Find Whole From Part Quiz: Determining The Whole From Known Part And Percentage

1) If 60% of a class equals 27 students, what is the total class size?

40

45

50

55

Whole = 27 divided by 0.60 = 45. Check: 60% of 45 = 0.60 times 45 = 27. Option A gives 40, where 60% would be 24. Option C gives 50, where 60% would be 30. Option D gives 55, where 60% would be 33. Only 45 satisfies the verification check exactly.

Explanation

Whole = 27 divided by 0.60 = 45. Check: 60% of 45 = 0.60 times 45 = 27. Option A gives 40, where 60% would be 24. Option C gives 50, where 60% would be 30. Option D gives 55, where 60% would be 33. Only 45 satisfies the verification check exactly.

2) If 0.5% of a warehouse inventory is 12 items, what is the total inventory?

1200

1800

2400

3000

Rate = 0.5% = 0.005. Whole = 12 divided by 0.005 = 2400. Check: 0.5% of 2400 = 0.005 times 2400 = 12. Option A gives 1200, where 0.5% would be 6. Option B gives 1800, where 0.5% would be 9. Option D gives 3000, where 0.5% would be 15. Only 2400 satisfies the verification check.

Explanation

Rate = 0.5% = 0.005. Whole = 12 divided by 0.005 = 2400. Check: 0.5% of 2400 = 0.005 times 2400 = 12. Option A gives 1200, where 0.5% would be 6. Option B gives 1800, where 0.5% would be 9. Option D gives 3000, where 0.5% would be 15. Only 2400 satisfies the verification check.

3) If 60% of a set is 30, then the total is 80.

True

False

The answer is False. Whole = 30 divided by 0.60 = 50, not 80. Check: 60% of 50 = 0.60 times 50 = 30, which confirms the correct total is 50. The statement claims 80, which would mean 60% of 80 = 48, not 30. The calculation clearly contradicts the stated total.

Explanation

The answer is False. Whole = 30 divided by 0.60 = 50, not 80. Check: 60% of 50 = 0.60 times 50 = 30, which confirms the correct total is 50. The statement claims 80, which would mean 60% of 80 = 48, not 30. The calculation clearly contradicts the stated total.

4) If 7.5% of a group equals 15 people, what is the total group size?

150

180

200

250

Whole = 15 divided by 0.075 = 200. Check: 7.5% of 200 = 0.075 times 200 = 15. Option A gives 150, where 7.5% would be 11.25. Option B gives 180, where 7.5% would be 13.5. Option D gives 250, where 7.5% would be 18.75. Only 200 satisfies the verification check.

Explanation

Whole = 15 divided by 0.075 = 200. Check: 7.5% of 200 = 0.075 times 200 = 15. Option A gives 150, where 7.5% would be 11.25. Option B gives 180, where 7.5% would be 13.5. Option D gives 250, where 7.5% would be 18.75. Only 200 satisfies the verification check.

5) If 4% of a quantity is 8, what is the full quantity?

200

160

$180

$220

Whole = 8 divided by 0.04 = 200. Check: 4% of 200 = 0.04 times 200 = 8. Option B gives 160, where 4% would be 6.4. Option C gives 180, where 4% would be 7.2. Option D gives 220, where 4% would be 8.8. Only 200 satisfies the verification check exactly.

Explanation

Whole = 8 divided by 0.04 = 200. Check: 4% of 200 = 0.04 times 200 = 8. Option B gives 160, where 4% would be 6.4. Option C gives 180, where 4% would be 7.2. Option D gives 220, where 4% would be 8.8. Only 200 satisfies the verification check exactly.

6) A city reports that 63% of residents, or 18,900 people, subscribed to alerts. What is the total population?

25,000

28,000

30,000

32,000

Whole = 18,900 divided by 0.63 = 30,000. Check: 63% of 30,000 = 0.63 times 30,000 = 18,900. Option A gives 25,000, where 63% would be 15,750. Option B gives 28,000, where 63% would be 17,640. Option D gives 32,000, where 63% would be 20,160. Only 30,000 satisfies the verification check.

