GED — All Questions

What is 15% of 240?

• a.45
• b.36✓
• c.24
• d.360

To find 15% of 240, multiply 240 by 0.15, which equals 36. Percent means 'per hundred,' so 15% is 0.15 in decimal form. This is a basic percentage calculation.

Solve for x: 3x + 7 = 22.

• a.15
• b.3
• c.5✓
• d.7

Subtract 7 from both sides to get 3x = 15, then divide by 3 to find x = 5. Isolating the variable step by step solves a linear equation. Checking: 3(5) + 7 = 22, which is correct.

A rectangle has a length of 12 cm and a width of 5 cm. What is its area?

• a.60 cm²✓
• b.34 cm²
• c.120 cm²
• d.17 cm²

Area of a rectangle is length times width: 12 × 5 = 60 square centimeters. Area is always expressed in square units. The perimeter, by contrast, would be 2(12 + 5) = 34 cm.

What is the value of 2³ + 4²?

• a.24✓
• b.20
• c.14
• d.18

2³ equals 8 and 4² equals 16, and their sum is 24. An exponent tells how many times to multiply the base by itself. Evaluating exponents before adding follows the order of operations.

Simplify the fraction 18/24 to lowest terms.

• a.6/8
• b.9/12
• c.2/3
• d.3/4✓

The greatest common factor of 18 and 24 is 6, and dividing both by 6 gives 3/4. A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. Forms like 6/8 and 9/12 are equal in value but not fully reduced.

If a car travels 180 miles in 3 hours, what is its average speed?

• a.540 mph
• b.63 mph
• c.50 mph
• d.60 mph✓

Average speed equals distance divided by time: 180 ÷ 3 = 60 miles per hour. This uses the relationship speed = distance/time. The units confirm the answer is in miles per hour.

What is the mean (average) of 4, 8, 10, and 14?

• a.36
• b.10
• c.8
• d.9✓

Add the numbers to get 36, then divide by the count of 4, giving 9. The mean is the sum of values divided by how many values there are. The total, 36, is not the average itself.

Solve for y: y/4 = 9.

• a.5
• b.36✓
• c.13
• d.2.25

Multiply both sides by 4 to undo the division, giving y = 36. Since y divided by 4 equals 9, y must be 4 times 9. Checking: 36 ÷ 4 = 9, which is correct.

A shirt originally costs $40 and is on sale for 25% off. What is the sale price?

• a.$30✓
• b.$10
• c.$15
• d.$35

A 25% discount on $40 is $10, so the sale price is $40 − $10 = $30. You can also multiply $40 by 0.75 to get $30 directly. The discount is subtracted from the original price.

What is the slope of the line passing through the points (1, 2) and (3, 8)?

• a.6
• b.4
• c.3✓
• d.2

Slope equals the change in y over the change in x: (8 − 2) / (3 − 1) = 6/2 = 3. Slope measures how steep a line is. A positive slope means the line rises from left to right.

The ratio of boys to girls in a class is 3:5. If there are 24 students, how many are girls?

• a.12
• b.9
• c.15✓
• d.18

The ratio 3:5 has 8 parts total, so each part equals 24 ÷ 8 = 3 students. Girls make up 5 parts: 5 × 3 = 15. Ratios divide a whole into proportional shares.

What is 3/4 written as a decimal?

• a.0.75✓
• b.0.34
• c.1.33
• d.0.43

Dividing the numerator 3 by the denominator 4 gives 0.75. A fraction represents division of the top number by the bottom number. This is a common fraction-to-decimal conversion.

A circle has a radius of 6 cm. What is its circumference? (Use π ≈ 3.14.)

• a.18.84 cm
• b.37.68 cm✓
• c.113.04 cm
• d.12 cm

Circumference equals 2πr: 2 × 3.14 × 6 = 37.68 cm. The radius is the distance from center to edge. Using the area formula πr² would instead give about 113 cm².

Evaluate the expression 5(x − 2) when x = 6.

• a.20✓
• b.28
• c.10
• d.40

Substitute x = 6 to get 5(6 − 2) = 5(4) = 20. Following order of operations, solve inside the parentheses first, then multiply. Substituting values into expressions is a key algebra skill.

What is the next number in the pattern: 3, 6, 12, 24, ___?

• a.48✓
• b.30
• c.72
• d.36

Each term is double the one before it, so 24 × 2 = 48. Recognizing that the pattern multiplies by 2 reveals the rule. This is a geometric sequence.

