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📝 Finding a percentage of a number (13 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 13 questions available

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What is Finding a percentage of a number?

Definition:
Finding a percentage of a number means calculating the part that corresponds to a given percentage of a whole. Use the formula $\text{Part} = \text{Percent (as decimal)} \times \text{Whole}$ . For example, to find 35% of 200, compute $0.35 \times 200 = 70$ .

Working:
Step 1: Convert the percent to a decimal by dividing by 100. Step 2: Multiply by the whole number. For example, 45% of 80: $0.45 \times 80 = 36$ .

Example:
Problem: 'What is 60% of 150?' $0.60 \times 150 = 90$ .

Reason:
This is the most common percent application, used in calculating tips, discounts, and exam scores.

Easy

Medium

Hard

📝 All Finding a percentage of a number MCQs

Q1. A school has 480 students, and 35% participate in at least one science activity. Which calculation correctly models the number of participating students?

A.480 + 0.35

B.480 × 0.35 ✅

C.480 ÷ 35

D.480 × 35

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: To find 35% of 480, convert 35% to the decimal $0.35$ and multiply by 480. Thus $480 \times 0.35=168$ . The other choices either add percentages incorrectly or use an inappropriate operation.

Q2. Which statement best explains why finding 18% of 250 requires multiplication by $0.18$ rather than multiplication by 18?

A.A percentage must always be converted to a decimal before multiplication ✅

B.The number 18 is smaller than 250

C.Percent means subtracting from the whole

D.Multiplication by 18 automatically changes the answer into a percentage

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: A percentage represents a fraction of 100, so $18\%=18/100=0.18$ . Multiplying 250 by $0.18$ finds the requested portion. Multiplying directly by 18 would make the result 100 times too large.

Q3. A retailer marks 22% of 750 products as eligible for a special inspection. A student calculates $750\times22=16,500$ . What is the best diagnosis of the student's reasoning?

A.The student should divide 750 by 22

B.The student used 22% correctly, so the answer is reasonable

C.The student treated 22% as 22 instead of

0.22

✅

D.The student should add 22 to 750

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The calculation uses 22 rather than its decimal equivalent $0.22$ . Since 22% means 22 out of 100, the correct model is $750\times0.22=165$ . The original answer is impossible because it exceeds the total.

Q4. A community center spends 64% of a monthly budget of Rs. 125,000 on staff and operations. Which interpretation of $125000\times0.64$ is most accurate?

A.It finds the amount remaining after expenses

B.It finds 64% of the total budget ✅

C.It finds 64 percentage points more than the budget

D.It converts the budget into a percentage

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The expression $125000\times0.64$ calculates the portion represented by 64% of the entire budget. Its value is Rs. 80,000. The remaining 36% would require a separate calculation using $0.36$ .

Q5. A farmer harvests 2,400 kg of produce. Of this amount, 12.5% is donated. Instead of converting 12.5% to a decimal, which mental strategy gives the donated amount most efficiently?

A.Find

1/8

of 2,400 ✅

B.Find

1/12.5

of 2,400

C.Multiply 2,400 by 12.5

D.Subtract 12.5 from 2,400

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Since $12.5\%=12.5/100=1/8$ , finding $1/8$ of 2,400 is efficient. Dividing 2,400 by 8 gives 300 kg. This method also demonstrates why recognizing equivalent fractional forms can simplify percentage calculations.

Q6. A library receives 1,600 donated books. The first review identifies 15% as reference books. Later, 25% of the reference books are selected for digitization. How many reference books are selected?

A.60 ✅

B.240

C.400

D.1000

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: First calculate the reference books: $1600\times0.15=240$ . Then calculate 25% of those reference books: $240\times0.25=60$ . The key reasoning is that the second percentage applies only to the already identified subgroup, not to all 1,600 books.

Q7. A transport company records 3,200 trips in one month. Electric vehicles account for 27.5% of the trips. The manager estimates that 900 trips were electric. Which conclusion is most justified?