Explanation

Whole = 18,900 divided by 0.63 = 30,000. Check: 63% of 30,000 = 0.63 times 30,000 = 18,900. Option A gives 25,000, where 63% would be 15,750. Option B gives 28,000, where 63% would be 17,640. Option D gives 32,000, where 63% would be 20,160. Only 30,000 satisfies the verification check.

7) If 2% of a school is 14 students, what is the total number of students?

600

650

700

750

Whole = 14 divided by 0.02 = 700. Check: 2% of 700 = 0.02 times 700 = 14. Option A gives 600, where 2% would be 12. Option B gives 650, where 2% would be 13. Option D gives 750, where 2% would be 15. Only 700 produces exactly 14 when multiplied by 2%.

Explanation

Whole = 14 divided by 0.02 = 700. Check: 2% of 700 = 0.02 times 700 = 14. Option A gives 600, where 2% would be 12. Option B gives 650, where 2% would be 13. Option D gives 750, where 2% would be 15. Only 700 produces exactly 14 when multiplied by 2%.

8) If 30% of a class equals 18 students, what is the total class size?

54

72

60

48

Whole = part divided by rate = 18 divided by 0.30 = 60. Check: 30% of 60 = 0.30 times 60 = 18. Option A gives 54, which would mean 18 is 33% of 54. Option B gives 72, which would mean 18 is 25% of 72. Option D gives 48, which would mean 18 is 37.5% of 48. Only 60 satisfies the 30% condition.

Explanation

Whole = part divided by rate = 18 divided by 0.30 = 60. Check: 30% of 60 = 0.30 times 60 = 18. Option A gives 54, which would mean 18 is 33% of 54. Option B gives 72, which would mean 18 is 25% of 72. Option D gives 48, which would mean 18 is 37.5% of 48. Only 60 satisfies the 30% condition.

9) If 12.5% of a club equals 25 members, what is the total membership?

200

175

$180

225

Whole = 25 divided by 0.125 = 200. Check: 12.5% of 200 = 0.125 times 200 = 25. Option B gives 175, where 12.5% would be 21.875. Option C gives 180, where 12.5% would be 22.5. Option D gives 225, where 12.5% would be 28.125. Only 200 satisfies the verification check.

Explanation

Whole = 25 divided by 0.125 = 200. Check: 12.5% of 200 = 0.125 times 200 = 25. Option B gives 175, where 12.5% would be 21.875. Option C gives 180, where 12.5% would be 22.5. Option D gives 225, where 12.5% would be 28.125. Only 200 satisfies the verification check.

10) If 35% of the attendees is 49 people, what is the total attendance?

120

130

140

150

Whole = 49 divided by 0.35 = 140. Check: 35% of 140 = 0.35 times 140 = 49. Option A gives 120, where 35% would be 42. Option B gives 130, where 35% would be 45.5. Option D gives 150, where 35% would be 52.5. Only 140 satisfies the verification check exactly.

Explanation

Whole = 49 divided by 0.35 = 140. Check: 35% of 140 = 0.35 times 140 = 49. Option A gives 120, where 35% would be 42. Option B gives 130, where 35% would be 45.5. Option D gives 150, where 35% would be 52.5. Only 140 satisfies the verification check exactly.

11) If 10% of the class is 5 students, then the class size is 50.

True

False

The answer is True. Whole = 5 divided by 0.10 = 50. Check: 10% of 50 = 0.10 times 50 = 5. The statement is confirmed by the calculation. Dividing the known part by the decimal rate is the standard method for finding the whole when the part and percent are both given.

Explanation

The answer is True. Whole = 5 divided by 0.10 = 50. Check: 10% of 50 = 0.10 times 50 = 5. The statement is confirmed by the calculation. Dividing the known part by the decimal rate is the standard method for finding the whole when the part and percent are both given.

12) In a survey, 12 respondents represent 20% of all respondents. What is the total number of respondents?

48

50

55

60

Whole = 12 divided by 0.20 = 60. Check: 20% of 60 = 0.20 times 60 = 12. Option A gives 48, where 20% would be 9.6. Option B gives 50, where 20% would be 10. Option C gives 55, where 20% would be 11. Only 60 produces exactly 12 when multiplied by 20%.

