Reverse Percent Decrease Quiz: Reverse Percent Decrease Original Amount

1) A bike sells for $270 after a 40% decrease. What was the original price?

$405

$425

$450

$475

A 40% decrease applies a factor of 0.60. Original = 270 divided by 0.60 = $450. Check: 450 times 0.60 = 270. Option A gives $405 = 270 divided by 0.667. Option B gives $425 = 270 divided by 0.635. Option D gives $475 = 270 divided by 0.568. Only $450 correctly reverses the 40% decrease.

Explanation

A 40% decrease applies a factor of 0.60. Original = 270 divided by 0.60 = $450. Check: 450 times 0.60 = 270. Option A gives $405 = 270 divided by 0.667. Option B gives $425 = 270 divided by 0.635. Option D gives $475 = 270 divided by 0.568. Only $450 correctly reverses the 40% decrease.

2) If the final price is $240 after a 25% decrease, then the original price is less than $240.

True

False

The answer is False. The original must always be greater than the final price after a decrease. Original = 240 divided by 0.75 = $320. Since $320 is greater than $240, the statement is false. After any percent decrease the final price is always smaller than the original, so the original recovered by reversing the decrease must always exceed the final amount.

Explanation

The answer is False. The original must always be greater than the final price after a decrease. Original = 240 divided by 0.75 = $320. Since $320 is greater than $240, the statement is false. After any percent decrease the final price is always smaller than the original, so the original recovered by reversing the decrease must always exceed the final amount.

3) After a 30% decrease, a jacket costs $84. What was the original price?

$140

$120

$109.20

$100

A 30% decrease means the final price equals the original times 0.70. To reverse, divide by 0.70: original = 84 divided by 0.70 = $120. Check: 120 times 0.70 = 84. Option A gives $140, which would mean 84 divided by 0.60. Option C gives $109.20, which is 84 divided by 0.77. Option D gives $100, which would require a 16% decrease not 30%.

Explanation

A 30% decrease means the final price equals the original times 0.70. To reverse, divide by 0.70: original = 84 divided by 0.70 = $120. Check: 120 times 0.70 = 84. Option A gives $140, which would mean 84 divided by 0.60. Option C gives $109.20, which is 84 divided by 0.77. Option D gives $100, which would require a 16% decrease not 30%.

4) A price of $48 is the result of a 20% decrease from $60, and reversing gives 48 divided by 0.80 = $60.

True

False

The answer is True. Forward direction: 60 times 0.80 = 48, confirming the 20% decrease. Reverse direction: 48 divided by 0.80 = 60, confirming the original is recovered. Both the forward and reverse calculations are consistent, demonstrating that dividing by the decimal multiplier correctly undoes any percent decrease.

Explanation

The answer is True. Forward direction: 60 times 0.80 = 48, confirming the 20% decrease. Reverse direction: 48 divided by 0.80 = 60, confirming the original is recovered. Both the forward and reverse calculations are consistent, demonstrating that dividing by the decimal multiplier correctly undoes any percent decrease.

5) A tablet is $81 after a 10% decrease. What was the original price?

$88

$89

$90

$91

A 10% decrease applies a factor of 0.90. Original = 81 divided by 0.90 = $90. Check: 90 times 0.90 = 81. Option A gives $88 = 81 divided by 0.920. Option B gives $89 = 81 divided by 0.910. Option D gives $91 = 81 divided by 0.890. Only $90 correctly reverses the 10% decrease.

Explanation

A 10% decrease applies a factor of 0.90. Original = 81 divided by 0.90 = $90. Check: 90 times 0.90 = 81. Option A gives $88 = 81 divided by 0.920. Option B gives $89 = 81 divided by 0.910. Option D gives $91 = 81 divided by 0.890. Only $90 correctly reverses the 10% decrease.

6) A book costs $72 after a 20% decrease. What was the original price?

