GED Math Sample Questions and Explanations

1. Parentheses first: 2 + 4 = 6.
2. Multiply and divide from left to right: 3 × 6 = 18, then 18 ÷ 9 = 2.
3. Subtract last: 18 − 2 = 16.

Check: On a calculator that follows the order of operations, 18 − 3 × 6 ÷ 9 also gives 16.

Wrong choices

• 10: 10 works strictly left to right: (18 − 3) × 6 ÷ 9. Subtraction must wait until multiplication and division are done.
• 0: 0 subtracts 3 × 6 from 18 first and then divides by 9; the division belongs to the 3 × 6 part only.
• 2: 2 is only the value of 3 × 6 ÷ 9; it still has to be subtracted from 18.

1. Slope = (y₂ − y₁) / (x₂ − x₁).
2. Change in y: 12 − 3 = 9.
3. Change in x: 4 − 1 = 3.
4. Slope = 9 / 3 = 3.

Check: Starting at (1, 3), go right 1 and up 3 three times: (2, 6), (3, 9), (4, 12).

Wrong choices

• 1/3: 1/3 puts the change in x over the change in y; slope is rise over run.
• −3: −3 has the wrong sign; y goes up as x goes up, so the slope is positive.
• 5: 5 adds the y-values (12 + 3) instead of subtracting them.

1. Change 18% to a decimal: 18% = 0.18.
2. Multiply: 0.18 × $45.00 = $8.10.

Check: 10% of $45 is $4.50, so 20% is $9.00. 18% should be a little less than $9.00, and $8.10 is.

Wrong choices

• $0.81: $0.81 uses 0.018 instead of 0.18; the decimal point was moved one place too far.
• $2.50: $2.50 divides 45 by 18 instead of finding 18% of 45.
• $53.10: $53.10 is the bill plus the tip, not the tip alone.

1. Compare with y = mx + b.
2. The number multiplied by x is m = −2, the slope.
3. The number added on is b = 5, the y-intercept.

Check: When x = 0, y = −2(0) + 5 = 5, so the line crosses the y-axis at (0, 5).

Wrong choices

• Slope 5, y-intercept −2: Slope 5, y-intercept −2 switches the two numbers.
• Slope 2, y-intercept 5: Slope 2 drops the negative sign; the line goes down from left to right.
• Slope −2, y-intercept −5: The y-intercept is +5, not −5; at x = 0, y = 5.

1. Amount of increase: $1,290 − $1,200 = $90.
2. Divide by the original amount: 90 ÷ 1,200 = 0.075.
3. Change to a percent: 0.075 × 100 = 7.5%.

Check: 7.5% of $1,200 is $90, and $1,200 + $90 = $1,290.

Wrong choices

• 7.0%: 7.0% divides by the new rent ($1,290) instead of the original rent; 90 ÷ 1,290 is about 0.070.
• 9%: 9% treats the $90 increase as if it were 9 percent.
• 90%: 90% uses the dollar increase as the percent without dividing by the original rent.

1. Add 8 to both sides: 5x = 35.
2. Divide both sides by 5: x = 7.

Check: 5(7) − 8 = 35 − 8 = 27.

Wrong choices

• x = 3.8: x = 3.8 subtracts 8 instead of adding it: (27 − 8) ÷ 5.
• x = 35: x = 35 is the value of 5x; it still has to be divided by 5.
• x = 5.4: x = 5.4 divides 27 by 5 and ignores the −8.

1. Change the fractions to decimals: 3/5 = 0.6 and 5/8 = 0.625.
2. Now compare four decimals: 0.65, 0.625, 0.58, 0.6.
3. From least to greatest: 0.58, 0.6, 0.625, 0.65.
4. Write them in their original form: 0.58, 3/5, 5/8, 0.65.

Check: 0.58 < 0.60 < 0.625 < 0.65, so each number is bigger than the one before it.

Wrong choices

• 3/5, 5/8, 0.58, 0.65: 3/5 (0.6) is larger than 0.58, so 3/5 cannot come first.
• 0.58, 0.65, 3/5, 5/8: This lists the decimals first and the fractions after, but 3/5 (0.6) and 5/8 (0.625) are smaller than 0.65.
• 0.65, 5/8, 3/5, 0.58: This is the right order but backward: it goes from greatest to least.

1. Subtract 3 from both sides: x/4 = 7.
2. Multiply both sides by 4: x = 28.

Check: 28 ÷ 4 + 3 = 7 + 3 = 10.

Wrong choices

• x = 52: x = 52 adds 3 instead of subtracting it: (10 + 3) × 4.
• x = 7: x = 7 is the value of x/4, not x.
• x = 1.75: x = 1.75 divides 7 by 4 instead of multiplying.

1. Add the values: 7 + 10 + 12 + 19 + 22 = 70.
2. Divide by the number of days: 70 ÷ 5 = 14.

Check: 14 × 5 = 70, which matches the total.

Wrong choices

• 12: 12 is the median (the middle value), not the mean.
• 15: 15 is the range (22 − 7), not the mean.
• 70: 70 is the total; it still has to be divided by 5.

1. Group the like terms: (4x − 2x) + (7 + 3).
2. 4x − 2x = 2x.
3. 7 + 3 = 10.
4. The result is 2x + 10.

Check: Try x = 1. The original is 4 + 7 − 2 + 3 = 12, and 2(1) + 10 = 12.

Wrong choices

• 6x + 10: 6x + 10 adds 4x and 2x, but the 2x is being subtracted.
• 12x: 12x combines numbers and x-terms together; only like terms can be combined.
• 2x + 4: 2x + 4 subtracts 3 from 7, but the 3 is being added.