Explanation

Whole = 12 divided by 0.20 = 60. Check: 20% of 60 = 0.20 times 60 = 12. Option A gives 48, where 20% would be 9.6. Option B gives 50, where 20% would be 10. Option C gives 55, where 20% would be 11. Only 60 produces exactly 12 when multiplied by 20%.

13) A school reports that 40% of its students, or 52 students, joined the club. What is the total enrollment?

120

130

$140.00

$150

Whole = 52 divided by 0.40 = 130. Check: 40% of 130 = 0.40 times 130 = 52. Option A gives 120, where 40% would be 48. Option C gives 140, where 40% would be 56. Option D gives 150, where 40% would be 60. Only 130 produces exactly 52 when multiplied by 40%.

Explanation

Whole = 52 divided by 0.40 = 130. Check: 40% of 130 = 0.40 times 130 = 52. Option A gives 120, where 40% would be 48. Option C gives 140, where 40% would be 56. Option D gives 150, where 40% would be 60. Only 130 produces exactly 52 when multiplied by 40%.

14) If 15% of a group is 24 people, what is the total group size?

140

150

160

180

Whole = 24 divided by 0.15 = 160. Check: 15% of 160 = 0.15 times 160 = 24. Option A gives 140, where 15% would be 21 not 24. Option B gives 150, where 15% would be 22.5. Option D gives 180, where 15% would be 27. Only 160 satisfies the verification check.

Explanation

Whole = 24 divided by 0.15 = 160. Check: 15% of 160 = 0.15 times 160 = 24. Option A gives 140, where 15% would be 21 not 24. Option B gives 150, where 15% would be 22.5. Option D gives 180, where 15% would be 27. Only 160 satisfies the verification check.

15) If 25% of a team is 45 people, then the total team size is 180.

True

False

The answer is True. Whole = part divided by rate = 45 divided by 0.25 = 180. Check: 25% of 180 = 0.25 times 180 = 45. 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 = part divided by rate = 45 divided by 0.25 = 180. Check: 25% of 180 = 0.25 times 180 = 45. 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.

16) If 35% of a group is 70 people, then the total group is 200.

True

False

The answer is True. Whole = 70 divided by 0.35 = 200. Check: 35% of 200 = 0.35 times 200 = 70. 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 = 70 divided by 0.35 = 200. Check: 35% of 200 = 0.35 times 200 = 70. 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.

17) If one fifth of a team is 9 people, then the team has 45 people in total.

True

False

The answer is True. One fifth equals 20% which equals 0.20 as a decimal. Whole = 9 divided by 0.20 = 45. Check: 20% of 45 = 0.20 times 45 = 9. The fraction one fifth and the percent 20% are equivalent rates, and both correctly produce a total of 45 people from a known part of 9.

Explanation

The answer is True. One fifth equals 20% which equals 0.20 as a decimal. Whole = 9 divided by 0.20 = 45. Check: 20% of 45 = 0.20 times 45 = 9. The fraction one fifth and the percent 20% are equivalent rates, and both correctly produce a total of 45 people from a known part of 9.

18) Select all pairs of percent and decimal that represent the same rate.

20% and 0.20

25% and 0.25

12.5% and 0.125

30% and 0.03

Converting percent to decimal means dividing by 100. 20 divided by 100 = 0.20, confirming A. 25 divided by 100 = 0.25, confirming B. 12.5 divided by 100 = 0.125, confirming C. Option D states 30% and 0.03, but 30 divided by 100 = 0.30, not 0.03. The value 0.03 represents 3%, not 30%.

Explanation

Converting percent to decimal means dividing by 100. 20 divided by 100 = 0.20, confirming A. 25 divided by 100 = 0.25, confirming B. 12.5 divided by 100 = 0.125, confirming C. Option D states 30% and 0.03, but 30 divided by 100 = 0.30, not 0.03. The value 0.03 represents 3%, not 30%.

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19) 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

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

For 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.

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

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