$80

$90

$85

$75

A 20% decrease applies a factor of 0.80. Original = 72 divided by 0.80 = $90. Check: 90 times 0.80 = 72. Option A gives $80 = 72 divided by 0.90, which reverses a 10% decrease not 20%. Option C gives $85 = 72 divided by 0.847. Option D gives $75 = 72 divided by 0.96. Only $90 correctly reverses the 20% decrease.

Explanation

A 20% decrease applies a factor of 0.80. Original = 72 divided by 0.80 = $90. Check: 90 times 0.80 = 72. Option A gives $80 = 72 divided by 0.90, which reverses a 10% decrease not 20%. Option C gives $85 = 72 divided by 0.847. Option D gives $75 = 72 divided by 0.96. Only $90 correctly reverses the 20% decrease.

7) If the final price F comes from a 20% decrease, then the original price is F divided by 0.80.

True

False

The answer is True. A 20% decrease multiplies the original by 0.80, giving F = original times 0.80. To reverse this and recover the original, divide both sides by 0.80: original = F divided by 0.80. This is the standard method for reversing any percent decrease — divide the final amount by the decimal multiplier that was applied.

Explanation

The answer is True. A 20% decrease multiplies the original by 0.80, giving F = original times 0.80. To reverse this and recover the original, divide both sides by 0.80: original = F divided by 0.80. This is the standard method for reversing any percent decrease — divide the final amount by the decimal multiplier that was applied.

8) A calculator is $45 after a 10% decrease. What was the original price?

$44

$40

$49.50

$50

A 10% decrease applies a factor of 0.90. Original = 45 divided by 0.90 = $50. Check: 50 times 0.90 = 45. Option A gives $44, which is less than the final price and cannot be the original. Option B gives $40, which would require 45 divided by 0.90 = 50 not 40. Option C gives $49.50 = 45 times 1.10, which incorrectly adds 10% instead of reversing the decrease.

Explanation

A 10% decrease applies a factor of 0.90. Original = 45 divided by 0.90 = $50. Check: 50 times 0.90 = 45. Option A gives $44, which is less than the final price and cannot be the original. Option B gives $40, which would require 45 divided by 0.90 = 50 not 40. Option C gives $49.50 = 45 times 1.10, which incorrectly adds 10% instead of reversing the decrease.

9) A sweater is $63 after a 30% decrease. What was the original price?

$85

$90

$95

$88

A 30% decrease applies a factor of 0.70. Original = 63 divided by 0.70 = $90. Check: 90 times 0.70 = 63. Option A gives $85 = 63 divided by 0.741. Option C gives $95 = 63 divided by 0.663. Option D gives $88 = 63 divided by 0.716. Only $90 correctly reverses the 30% decrease.

Explanation

A 30% decrease applies a factor of 0.70. Original = 63 divided by 0.70 = $90. Check: 90 times 0.70 = 63. Option A gives $85 = 63 divided by 0.741. Option C gives $95 = 63 divided by 0.663. Option D gives $88 = 63 divided by 0.716. Only $90 correctly reverses the 30% decrease.

10) A laptop is $340 after a 15% decrease. What was the original price?

$360

$380

$400

$320

A 15% decrease applies a factor of 0.85. Original = 340 divided by 0.85 = $400. Check: 400 times 0.85 = 340. Option A gives $360 = 340 divided by 0.944, not 0.85. Option B gives $380 = 340 divided by 0.895. Option D gives $320, which is less than the final price and can never be the original after a decrease.

Explanation

A 15% decrease applies a factor of 0.85. Original = 340 divided by 0.85 = $400. Check: 400 times 0.85 = 340. Option A gives $360 = 340 divided by 0.944, not 0.85. Option B gives $380 = 340 divided by 0.895. Option D gives $320, which is less than the final price and can never be the original after a decrease.

11) If a quantity decreased by d percent, the original equals the final times (1 minus d divided by 100).

True

False

The answer is False. The correct relationship is final = original times (1 minus d divided by 100). To recover the original you must divide, not multiply: original = final divided by (1 minus d divided by 100). Multiplying the final by the same factor would apply the decrease a second time, producing a result even smaller than the final price, not the original.

