Percent Whole Part Quiz: Master Percents Find Whole From Part Quiz

1) If one quarter of the cookies is 48, then there are 192 cookies in total.

True

False

The answer is True. One quarter equals 25% which equals 0.25 as a decimal. Whole = 48 divided by 0.25 = 192. Check: 25% of 192 = 0.25 times 192 = 48. The fraction one quarter and the percent 25% are equivalent rates, and both correctly produce a total of 192 from a known part of 48.

Explanation

The answer is True. One quarter equals 25% which equals 0.25 as a decimal. Whole = 48 divided by 0.25 = 192. Check: 25% of 192 = 0.25 times 192 = 48. The fraction one quarter and the percent 25% are equivalent rates, and both correctly produce a total of 192 from a known part of 48.

2) If 1% of the fleet is 45 vehicles, then the total fleet is 4,500.

True

False

The answer is True. Whole = 45 divided by 0.01 = 4,500. Check: 1% of 4,500 = 0.01 times 4,500 = 45. The statement matches the calculation exactly. With a rate as small as 1%, the whole must be 100 times the part, which is why 45 times 100 = 4,500 gives the correct total.

Explanation

The answer is True. Whole = 45 divided by 0.01 = 4,500. Check: 1% of 4,500 = 0.01 times 4,500 = 45. The statement matches the calculation exactly. With a rate as small as 1%, the whole must be 100 times the part, which is why 45 times 100 = 4,500 gives the correct total.

3) If 62.5% of the warehouse equals 500 items, what is the total inventory?

700

750

800

$850.00

Rate = 62.5% = 0.625. Whole = 500 divided by 0.625 = 800. Check: 62.5% of 800 = 0.625 times 800 = 500. Option A gives 700, where 62.5% would be 437.5. Option B gives 750, where 62.5% would be 468.75. Option D gives 850, where 62.5% would be 531.25. Only 800 satisfies the verification check.

Explanation

Rate = 62.5% = 0.625. Whole = 500 divided by 0.625 = 800. Check: 62.5% of 800 = 0.625 times 800 = 500. Option A gives 700, where 62.5% would be 437.5. Option B gives 750, where 62.5% would be 468.75. Option D gives 850, where 62.5% would be 531.25. Only 800 satisfies the verification check.

4) If 0.2% of factory output is 18 units, what is the total output?

7,000

8,000

9,000

10,000

Rate = 0.2% = 0.002. Whole = 18 divided by 0.002 = 9,000. Check: 0.2% of 9,000 = 0.002 times 9,000 = 18. Option A gives 7,000, where 0.2% would be 14. Option B gives 8,000, where 0.2% would be 16. Option D gives 10,000, where 0.2% would be 20. Only 9,000 satisfies the verification check.

Explanation

Rate = 0.2% = 0.002. Whole = 18 divided by 0.002 = 9,000. Check: 0.2% of 9,000 = 0.002 times 9,000 = 18. Option A gives 7,000, where 0.2% would be 14. Option B gives 8,000, where 0.2% would be 16. Option D gives 10,000, where 0.2% would be 20. Only 9,000 satisfies the verification check.

5) If 12% of a number is 33.6, what is the number?

260

270

280

290

Whole = 33.6 divided by 0.12 = 280. Check: 12% of 280 = 0.12 times 280 = 33.6. Option A gives 260, where 12% would be 31.2. Option B gives 270, where 12% would be 32.4. Option D gives 290, where 12% would be 34.8. Only 280 satisfies the verification check exactly.

Explanation

Whole = 33.6 divided by 0.12 = 280. Check: 12% of 280 = 0.12 times 280 = 33.6. Option A gives 260, where 12% would be 31.2. Option B gives 270, where 12% would be 32.4. Option D gives 290, where 12% would be 34.8. Only 280 satisfies the verification check exactly.

6) At an event, 35% of attendees is 77 people. What is the total attendance?

200

210

220

230

Whole = 77 divided by 0.35 = 220. Check: 35% of 220 = 0.35 times 220 = 77. Option A gives 200, where 35% would be 70. Option B gives 210, where 35% would be 73.5. Option D gives 230, where 35% would be 80.5. Only 220 satisfies the verification check exactly.

Explanation

Whole = 77 divided by 0.35 = 220. Check: 35% of 220 = 0.35 times 220 = 77. Option A gives 200, where 35% would be 70. Option B gives 210, where 35% would be 73.5. Option D gives 230, where 35% would be 80.5. Only 220 satisfies the verification check exactly.

7) If 2% of inventory is 18 items, what is the total inventory?

700

800

900

1000

Whole = 18 divided by 0.02 = 900. Check: 2% of 900 = 0.02 times 900 = 18. Option A gives 700, where 2% would be 14. Option B gives 800, where 2% would be 16. Option D gives 1,000, where 2% would be 20. Only 900 satisfies the verification check.

