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Mixed Quantitative Reasoning (Problem Solving) Flashcards

34 cards from real GRE practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 20 Mixed Quantitative Reasoning (Problem Solving) flashcards as text

  1. A store offers a 30% discount on an item already marked down 20% from its original price. If the final price is $112, what was the original price? (A) $180 (B) $200 (C) $220 (D) $240

    Answer: $200

    Final price = Original × 0.80 × 0.70 = Original × 0.56. 112 = 0.56 × P → P = 200.

  2. If 3x − 7 = 2(x + 4), what is the value of x? (A) 13 (B) 14 (C) 15 (D) 16

    Answer: 15

    3x − 7 = 2x + 8 → x = 15.

  3. Two trains leave the same station at the same time, traveling in opposite directions. Train A travels at 60 mph and Train B at 80 mph. After how many hours are they 350 miles apart? (A) 2.0 hours (B) 2.5 hours (C) 3.0 hours (D) 3.5 hours

    Answer: 2.5 hours

    Combined speed = 60 + 80 = 140 mph. Time = 350/140 = 2.5 hours.

  4. A rectangular garden has a perimeter of 54 meters. If its length is twice its width, what is the area of the garden? (A) 81 m² (B) 108 m² (C) 162 m² (D) 180 m²

    Answer: 108 m²

    Width = w, length = 2w. Perimeter: 2(w + 2w) = 54 → 6w = 54 → w = 9. Length = 18. Area = 9 × 18 = 162 m².

  5. A solution is 20% salt by weight. How many grams of pure salt must be added to 300 grams of this solution to make it 25% salt? (A) 15g (B) 18g (C) 20g (D) 24g

    Answer: 20g

    Start: 60g salt in 300g. Add x grams of salt: (60+x)/(300+x) = 0.25. 60+x = 75+0.25x → 0.75x = 15 → x = 20.

  6. A car travels 120 miles at 40 mph, then another 120 miles at 60 mph. What is the average speed for the entire trip? (A) 48 mph (B) 50 mph (C) 52 mph (D) 55 mph

    Answer: 48 mph

    Total distance = 240 miles. Time = 120/40 + 120/60 = 3 + 2 = 5 hours. Avg speed = 240/5 = 48 mph.

  7. A company's profits increased by 25% in 2022 and then decreased by 20% in 2023. What was the net percentage change over the two years? (A) 0% (B) +5% (C) −5% (D) +10%

    Answer: 0%

    1.25 × 0.80 = 1.00. The profit returned to exactly the original amount — 0% net change.

  8. In a class of 36 students, 20 passed the math test, 18 passed the English test, and 8 passed both. How many students failed both tests? (A) 4 (B) 6 (C) 8 (D) 10

    Answer: 6

    Passed at least one = 20 + 18 − 8 = 30. Failed both = 36 − 30 = 6.

  9. What is the slope of a line perpendicular to the line 3x − 4y = 12? (A) 3/4 (B) 4/3 (C) −4/3 (D) −3/4

    Answer: −4/3

    Rearrange: y = (3/4)x − 3. Slope = 3/4. Perpendicular slope = −1/(3/4) = −4/3.

  10. A jar contains 5 red, 4 blue, and 3 green marbles. Two marbles are drawn without replacement. What is the probability that both are red? (A) 5/33 (B) 5/22 (C) 2/11 (D) 5/12

    Answer: 5/33

    P = (5/12) × (4/11) = 20/132 = 5/33.

  11. If f(x) = 2x² − 3x + 1, what is f(−2)? (A) 11 (B) 13 (C) 15 (D) 17

    Answer: 15

    f(−2) = 2(−2)² − 3(−2) + 1 = 2(4) + 6 + 1 = 8 + 6 + 1 = 15.

  12. A bicycle wheel has a radius of 35 cm. How many complete revolutions does it make while traveling 1,100 meters? (Use π ≈ 22/7) (A) 400 (B) 500 (C) 550 (D) 600

    Answer: 500

    Circumference = 2π r = 2 × (22/7) × 35 = 220 cm = 2.2 m. Revolutions = 1100/2.2 = 500.

  13. 5 workers can complete a project in 12 days. How many days would it take 8 workers (working at the same rate) to complete the same project? (A) 6 days (B) 7.5 days (C) 8 days (D) 9 days

    Answer: 7.5 days

    Total work = 5 × 12 = 60 worker-days. Time for 8 workers = 60/8 = 7.5 days.

  14. In a geometric sequence, the first term is 3 and the common ratio is 2. What is the sum of the first 6 terms? (A) 186 (B) 189 (C) 192 (D) 195

    Answer: 189

    S₆ = 3(2⁶ − 1)/(2 − 1) = 3(64 − 1) = 3 × 63 = 189.

  15. A cylindrical tank has a radius of 3 meters and height of 7 meters. What is the volume of the tank? (Use π ≈ 22/7) (A) 154 m³ (B) 198 m³ (C) 186 m³ (D) 210 m³

    Answer: 198 m³

    V = πr²h = (22/7) × 9 × 7 = 22 × 9 = 198 m³.

  16. If a > 0, b > 0, and (a + b)² = 100, ab = 20, what is the value of a² + b²? (A) 50 (B) 60 (C) 70 (D) 80

    Answer: 60

    (a+b)² = a² + 2ab + b² = 100. a² + b² = 100 − 2ab = 100 − 40 = 60.

  17. The ratio of boys to girls in a school is 3:5. If there are 720 students in total, how many more girls are there than boys? (A) 90 (B) 150 (C) 180 (D) 270

    Answer: 180

    Boys = (3/8) × 720 = 270. Girls = (5/8) × 720 = 450. Difference = 450 − 270 = 180.

  18. If p and q are roots of the equation x² − 5x + 6 = 0, what is the value of p² + q²? (A) 11 (B) 13 (C) 15 (D) 17

    Answer: 13

    p + q = 5, pq = 6. p² + q² = (p+q)² − 2pq = 25 − 12 = 13.

  19. A tank is filled by pipe A in 6 hours and drained by pipe B in 10 hours. If both are open simultaneously, how long does it take to fill an empty tank? (A) 10 hours (B) 12 hours (C) 15 hours (D) 18 hours

    Answer: 15 hours

    Net rate = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15. Time = 15 hours.

  20. A ladder 10 meters long leans against a wall. Its base is 6 meters from the wall. How high does the ladder reach up the wall? (A) 6 m (B) 7 m (C) 8 m (D) 9 m

    Answer: 8 m

    By the Pythagorean theorem: h² + 6² = 10² → h² = 100 − 36 = 64 → h = 8.