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Fractions, decimals, and percents — ISEE Upper practice questions

On the ISEE Upper Quantitative Reasoning section, Fractions, decimals, and percents covers converting among those three forms and applying them to prices, rates, and parts of a whole. A student has to match a stated percent to exact counts, convert mixed representations, and follow successive percent increases and decreases without treating them as if they cancel. Items are short word problems whose answer choices are nearby numbers or comparisons with the original amount. Common traps include applying percents additively, reversing the order of changes, and selecting counts that cannot produce an exact given percent.

  • Section: Quantitative Reasoning 37 questions on the paper
  • 108 practice questions in the app

Sample questions

Question 1

A volleyball team makes 60%60\% of its serves during a match. Which could be the exact number of serves made and serves missed?

  1. A18 made, 10 missed
  2. B20 made, 15 missed
  3. C30 made, 18 missed
  4. D27 made, 18 missed
Show answer

Answer: D — 27 made, 18 missed

Need mademade+missed=0.60\dfrac{\text{made}}{\text{made}+\text{missed}}=0.60. For D, 27/(27+18)=27/45=0.6027/(27+18)=27/45=0.60. A is 18/28≈0.6418/28\approx 0.64; B is 20/35≈0.5720/35\approx 0.57; C is 30/48=0.62530/48=0.625.

Question 2

A positive number is increased by 28%28\% and the result is then decreased by 28%28\%.

Column AColumn B
The original numberThe final number
  1. AThe quantity in Column A is greater
  2. BThe quantity in Column B is greater
  3. CThe two quantities are equal
  4. DThe relationship cannot be determined from the information given
Show answer

Answer: A — The quantity in Column A is greater

A 28%28\% increase multiplies by 1.28. A 28%28\% decrease then multiplies by 0.72. The net factor is 1.28×0.72=0.9216<11.28\times 0.72=0.9216<1, so the original number is greater.

Question 3

A bicycle costs $360 in February. In March the price is 25%25\% less than the February price. In April the price is 25%25\% higher than the March price. What is the April price?

  1. A$270
  2. B$300
  3. C$345
  4. D$337.50
Show answer

Answer: D — $337.50

March: 360×0.75=$270360\times 0.75=\$270. April: 270×1.25=$337.50270\times 1.25=\$337.50. $270 is the March price; returning to $360 would require a 33.3‾%33.\overline{3}\% increase from March.

Practice 108 Fractions, decimals, and percents questions in the app

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