Explanation

Whole = 18 divided by 0.02 = 900. Check: 2% of 900 = 0.02 times 900 = 18. Option A gives 700, where 2% would be 14. Option B gives 800, where 2% would be 16. Option D gives 1,000, where 2% would be 20. Only 900 satisfies the verification check.

8) If 25% of a number is 60, what is the number?

180

200

240

260

Whole = part divided by rate = 60 divided by 0.25 = 240. Check: 25% of 240 = 0.25 times 240 = 60. Option A gives 180, where 25% would be 45. Option B gives 200, where 25% would be 50. Option D gives 260, where 25% would be 65. Only 240 satisfies the verification check.

Explanation

Whole = part divided by rate = 60 divided by 0.25 = 240. Check: 25% of 240 = 0.25 times 240 = 60. Option A gives 180, where 25% would be 45. Option B gives 200, where 25% would be 50. Option D gives 260, where 25% would be 65. Only 240 satisfies the verification check.

9) If 7.5% of a group equals 45 people, what is the total group size?

560

580

600

620

Whole = 45 divided by 0.075 = 600. Check: 7.5% of 600 = 0.075 times 600 = 45. Option A gives 560, where 7.5% would be 42. Option B gives 580, where 7.5% would be 43.5. Option D gives 620, where 7.5% would be 46.5. Only 600 satisfies the verification check exactly.

Explanation

Whole = 45 divided by 0.075 = 600. Check: 7.5% of 600 = 0.075 times 600 = 45. Option A gives 560, where 7.5% would be 42. Option B gives 580, where 7.5% would be 43.5. Option D gives 620, where 7.5% would be 46.5. Only 600 satisfies the verification check exactly.

10) If 6% of a city's population equals 12,000 people, what is the total population?

120,000

180,000

$200000

220,000

Whole = 12,000 divided by 0.06 = 200,000. Check: 6% of 200,000 = 0.06 times 200,000 = 12,000. Option A gives 120,000, where 6% would be 7,200. Option B gives 180,000, where 6% would be 10,800. Option D gives 220,000, where 6% would be 13,200. Only 200,000 satisfies the verification check.

Explanation

Whole = 12,000 divided by 0.06 = 200,000. Check: 6% of 200,000 = 0.06 times 200,000 = 12,000. Option A gives 120,000, where 6% would be 7,200. Option B gives 180,000, where 6% would be 10,800. Option D gives 220,000, where 6% would be 13,200. Only 200,000 satisfies the verification check.

11) If 0.5% of stock is 35 units, what is the total stock?

5,000

6,000

7,000

8,000

Rate = 0.5% = 0.005. Whole = 35 divided by 0.005 = 7,000. Check: 0.5% of 7,000 = 0.005 times 7,000 = 35. Option A gives 5,000, where 0.5% would be 25. Option B gives 6,000, where 0.5% would be 30. Option D gives 8,000, where 0.5% would be 40. Only 7,000 satisfies the verification check.

Explanation

Rate = 0.5% = 0.005. Whole = 35 divided by 0.005 = 7,000. Check: 0.5% of 7,000 = 0.005 times 7,000 = 35. Option A gives 5,000, where 0.5% would be 25. Option B gives 6,000, where 0.5% would be 30. Option D gives 8,000, where 0.5% would be 40. Only 7,000 satisfies the verification check.

12) If 15% of a team is 27 people, then the team size is 180.

True

False

The answer is True. Whole = 27 divided by 0.15 = 180. Check: 15% of 180 = 0.15 times 180 = 27. The statement matches the calculation exactly. This confirms that dividing the known part by the decimal rate correctly recovers the whole in any part-percent-whole problem.

Explanation

The answer is True. Whole = 27 divided by 0.15 = 180. Check: 15% of 180 = 0.15 times 180 = 27. The statement matches the calculation exactly. This confirms that dividing the known part by the decimal rate correctly recovers the whole in any part-percent-whole problem.

13) In a club, 22 members represent 55% of the total. What is the total membership?

30

35

40

45

Whole = 22 divided by 0.55 = 40. Check: 55% of 40 = 0.55 times 40 = 22. Option A gives 30, where 55% would be 16.5. Option B gives 35, where 55% would be 19.25. Option D gives 45, where 55% would be 24.75. Only 40 satisfies the verification check.

Explanation

Whole = 22 divided by 0.55 = 40. Check: 55% of 40 = 0.55 times 40 = 22. Option A gives 30, where 55% would be 16.5. Option B gives 35, where 55% would be 19.25. Option D gives 45, where 55% would be 24.75. Only 40 satisfies the verification check.

14) 18 is 30% of what number?