A.The estimate is exact because 27.5% is close to 30%

B.The estimate is too high because the exact value is 880 trips ✅

C.The estimate is too low because the exact value is 1,100 trips

D.The estimate is impossible because percentages cannot contain decimals

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Calculate $3200\times0.275=880$ . The manager's estimate of 900 is therefore 20 trips too high, although it is reasonably close. This requires both accurate percentage computation and evaluation of whether an estimate is consistent with the model.

Q8. A student claims that 40% of 350 is 490 because $350+40\%=390$ , followed by another addition of 100. Which correction best explains the error?

A.Percentages should be added to the original number as whole numbers

B.A percentage of a number represents multiplication by its decimal form, so

350\times0.40=140

✅

C.The correct operation is

350-40=310

D.The answer should be found by dividing 350 by 0.40

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The student's reasoning treats a percentage as if it were a fixed number of units that can simply be added. To find 40% of 350, use $350\times0.40=140$ . If the question asks for the increased total, then 350 plus 140 would be 490.

Q9. Two analysts calculate 16% of 625. Analyst A computes $625\times0.16=100$ . Analyst B computes $625\div16=39.0625$ . Which analysis is correct, and why?

A.Only Analyst A, because a percentage of a quantity is found by multiplying by the decimal percentage ✅

B.Only Analyst B, because division always finds percentages

C.Both analysts, because multiplication and division give equivalent percentage results

D.Neither analyst, because 16% cannot be applied to 625

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Analyst A is correct because $16\%=0.16$ , giving $625\times0.16=100$ . Dividing by 16 does not represent finding 16% of a quantity. The operation must reflect the meaning of a percentage as a fraction of the whole.

Q10. A bar graph shows four departments with budgets of Rs. 50,000, Rs. 80,000, Rs. 120,000, and Rs. 150,000. If 20% of each department's budget is reserved for training, which department reserves the greatest amount?

A.Rs. 50,000 department

B.Rs. 80,000 department

C.Rs. 120,000 department

D.Rs. 150,000 department ✅

💡 Difficulty: medium | ✅ Correct: D

📖 Explanation: Because the same percentage, 20%, is applied to every budget, the largest original budget produces the largest training allocation. Specifically, $150000\times0.20=30000$ , which exceeds the corresponding amounts for all smaller budgets.

Q11. A charity receives Rs. 240,000 and allocates 30% to food, 25% to education, and 15% to transportation. The remaining amount is saved. What percentage of the donation is saved, and how much is that?

A.30% and Rs. 72,000

B.30% and Rs. 72,000 ✅

C.70% and Rs. 168,000

D.30% and Rs. 168,000

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The allocated percentages total $30\%+25\%+15\%=70\%$ , so the remaining percentage is 30%. Therefore the saved amount is $240000\times0.30=72000$ . This combines percentage-of-a-number reasoning with interpreting complementary portions of a total.

Q12. A manufacturer produces 1,250 devices. Quality control rejects 8% of them. Of the rejected devices, 20% can be repaired. How many rejected devices cannot be repaired?

A.20

B.80 ✅

C.100

D.1050

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: First find the rejected devices: $1250\times0.08=100$ . Then 20% of those can be repaired: $100\times0.20=20$ . Therefore $100-20=80$ rejected devices cannot be repaired. The problem requires applying percentages sequentially to different groups.

Q13. A contest has $n$ participants. One team argues that 12% of $n$ is larger than 15% of $n$ because 12 is closer to 100 than 15. For positive $n$ , which statement definitively resolves the disagreement?

A.12% of

n

is always larger

B.15% of

n

is always larger ✅

C.They are equal for every positive

n

D.Their order depends on whether

n

is greater than 100

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: For any positive $n$ , $12\% \text{ of } n=0.12n$ and $15\% \text{ of } n=0.15n$ . Since $0.15>0.12$ , the 15% amount is always larger. The absolute size of $n$ does not reverse the comparison.

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