GED Mathematical reasoning 2 — Questions and Answers

Question 1: A store sells apples for $1.25 each. If Maria buys 8 apples and pays with a $20 bill, how much change will she receive?

$9.00
$10.00 (Correct answer)
$11.00
$12.00

Correct answer: $10.00

8 apples × $1.25 = $10.00. Change = $20.00 − $10.00 = $10.00.

To find the total cost, multiply the price per apple ($1.25) by the number of apples (8): $1.25 × 8 = $10.00. Next, subtract the total cost from the amount paid: $20.00 − $10.00 = $10.00 in change. A useful mental math shortcut: $1.25 = 5/4, so 8 × 5/4 = 40/4 = $10.00. Recognizing common fraction-decimal equivalents speeds up GED arithmetic problems. Always double-check by adding the change back to the cost: $10.00 + $10.00 = $20.00 ✓

Question 2: Which of the following is equivalent to 3/8 expressed as a decimal?

0.267
0.375 (Correct answer)
0.425
0.380

Correct answer: 0.375

3 ÷ 8 = 0.375. Dividing the numerator by the denominator converts a fraction to a decimal.

To convert a fraction to a decimal, perform the division: numerator ÷ denominator. So 3 ÷ 8 = 0.375. You can verify this by multiplying back: 0.375 × 8 = 3.000 ✓ Common fraction-to-decimal conversions worth memorizing for the GED: 1/4 = 0.25, 1/2 = 0.5, 3/4 = 0.75, 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875. Alternately, since 8 × 125 = 1000, you can write 3/8 = 375/1000 = 0.375 by scaling the fraction to a denominator of 1000.

Question 3: What is 15% of 240?

30
36 (Correct answer)
40
45

Correct answer: 36

15% of 240 = 0.15 × 240 = 36.

To find a percentage of a number, convert the percent to a decimal and multiply: 15% = 0.15, then 0.15 × 240 = 36. A useful mental math approach: 10% of 240 = 24, and 5% = half of 10% = 12. Add them: 24 + 12 = 36. Percentage problems are common on the GED Mathematical Reasoning test. Understanding the relationship between percents, decimals, and fractions (15% = 15/100 = 3/20) gives you multiple ways to attack the same problem. To check: 36 ÷ 240 = 0.15 = 15% ✓

Question 4: Order the following numbers from least to greatest: −3, 1/2, −1.5, 0, 2

−3, −1.5, 0, 1/2, 2 (Correct answer)
−1.5, −3, 0, 1/2, 2
2, 1/2, 0, −1.5, −3
−3, −1.5, 1/2, 0, 2

Correct answer: −3, −1.5, 0, 1/2, 2

On a number line: −3 < −1.5 < 0 < 0.5 < 2. Converting all to decimals makes comparison straightforward.

Converting all values to decimals: −3 = −3.0, 1/2 = 0.5, −1.5 = −1.5, 0 = 0.0, 2 = 2.0. On a number line, numbers increase from left to right. Negative numbers are to the left of zero, and the farther from zero a negative number is, the smaller it is. So −3 < −1.5 < 0 < 0.5 < 2. A common mistake is thinking −3 is greater than −1.5 because 3 > 1.5 in absolute value. Remember: with negative numbers, the larger the absolute value, the smaller the actual number. The correct order from least to greatest is: −3, −1.5, 0, 1/2, 2.

Question 5: A recipe calls for 2 1/4 cups of flour. If you want to make 1.5 times the recipe, how many cups of flour do you need?

3 cups
3 3/8 cups (Correct answer)
3 1/2 cups
3 3/4 cups

Correct answer: 3 3/8 cups

2 1/4 × 1.5 = 9/4 × 3/2 = 27/8 = 3 3/8 cups.

First, convert 2 1/4 to an improper fraction: 2 1/4 = (2×4 + 1)/4 = 9/4. Next, convert 1.5 to a fraction: 1.5 = 3/2. Multiply: 9/4 × 3/2 = 27/8. Convert back to a mixed number: 27 ÷ 8 = 3 remainder 3, so 27/8 = 3 3/8 cups. You can verify by estimating: 2.25 × 1.5 ≈ 2.25 + 1.125 = 3.375 = 3 3/8 ✓. Working with mixed numbers by converting to improper fractions first prevents errors on the GED.

Question 6: The population of a town was 45,000 in 2010 and 54,000 in 2020. What was the percent increase in population?

9%
16.7%
20% (Correct answer)
25%

Correct answer: 20%

Percent increase = (54,000 − 45,000) / 45,000 × 100 = 9,000 / 45,000 × 100 = 20%.

The percent increase formula is: [(New Value − Old Value) / Old Value] × 100. New Value = 54,000; Old Value = 45,000. Change = 54,000 − 45,000 = 9,000. Percent increase = (9,000 / 45,000) × 100 = 0.20 × 100 = 20%. A quick check: 20% of 45,000 = 0.20 × 45,000 = 9,000 (the actual increase) ✓. Note: The percent increase is based on the ORIGINAL (old) value, not the new value. If you accidentally divide by 54,000, you get ≈16.7%, which is incorrect. Always divide by the starting value when calculating percent change.

GED Mathematical reasoning 2

A store sells apples for $1.25 each.
If Maria buys 8 apples and pays with a $20 bill, how much change will she receive?