54

60

$66.00

$72

Whole = 18 divided by 0.30 = 60. Check: 30% of 60 = 0.30 times 60 = 18. Option A gives 54, where 30% would be 16.2. Option C gives 66, where 30% would be 19.8. Option D gives 72, where 30% would be 21.6. Only 60 satisfies the verification check exactly.

Explanation

Whole = 18 divided by 0.30 = 60. Check: 30% of 60 = 0.30 times 60 = 18. Option A gives 54, where 30% would be 16.2. Option C gives 66, where 30% would be 19.8. Option D gives 72, where 30% would be 21.6. Only 60 satisfies the verification check exactly.

15) If 12.5% of a quantity is 45, what is the total quantity?

320

340

360

380

Whole = 45 divided by 0.125 = 360. Check: 12.5% of 360 = 0.125 times 360 = 45. Option A gives 320, where 12.5% would be 40. Option B gives 340, where 12.5% would be 42.5. Option D gives 380, where 12.5% would be 47.5. Only 360 satisfies the verification check.

Explanation

Whole = 45 divided by 0.125 = 360. Check: 12.5% of 360 = 0.125 times 360 = 45. Option A gives 320, where 12.5% would be 40. Option B gives 340, where 12.5% would be 42.5. Option D gives 380, where 12.5% would be 47.5. Only 360 satisfies the verification check.

16) If 40% of a class is 36, then the total class size is 90.

True

False

The answer is True. Whole = 36 divided by 0.40 = 90. Check: 40% of 90 = 0.40 times 90 = 36. The statement matches the calculation exactly. Dividing the known part by the decimal form of the percent always recovers the whole when part and percent are both known.

Explanation

The answer is True. Whole = 36 divided by 0.40 = 90. Check: 40% of 90 = 0.40 times 90 = 36. The statement matches the calculation exactly. Dividing the known part by the decimal form of the percent always recovers the whole when part and percent are both known.

17) Select all true statements about finding the whole from a known part and percent.

Divide the part by the decimal rate to get the whole

With a fixed part, a larger percent implies a smaller whole

With a fixed percent, a larger part implies a larger whole

Multiply the part by the percent as a decimal to get the whole

Whole = part divided by rate is the core formula, confirming A. If the part stays fixed and the rate increases, the denominator grows so the whole shrinks, confirming B. If the rate stays fixed and the part increases, the whole must increase proportionally, confirming C. Option D multiplies part by rate which gives the part again not the whole, making it false.

Explanation

Whole = part divided by rate is the core formula, confirming A. If the part stays fixed and the rate increases, the denominator grows so the whole shrinks, confirming B. If the rate stays fixed and the part increases, the whole must increase proportionally, confirming C. Option D multiplies part by rate which gives the part again not the whole, making it false.

Submit

18) Select all formulas that correctly compute the whole W from a known part P and percent p.

W = P divided by (p/100)

W = (P times 100) divided by p

W = P times (p/100)

W = P times (1 minus p/100)

The relationship is P = (p/100) times W. Solving for W gives W = P divided by (p/100), confirming A. This is algebraically identical to W = (P times 100) divided by p, confirming B. Option C multiplies by the rate instead of dividing, which gives the part not the whole. Option D uses the complement factor which applies a percent decrease, not a recovery of the whole.

Explanation

The relationship is P = (p/100) times W. Solving for W gives W = P divided by (p/100), confirming A. This is algebraically identical to W = (P times 100) divided by p, confirming B. Option C multiplies by the rate instead of dividing, which gives the part not the whole. Option D uses the complement factor which applies a percent decrease, not a recovery of the whole.

Submit

19) If 60 is 120% of a number, then the number is 50.

True

False

The answer is True. When the percent exceeds 100%, the whole is smaller than the part. Whole = 60 divided by 1.20 = 50. Check: 120% of 50 = 1.20 times 50 = 60. The same formula applies regardless of whether the percent is below or above 100 — always divide the part by the decimal rate to find the whole.

Explanation

The answer is True. When the percent exceeds 100%, the whole is smaller than the part. Whole = 60 divided by 1.20 = 50. Check: 120% of 50 = 1.20 times 50 = 60. The same formula applies regardless of whether the percent is below or above 100 — always divide the part by the decimal rate to find the whole.

20) If 125% of a value is 250, what is the value?

180

190

200

210

Whole = 250 divided by 1.25 = 200. Check: 125% of 200 = 1.25 times 200 = 250. Option A gives 180, where 125% would be 225. Option B gives 190, where 125% would be 237.5. Option D gives 210, where 125% would be 262.5. Only 200 satisfies the verification check.

Explanation

Whole = 250 divided by 1.25 = 200. Check: 125% of 200 = 1.25 times 200 = 250. Option A gives 180, where 125% would be 225. Option B gives 190, where 125% would be 237.5. Option D gives 210, where 125% would be 262.5. Only 200 satisfies the verification check.