Explanation

The answer is False. The correct relationship is final = original times (1 minus d divided by 100). To recover the original you must divide, not multiply: original = final divided by (1 minus d divided by 100). Multiplying the final by the same factor would apply the decrease a second time, producing a result even smaller than the final price, not the original.

12) A membership costs $212.50 after a 15% decrease. What was the original cost?

$230

$240

$250

$260

A 15% decrease applies a factor of 0.85. Original = 212.50 divided by 0.85 = $250. Check: 250 times 0.85 = 212.50. Option A gives $230 = 212.50 divided by 0.924. Option B gives $240 = 212.50 divided by 0.885. Option D gives $260 = 212.50 divided by 0.817. Only $250 satisfies the verification check.

Explanation

A 15% decrease applies a factor of 0.85. Original = 212.50 divided by 0.85 = $250. Check: 250 times 0.85 = 212.50. Option A gives $230 = 212.50 divided by 0.924. Option B gives $240 = 212.50 divided by 0.885. Option D gives $260 = 212.50 divided by 0.817. Only $250 satisfies the verification check.

13) An item costs $99 after a 10% decrease. What was the original price?

$108

$105

$112

110

A 10% decrease applies a factor of 0.90. Original = 99 divided by 0.90 = $110. Check: 110 times 0.90 = 99. Option A gives $108 = 99 divided by 0.917. Option B gives $105 = 99 divided by 0.943. Option C gives $112 = 99 divided by 0.884. Only $110 satisfies the verification check exactly.

Explanation

A 10% decrease applies a factor of 0.90. Original = 99 divided by 0.90 = $110. Check: 110 times 0.90 = 99. Option A gives $108 = 99 divided by 0.917. Option B gives $105 = 99 divided by 0.943. Option C gives $112 = 99 divided by 0.884. Only $110 satisfies the verification check exactly.

14) A monitor costs $211.20 after a 12% decrease. What was the original price?

$236.00

$240.00

$242.00

$248.00

A 12% decrease applies a factor of 0.88. Original = 211.20 divided by 0.88 = $240. Check: 240 times 0.88 = 211.20. Option A gives $236 = 211.20 divided by 0.895. Option C gives $242 = 211.20 divided by 0.873. Option D gives $248 = 211.20 divided by 0.852. Only $240 satisfies the verification check exactly.

Explanation

A 12% decrease applies a factor of 0.88. Original = 211.20 divided by 0.88 = $240. Check: 240 times 0.88 = 211.20. Option A gives $236 = 211.20 divided by 0.895. Option C gives $242 = 211.20 divided by 0.873. Option D gives $248 = 211.20 divided by 0.852. Only $240 satisfies the verification check exactly.

15) After a 35% discount, a phone costs $325. What was the original price?

$487.50

$500

520

550

A 35% decrease applies a factor of 0.65. Original = 325 divided by 0.65 = $500. Check: 500 times 0.65 = 325. Option A gives $487.50 = 325 divided by 0.667. Option C gives $520 = 325 divided by 0.625. Option D gives $550 = 325 divided by 0.591. Only $500 correctly reverses the 35% decrease.

Explanation

A 35% decrease applies a factor of 0.65. Original = 325 divided by 0.65 = $500. Check: 500 times 0.65 = 325. Option A gives $487.50 = 325 divided by 0.667. Option C gives $520 = 325 divided by 0.625. Option D gives $550 = 325 divided by 0.591. Only $500 correctly reverses the 35% decrease.

16) A pair of shoes costs $56 after a 30% decrease. What was the original price?

$70

$75

$80

$85

A 30% decrease applies a factor of 0.70. To find the original, divide by 0.70: original = 56 divided by 0.70 = $80. Check: 80 times 0.70 = 56. Option A gives $70, requiring 56 divided by 0.80, which is a 20% decrease. Option B gives $75, requiring a factor of 0.747. Option D gives $85, requiring a factor of 0.659, not 0.70.

