{80} = 0.6625 = 66.25\%

, which exceeds the requirement but isn't the minimum needed. Choice C (

52

) is correct because

\frac{52}{80} = 0.65 = 65\%

exactly meets the requirement. The key insight here is recognizing that "minimum" means finding the smallest number that satisfies the condition. Since

52

questions gives exactly

65\%

, answering

51

or fewer would result in failure, while

53

or more would be more than necessary. Strategy tip: In minimum/maximum problems involving percentages, always calculate the exact percentage first. If you get a whole number, that's usually your answer. If you get a decimal, consider whether the context requires rounding up or down based on what the question is asking.

Question 17

A water tank that holds $9{,}600$ liters is $87.5\%$ full. How many liters of water are in the tank?

$7{,}000$
$8{,}400$ (correct answer)
$8{,}750$
$9{,}875$

Explanation: When you see a percentage problem involving "part of a whole," you're calculating what fraction of the total amount you actually have. Here, you need to find 87.5% of the tank's 9,600-liter capacity. To find a percentage of a number, convert the percentage to a decimal and multiply. Convert 87.5% to a decimal by dividing by 100:

87.5 ÷ 100 = 0.875

. Then multiply by the tank's capacity:

0.875 × 9{,}600 = 8{,}400

liters. Let's examine why each answer choice is right or wrong. Choice A (7,000) would represent about 73% of the tank's capacity, which is significantly less than the stated 87.5%. Choice B (8,400) is correct—this equals exactly 87.5% of 9,600 liters. Choice C (8,750) represents about 91% of the tank, which overshoots the 87.5% mark. Choice D (9,875) is impossible since it exceeds the tank's total capacity of 9,600 liters. You can verify your answer by working backwards:

8{,}400 ÷ 9{,}600 = 0.875 = 87.5\%

✓ Strategy tip: When dealing with percentages, always check if your answer makes logical sense. If the percentage is less than 100%, your answer must be smaller than the original amount. Also, convert percentages to decimals carefully—87.5% becomes 0.875, not 0.0875.

Question 18

A recipe makes $48$ cookies. If $12.5\%$ of them are dusted with powdered sugar, how many cookies get powdered sugar?

$4$
$5$
$6$ (correct answer)
$8$

Explanation: This is a percentage calculation problem that tests your ability to find a percent of a whole number. When you see "X% of Y," you need to convert the percentage to a decimal and multiply. To find

12.5\%

48

cookies, first convert

12.5\%

to a decimal by dividing by

100

12.5 ÷ 100 = 0.125

. Then multiply:

48 × 0.125 = 6

cookies get powdered sugar. Here's why each wrong answer represents a common mistake: Choice A (

4

) likely comes from incorrectly calculating

10\%

48

instead of

12.5\%

, or from rounding errors in the conversion process. Choice B (

5

) might result from approximating

12.5\%

as roughly

10\%

and then adding a bit, but not calculating precisely. Choice D (

8

) could come from confusing

12.5\%

with a larger percentage like

16.7\%

, or from calculation errors when working with the decimal. The correct answer is C (

6

), which you can verify using an alternative method:

12.5\% = 12.5/100 = 1/8

, so you're finding

1/8

48

48 ÷ 8 = 6

. Strategy tip: When working with percentages, always double-check by using fraction equivalents when possible. Common conversions like

12.5\% = 1/8

25\% = 1/4

, and

20\% = 1/5

can make calculations faster and help you catch errors.

Question 19

What is $6.25\%$ of $64$ ?

$3$
$4$ (correct answer)
$5$
$8$

Explanation: When you see a percentage problem like this, you're working with the fundamental relationship: part = percent × whole. Here, you need to find what

6.25\%

64

equals. First, convert the percentage to a decimal:

6.25\% = 6.25 ÷ 100 = 0.0625

. Then multiply:

0.0625 × 64 = 4

. There's also a helpful shortcut here. Notice that

6.25\% = \frac{6.25}{100} = \frac{1}{16}

. So you're really finding

\frac{1}{16}

64

, which equals

64 ÷ 16 = 4

. Looking at the wrong answers: Choice (A) gives

3

, which would result from incorrectly calculating

6.25\% × 48

instead of

64

, or from other computational errors. Choice (C) gives

5

, which might come from rounding

6.25\%

8\%

and then calculating

8\% × 64 = 5.12 ≈ 5

. Choice (D) gives

8

, which is exactly what you'd get if you calculated

12.5\%

64

instead—this represents doubling the given percentage. The correct answer is (B)

4

. Study tip: Memorize that

6.25\% = \frac{1}{16}

and

12.5\% = \frac{1}{8}

. These percentages appear frequently on standardized tests, and recognizing them as simple fractions makes calculations much faster. Also, always double-check percentage problems by asking if your answer makes sense—

6.25\%

is pretty small, so the result should be much smaller than the original number.

Question 20

A jar holds $2{,}000$ marbles, $55\%$ of which are blue. How many blue marbles are there?

$900$
$1{,}000$
$1{,}100$ (correct answer)
$1{,}150$

Explanation: When you encounter percentage problems, you're converting a percentage to a decimal and multiplying by the total amount. The key is remembering that "percent" means "per hundred," so

55\% = \frac{55}{100} = 0.55

. To find the number of blue marbles, multiply the total number of marbles by the percentage that are blue:

2{,}000 \times 0.55 = 1{,}100

. You can think of this as finding

55\%

2{,}000

, which gives you

1{,}100

blue marbles. Let's examine why the other answers are incorrect. Choice A (

900

) would represent

45\%

of the marbles—this is the percentage that are NOT blue. It's a common error to calculate the complement instead of what's actually asked. Choice B (

1{,}000

) represents exactly

50\%

of the marbles, which might tempt you if you misremembered the percentage or rounded

55\%

incorrectly. Choice D (

1{,}150

) is what you'd get if you calculated

57.5\%

instead of

55\%

—this could result from a calculation error or misreading the problem. For percentage problems on the SHSAT, always double-check that you're finding the percentage of the right quantity and that you've converted the percentage correctly to a decimal. A quick sanity check: since

55\%

is more than half, your answer should be greater than

1{,}000

(which is half of

2{,}000

). Only choices C and D meet this criterion, making your final check easier.