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Mixed skills
10 original practice questions · Untimed · Fractions and exact decimals accepted
1. Using the subscriptions table, what is the percent increase from Year 1 to Year 2? Dataset 1.
Open full-size diagram ↗Optional written extension · self-assessment only
Explain your choice of denominator or operation and state the result with its unit.
Show your reasoning for each part. This task is not automatically scored.
2. After a 20% discount, a reference book costs $112. What was its original price in dollars?
gre-percents-1-13. An exterior angle of a triangle measures 104°. One remote interior angle measures 44°. What is the other remote interior angle, in degrees?
Answer: __________________
gre-triangle-structure-4-24. If 2x + 9 = 23, what is 3x − 2?
gre-equations-1-15. What is the exact value of 3 divided by 80? Enter a fraction or exact decimal.
Answer: __________________
gre-fractions-4-26. Two ropes of lengths 72 meters and 108 meters are cut into equal whole-meter pieces with no waste. What is the greatest possible piece length?
gre-integers-4-47. If x + y = 12 and 2x + 3y = 31, what is x?
gre-equations-4-18. Among 20 distinct scores sorted increasingly, a score is in position 9. Define its percentile rank as 100 times the fraction of scores strictly below it. What is its percentile rank?
Answer: __________________
gre-distribution-shape-2-39. Quantity A: 3% of 23. Quantity B: 23% of 3.
gre-percents-4-110. How many positive integers x satisfy 3x < 36?
gre-equations-2-3Answers & reasoning
1. 25 · Choice B
The increase is 15. Use Year 1, the earlier amount, as denominator. 100 × 15/60 = 25%.
Optional written extension · self-assessment only
Explain your choice of denominator or operation and state the result with its unit.
- Uses the correct table entries and operation (1 points)
- Interprets the result in the requested unit (1 points)
The increase is 15.
Use Year 1, the earlier amount, as denominator.
100 × 15/60 = 25%.
2. 140 · Choice C
After a 20% discount, 80% of the original price remains. Write 0.8p = 112. Divide by 0.8 to get p = 140.
gre-percents-1-13. 60
The remote angles sum to 104°. Subtract the known remote angle 44°. The other angle is 60°.
gre-triangle-structure-4-24. 19 · Choice E
Subtract 9 and divide by 2 to obtain x = 7. Substitute into the requested expression, not just x. 3(7) − 2 = 19.
gre-equations-1-15. 3/80
The quotient is 3/80. The numerator has no common prime factor with this denominator. The reduced fraction is 3/80.
gre-fractions-4-26. 36 · Choice B
The length must divide both original lengths. Factor the lengths as 12(6) and 18(6); gcd(12,18) = 6. The greatest common length is 6(6) = 36 meters.
gre-integers-4-47. 5 · Choice C
Double the first equation: 2x + 2y = 24. Subtract it from the second equation: y = 7. Then x = 12 − 7 = 5.
gre-equations-4-18. 40
There are 8 lower scores. The fraction is that count divided by 20. The percentile rank is 100(8)/20 = 40.
gre-distribution-shape-2-39. The two quantities are equal. · Choice C
Write each percent as a fraction over 100. Both quantities have the product of the same two numbers in the numerator. The quantities are equal.
gre-percents-4-110. 11 · Choice A
Divide by 3: x < 12. The positive integers are 1 through 11. There are 11 such integers.
gre-equations-2-3Original parameterized practice, independently checked by computation. Educator review pending. Not an official exam paper.