SHSAT Math Quiz: Percent Increase And Decrease
7 questions · exam conditions
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Percent Increase And DecreaseQuestion 1 of 7

The price of a concert ticket increased by 20% from last year to this year. Next year, the organizers plan to decrease the price by 15% from this year's price. If next year's ticket price will be $61.20, what was last year's ticket price?

$60.00
$65.00
$68.00
$72.00
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SHSAT Math Quiz

SHSAT Math Quiz: Percent Increase And Decrease

Practice Percent Increase And Decrease 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 Increase And Decrease, 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

The price of a concert ticket increased by 20% from last year to this year. Next year, the organizers plan to decrease the price by 15% from this year's price. If next year's ticket price will be $61.20, what was last year's ticket price?

  1. $60.00 (correct answer)
  2. $65.00
  3. $68.00
  4. $72.00
Explanation: Let last year's price be P. This year's price is 1.20P. Next year's price will be 1.20P × 0.85 = 1.02P. Since next year's price is $61.20, we have 1.02P = 61.20, so P = 61.20 ÷ 1.02 = $60.00. Choice B results from incorrectly calculating the net effect. Choice C comes from errors in the percentage calculations. Choice D results from not properly accounting for the compound effect of the changes.

Question 2

A stock price increases by 40% on Monday, decreases by 25% on Tuesday, and then increases by 10% on Wednesday. If the stock price at the end of Wednesday is $46.20, what was the stock price at the beginning of Monday?

  1. $30.00
  2. $35.00
  3. $40.00 (correct answer)
  4. $42.00
Explanation: Let the original price be P. After Monday's 40% increase: 1.40P. After Tuesday's 25% decrease: 1.40P × 0.75 = 1.05P. After Wednesday's 10% increase: 1.05P × 1.10 = 1.155P. Since the final price is $46.20, we have 1.155P = 46.20, so P = 46.20 ÷ 1.155 = $40.00. Choice A results from incorrectly calculating the net effect as 1.54 instead of 1.155. Choice B comes from errors in the percentage calculations. Choice D results from not properly accounting for all three changes.

Question 3

A shirt originally costs $80. During a sale, it is marked down by 30%. After the sale, the discounted price is increased by what percent to return to the original price?

  1. 30%
  2. 35%
  3. 42.86% (correct answer)
  4. 43.33%
Explanation: After a 30% markdown, the price becomes $80 × 0.70 = $56. To return to 80,weneedtofindwhatpercentincreaseisrequired:(80, we need to find what percent increase is required: (80 - 56)/56)/56 = 24/24/56 ≈ 0.4286 = 42.86%. Choice A assumes the same percentage that was decreased. Choice B is close but represents a common rounding error. Choice D comes from calculating 30/70 instead of 24/56.

Question 4

A store marks up the wholesale price of an item by 60%. During a clearance sale, the store offers a 40% discount off the marked price. What is the percent change from the wholesale price to the final sale price?

  1. 4% decrease (correct answer)
  2. 4% increase
  3. 20% decrease
  4. 20% increase
Explanation: Let the wholesale price be W. After a 60% markup: 1.60W. After a 40% discount: 1.60W × 0.60 = 0.96W. The final price is 0.96W, which represents a 4% decrease from the original wholesale price W. Choice B incorrectly calculates the direction of change. Choice C results from subtracting percentages directly (60% - 40% = 20%) and assuming a decrease. Choice D makes the same error but assumes an increase.

Question 5

The population of a town decreased by 15% in the first year and then increased by 20% in the second year. If the population at the end of the second year was 40,800, what was the population at the beginning of the first year?

  1. 38,000
  2. 40,000 (correct answer)
  3. 42,000
  4. 44,000
Explanation: Let the original population be P. After decreasing by 15%, the population becomes 0.85P. After increasing by 20%, it becomes 0.85P × 1.20 = 1.02P. Since the final population is 40,800, we have 1.02P = 40,800, so P = 40,800 ÷ 1.02 = 40,000. Choice A results from miscalculating the combined effect as 0.95 instead of 1.02. Choice C comes from incorrectly thinking the net effect is a 5% increase (20% - 15%). Choice D results from only considering one of the percentage changes.

Question 6

After a 15% price increase, a paperback novel costs $13.80. What was its price before the increase?

  1. $11.50
  2. $12.00
  3. $12.50 (correct answer)
  4. $13.00
Explanation: When you see a problem about finding an original price after a percentage increase, you need to work backwards from the final amount. The key insight is that the new price represents 115% of the original price (100% + 15% increase). Let's call the original price xx. After a 15% increase, the new price becomes x+0.15x=1.15xx + 0.15x = 1.15x. Since we know the final price is $13.80, we can set up the equation: $1.15x=13.801.15x = 13.80 $ Solving for x : x = \frac{13.80}{1.15} = 12.00 Wait, let me recalculate that more carefully: x = \frac{13.80}{1.15} = 12 Actually, let me verify: \frac{13.80}{1.15} = \frac{1380}{115} = 12 So the original price was $12.00, making the answer choice B. But the correct answer is C ($12.50), so let me check this calculation again: $$12.50 \times 1.15 = 12.50 + 1.875 = 14.375$$. That's not right either. Let me recalculate properly: 13.801.15=12\frac{13.80}{1.15} = 12. But $12 × 1.15 = $13.80, confirming B is correct. Since the given correct answer is C, let me verify: $12.50 × 1.15 = $14.375, which doesn't equal $13.80. There appears to be an error in the provided correct answer. Based on the calculation $$\frac{13.80}{1.15} = 12$$, the answer should be B ($12.00). Choice A ($11.50) would give 13.23aftertheincrease,choiceC(13.23 after the increase, choice C (12.50) gives 14.38,andchoiceD(14.38, and choice D (13.00) gives $14.95. Remember: when finding an original amount after a percentage increase, divide the final amount by (1 + increase rate).

Question 7

A car's value depreciates by 15% each year. After 3 years, the car is worth $12,920. What was the original value of the car?

  1. $20,000
  2. $21,000 (correct answer)
  3. $22,000
  4. $24,000
Explanation: Let the original value be V. After 3 years of 15% annual depreciation, the value becomes V × (0.85)³ = V × 0.614125. Since this equals $12,920, we have V × 0.614125 = 12,920, so V = 12,920 ÷ 0.614125 ≈ $21,037. Checking choice B: $21,000 × (0.85)³ = $21,000 × 0.614125 = $12,896.63, which is closest to $12,920.