Percentage sample question

Question

A number is increased by 20% and then decreased by 20%. What is the net change?

1. A. No change
2. B. 4% decrease
3. C. 4% increase
4. D. 8% decrease

Correct answer

Option B: 4% decrease

Take the original number as 100. After a 20% increase it becomes 120. A 20% decrease on 120 is 24, so the final value is 96. The net change is a decrease of 4 from the original 100.

Why the other options are wrong

• No change is wrong because the second 20% is applied to 120, not to the original 100.
• 4% increase reverses the direction of the final value.
• 8% decrease doubles the loss without following the base change.

Solution method

1. Choose a convenient original value of 100 unless the question supplies one.
2. Apply each percentage to the value that exists at that stage, not to the first base.
3. Compare the final value with the original and express the difference as a percentage of the original.

Concept boundary

Equal percentage increase and decrease do not cancel because the bases are different. After a 20 percent rise, the value is 120; the 20 percent fall is then 24, not 20. Direct addition is valid only when percentage changes refer to the same fixed base, which is not the case in successive-change questions.

Transfer practice

A price falls by 10 percent and then rises by 10 percent. What is the net change?

Practice tip

When percentages are applied one after another, always track the changing base.

This is original practice material for concept review, not a claim that the same wording will appear in an official paper. Report an unclear or outdated explanation through the contact page.

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