ASVAB Percentage Problems: Discounts, Tax and Change

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Identify the whole before finding a percent

ASVAB percentage word problems ask you to connect a part, a whole, and a rate out of one hundred. The most useful first question is “What amount does this percentage apply to?” Once you identify the base, the calculation becomes much clearer. A percentage without its base can be misleading.

Use part = decimal rate × whole. Convert 18% to 0.18, 5% to 0.05, and 125% to 1.25. A rate above 100% is possible: it represents more than the original whole. To find the percentage instead, divide the part by the whole and multiply by 100.

For example, 18 successful checks out of 24 is 18/24 = 3/4 = 75%. The denominator represents all checks, not just unsuccessful ones. Begin with the fraction and decimal review if these conversions are slowing you down.

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Discounts: calculate what remains

A jacket costs $80 before a 25% discount. The discount is 0.25 × 80 = $20, leaving a sale price of $60. You can also multiply the original price by the remaining 75%: 0.75 × 80 = 60. The two methods should agree.

Read whether the question asks for the discount or the sale price. Both $20 and $60 are meaningful quantities in the story, but only one answers each question. Label your intermediate result to avoid selecting the first number you calculate.

For a 15% discount without a calculator, find 10% and 5% separately. Ten percent of $120 is $12, and five percent is $6. The discount is $18, so the price becomes $102. Breaking a rate into familiar parts is especially helpful when the decimal multiplication feels cumbersome.

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Tax and successive changes use a new base

An item has a listed price of $80, a 25% discount, and then 8% sales tax on the discounted price. First find $60 after the discount. Tax is 0.08 × 60 = $4.80, producing a final total of $64.80. Applying tax to the original $80 would answer a different problem.

Two successive 10% discounts do not equal a 20% discount. Starting with $100, the first reduction leaves $90. The second reduces $90 by $9, leaving $81. The overall reduction is 19%. Each change applies to the amount that exists at that step.

Likewise, increasing a quantity by 20% and then decreasing it by 20% does not return it to its original value. $100 becomes $120, then $96. Write down the base beside each percentage when a problem contains multiple changes.

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Percent change and reverse percentages

To calculate percent increase, divide the increase by the original value. A count rises from 40 to 50, so the change is 10 and the increase is 10/40 = 25%. Dividing by the new value, 50, would produce 20%, which is not the requested percent increase from 40.

If a sale price is $72 after a 20% discount, $72 represents 80% of the original price. Let the original be x: 0.80x = 72, so x = 90. Adding 20% of $72 would produce $86.40 and would not reverse the original discount.

A reliable way to check a reverse problem is to apply the stated change to your proposed original value. Twenty percent of $90 is $18, and $90 − $18 = $72. That substitution confirms both the calculation and the base.

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Build a percentage practice checklist

Practice four different questions: find a part from a whole, find a percentage from a part and whole, find a whole from a part and percentage, and apply successive changes. Write the relationship before calculating. This prevents a familiar-looking story from pushing you into the wrong operation.

Estimate your result as well. A 12% discount on $50 should be a little more than $5, not $60. A 150% increase means adding one and a half times the original, so the final quantity is 250% of the original. Distinguish the size of the change from the final amount.