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Percents, Ratios, and Proportions Flashcards

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

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  1. If the ratio of boys to girls in a class is 3:5 and there are 40 students total, how many boys are there?

    Answer: 15

    Boys = (3/8) × 40 = 15.

  2. If a:b = 2:3 and b:c = 4:5, what is a:c?

    Answer: 8:15

    a/c = (a/b) × (b/c) = (2/3) × (4/5) = 8/15, so a:c = 8:15.

  3. The ratio of the length to the width of a rectangle is 5:3. If the perimeter is 96, what is the length?

    Answer: 30

    Let length = 5k and width = 3k; perimeter 2(5k + 3k) = 96 gives k = 6, so length = 30.

  4. If x:y = 3:7, what is (x + y):(y − x)?

    Answer: 5:2

    Let x = 3k, y = 7k; then x + y = 10k and y − x = 4k, giving the ratio 10:4 = 5:2.

  5. A recipe calls for flour and sugar in a ratio of 4:1. If you want to use exactly 5 cups in total, how many cups of flour do you need?

    Answer: 4

    Flour's share is 4/(4+1) = 4/5 of the total; 4/5 × 5 = 4 cups.

  6. If the ratio of red to green to blue balls is 2:3:5 and there are 30 blue balls, how many total balls are there?

    Answer: 60

    Blue = 5k = 30, so k = 6; total = (2 + 3 + 5)k = 10 × 6 = 60.

  7. In a mixture of juice and water, the ratio is 3:2. After 10 liters of water are added, the ratio becomes 3:4. How much juice was in the original mixture?

    Answer: 15 liters

    Let juice = 3k, water = 2k; setting up 3k/(2k + 10) = 3/4 gives k = 5, so juice = 15 liters.