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Fractions, decimals, and percents; percent change — ISEE Upper practice questions

On the ISEE Upper, the Mathematics Achievement topic Fractions, decimals, and percents; percent change covers converting among those three forms, finding a percent of a whole, and tracking successive percent increase and decrease. A student must rewrite a decimal as an equivalent fraction, compute a stated percent of a given number, and recover an original amount after a quantity first increases by a percent and then decreases by another. Questions are typically a single stem with four choices that look like simplified fractions or whole numbers. A frequent trap is adding or subtracting successive percent changes instead of applying each one to the changing base.

  • Section: Mathematics Achievement 47 questions on the paper
  • 99 practice questions in the app

Sample questions

Question 1

Which fraction is equivalent to 0.625?

  1. A35\dfrac{3}{5}
  2. B58\dfrac{5}{8}
  3. C23\dfrac{2}{3}
  4. D78\dfrac{7}{8}
Show answer

Answer: B — 58\dfrac{5}{8}

0.625=62510000.625=\dfrac{625}{1000}. Dividing the numerator and denominator by 125 gives 58\dfrac{5}{8}.

Question 2

What is 15%15\% of 240?

  1. A24
  2. B30
  3. C36
  4. D48
Show answer

Answer: C — 36

10%10\% of 240 is 24, and 5%5\% of 240 is 12. Therefore, 15%15\% of 240 is 24+12=3624+12=36.

Question 3

A plant population increased by 20%20\% during one month and then decreased by 10%10\% during the next month. At the end of the two months, the population was 324. What was the population at the beginning of the first month?

  1. A270
  2. B300
  3. C330
  4. D360
Show answer

Answer: B — 300

If the original population was xx, then x(1.20)(0.90)=324x(1.20)(0.90)=324. Since 1.20⋅0.90=1.081.20\cdot0.90=1.08, the equation is 1.08x=3241.08x=324, so x=300x=300.

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