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Quantitative Literacy Flashcards

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

Read the first 6 Quantitative Literacy flashcards as text

  1. A shopkeeper marks up goods by 40% above cost price and then offers a 15% discount on the marked price. A further loyalty discount of 5% is applied to that discounted price. What is the net percentage profit or loss relative to the original cost price?

    Answer: 13.05% profit

    Let cost price = 100. Marked price = 140. After 15% discount: 140 × 0.85 = 119. After 5% loyalty discount: 119 × 0.95 = 113.05. The selling price is 113.05% of cost, giving a net profit of 13.05%. Successive discounts must be applied to the running total, not the original price — they compound rather than add.

  2. The mean of 8 numbers is 14.5. When two numbers are removed, the mean of the remaining 6 numbers drops to 12. What is the mean of the two removed numbers?

    Answer: 22.0

    Total sum of all 8 numbers = 8 × 14.5 = 116. Sum of the remaining 6 numbers = 6 × 12 = 72. Sum of the two removed numbers = 116 − 72 = 44. Mean of the removed pair = 44 ÷ 2 = 22.0.

  3. Country X's GDP grew at a compound annual rate of 6% for 5 years. Country Y's GDP grew at a simple annual rate of 8% over the same period. Both started at $200 billion. After 5 years, which country has a higher GDP and by approximately how much?

    Answer: Country Y by $12.4 billion

    Country X (compound): 200 × (1.06)^5 = 200 × 1.3382 = $267.65 billion. Country Y (simple): 200 × (1 + 0.08 × 5) = 200 × 1.40 = $280 billion. Country Y is higher. Difference = 280 − 267.65 ≈ $12.4 billion. Over short periods with a sufficiently higher rate, simple growth can outpace compound growth.

  4. A sorted data set of 7 values has a median of 18, a range of 22, a minimum of 8, and a mode of 15. Which of the following sets CANNOT satisfy all these conditions?

    Answer: {8, 12, 15, 15, 18, 25, 30}

    All sets need: min = 8, max = 30 (range = 22), 4th value = 18 (median), and 15 as the most frequent value. Sorting Option C: {8, 12, 15, 15, 18, 25, 30} — the 4th value (median) is 15, not 18. This violates the median condition, so Option C cannot be a valid data set. The other three sets all have 18 as their 4th sorted value.

  5. An investment loses 25% in Year 1, gains 20% in Year 2, loses 10% in Year 3, and gains 15% in Year 4. What is the portfolio's net percentage change over all four years?

    Answer: −6.85% loss

    Applying changes multiplicatively: 1 × 0.75 × 1.20 × 0.90 × 1.15 = 0.75 × 1.20 = 0.90; 0.90 × 0.90 = 0.81; 0.81 × 1.15 = 0.9315. Net change = −6.85%. The common error is adding the percentages (−25 + 20 − 10 + 15 = 0%), which ignores that each percentage acts on a different base value.

  6. A cylindrical water tank has its radius increased by 20% and its height decreased by 30%. What is the net percentage change in the volume of the tank? (Volume of a cylinder = πr²h)

    Answer: +0.8%

    New volume = π(1.2r)²(0.7h) = π × 1.44r² × 0.7h = 1.008πr²h. The volume increases by 0.8%. The key insight is that the radius is squared in the formula, so a 20% radius increase produces a 44% increase in r² — this more than offsets the 30% height reduction. (1.44 × 0.70 = 1.008.)