Explanation

A 30% decrease applies a factor of 0.70. To find the original, divide by 0.70: original = 56 divided by 0.70 = $80. Check: 80 times 0.70 = 56. Option A gives $70, requiring 56 divided by 0.80, which is a 20% decrease. Option B gives $75, requiring a factor of 0.747. Option D gives $85, requiring a factor of 0.659, not 0.70.

17) The final price F comes from a 20% decrease. Select all methods that correctly find the original price.

F divided by 0.80

F divided by (1 minus 0.20)

F times 1.20

F times 0.80

A 20% decrease means original times 0.80 = F. Reversing by dividing by 0.80 confirms A. Since 1 minus 0.20 = 0.80, dividing by (1 minus 0.20) is identical to option A, confirming B. Option C multiplies by 1.20, which reverses a 16.67% decrease not a 20% decrease. Option D multiplies by 0.80, applying another 20% decrease instead of reversing one.

Explanation

A 20% decrease means original times 0.80 = F. Reversing by dividing by 0.80 confirms A. Since 1 minus 0.20 = 0.80, dividing by (1 minus 0.20) is identical to option A, confirming B. Option C multiplies by 1.20, which reverses a 16.67% decrease not a 20% decrease. Option D multiplies by 0.80, applying another 20% decrease instead of reversing one.

Submit

18) The final amount F comes from a 33 and 1/3 percent decrease. Select all expressions that equal the original.

F divided by (2/3)

1.5F

F times 0.666...

F divided by 1.333...

A 33 and 1/3 percent decrease applies a factor of 2/3. Reversing by dividing by 2/3 confirms A. Dividing by 2/3 is the same as multiplying by 3/2 = 1.5, confirming B. Option C multiplies by 0.666..., which applies the decrease again instead of reversing it. Option D divides by 1.333..., which equals multiplying by 0.75, corresponding to a 25% decrease reversal not 33 and 1/3 percent.

Explanation

A 33 and 1/3 percent decrease applies a factor of 2/3. Reversing by dividing by 2/3 confirms A. Dividing by 2/3 is the same as multiplying by 3/2 = 1.5, confirming B. Option C multiplies by 0.666..., which applies the decrease again instead of reversing it. Option D divides by 1.333..., which equals multiplying by 0.75, corresponding to a 25% decrease reversal not 33 and 1/3 percent.

Submit

19) The final price is F after a 25% decrease. Select all formulas that correctly recover the original price.

Original = F divided by 0.75

Original = F times (4/3)

Original = 0.75F

Original = 1.25F

A 25% decrease multiplies by 0.75. Reversing requires dividing by 0.75, confirming A. Dividing by 0.75 is mathematically identical to multiplying by 4/3, confirming B. Option C multiplies by 0.75 which would apply another 25% decrease, not reverse one. Option D multiplies by 1.25 which reverses a 20% decrease, not a 25% decrease.

Explanation

A 25% decrease multiplies by 0.75. Reversing requires dividing by 0.75, confirming A. Dividing by 0.75 is mathematically identical to multiplying by 4/3, confirming B. Option C multiplies by 0.75 which would apply another 25% decrease, not reverse one. Option D multiplies by 1.25 which reverses a 20% decrease, not a 25% decrease.

Submit

20) A shirt costs $90 after a 10% decrease. Select all values that could be the original price.

$100

$99

$110

$81

A 10% decrease applies a factor of 0.90. Original = 90 divided by 0.90 = $100. Only $100 correctly reverses the 10% decrease. Option B gives $99, which would produce 99 times 0.90 = $89.10, not $90. Option C gives $110, which would produce 110 times 0.90 = $99, not $90. Option D gives $81, which is less than the final price and can never be the original after a decrease.

Explanation

A 10% decrease applies a factor of 0.90. Original = 90 divided by 0.90 = $100. Only $100 correctly reverses the 10% decrease. Option B gives $99, which would produce 99 times 0.90 = $89.10, not $90. Option C gives $110, which would produce 110 times 0.90 = $99, not $90. Option D gives $81, which is less than the final price and can never be the original after a decrease.