A recipe needs 2 cups of flour for 12 cookies. How many cups are needed for 30 cookies?

• a.2.5 cups
• b.4 cups
• c.5 cups✓
• d.6 cups

Set up a proportion: 2/12 = x/30, so x = (2 × 30)/12 = 5 cups. Proportions keep the ratio of flour to cookies constant. Scaling recipes uses this direct relationship.

What is the area of a triangle with a base of 10 cm and a height of 6 cm?

• a.24 cm²
• b.30 cm²✓
• c.16 cm²
• d.60 cm²

Area of a triangle is one-half the base times the height: (1/2)(10)(6) = 30 cm². The factor of one-half distinguishes a triangle from a rectangle of the same base and height. Area is measured in square units.

Solve the inequality: 2x − 3 < 7.

• a.x > 5
• b.x < 2
• c.x < 5✓
• d.x < 10

Add 3 to both sides to get 2x < 10, then divide by 2 to get x < 5. When dividing an inequality by a positive number, the direction of the sign stays the same. The solution is all values less than 5.

What is 0.6 written as a percent?

• a.0.6%
• b.600%
• c.6%
• d.60%✓

To convert a decimal to a percent, multiply by 100, so 0.6 becomes 60%. This moves the decimal point two places to the right. Percent means 'out of one hundred.'

A box contains 3 red, 4 blue, and 5 green marbles. What is the probability of drawing a blue marble at random?

• a.1/2
• b.1/4
• c.5/12
• d.1/3✓

Probability is favorable outcomes over total outcomes. There are 4 blue marbles out of 3 + 4 + 5 = 12, so the probability is 4/12, which reduces to 1/3. The 1/4 figure is the probability of drawing a red marble (3 out of 12), and 5/12 is the probability of drawing a green one — both are answers to a question that was not asked. And 1/2 would require six blue marbles rather than four.

If 5 pencils cost $1.25, how much do 8 pencils cost at the same rate?

• a.$1.85
• b.$1.60
• c.$2.00✓
• d.$2.50

Each pencil costs $1.25 ÷ 5 = $0.25, so 8 pencils cost 8 × $0.25 = $2.00. Finding the unit rate lets you scale to any quantity. Unit pricing is a common real-world calculation.

What is the value of the expression -4 + 9 − 3?

• a.2✓
• b.10
• c.8
• d.-10

Working left to right: -4 + 9 = 5, and 5 − 3 = 2. Adding a positive to a negative moves toward zero and beyond. Careful sign handling gives the correct result of 2.

A square has a perimeter of 36 cm. What is the length of one side?

• a.12 cm
• b.9 cm✓
• c.18 cm
• d.6 cm

A square has four equal sides, so divide the perimeter by 4: 36 ÷ 4 = 9 cm. Perimeter is the total distance around a shape. Each side of this square measures 9 cm.

Which value of x makes the equation 2x = 5x − 12 true?

• a.6
• b.4✓
• c.3
• d.2

Subtract 2x from both sides to get 0 = 3x − 12, then add 12 and divide by 3 to find x = 4. Gathering variables on one side isolates x. Checking: 2(4) = 8 and 5(4) − 12 = 8, which matches.

The temperature rose from -5°F to 12°F. By how many degrees did it rise?

• a.17°F✓
• b.12°F
• c.7°F
• d.-17°F

The change equals 12 − (−5) = 12 + 5 = 17 degrees. Subtracting a negative is the same as adding its positive. The temperature climbed 17°F.

What is 3/5 + 1/5?

• a.4/5✓
• b.2/5
• c.3/25
• d.4/10

When fractions share a denominator, add the numerators: 3 + 1 = 4, giving 4/5. The denominator stays the same at 5. This result is already in lowest terms.

A phone plan costs $30 per month plus $0.10 per text. Which expression gives the total monthly cost for t texts?

• a.30 + 0.10t✓
• b.30t + 0.10
• c.30.10t
• d.30 + 0.10 + t

The $30 fee is charged once whatever happens, so it stands alone; the 10 cents is charged per text, so it is multiplied by the number of texts. That gives 30 + 0.10t. Writing 30t + 0.10 swaps the two roles, charging $30 per text and a flat dime a month. Writing 30 + 0.10 + t adds the number of texts to the money instead of multiplying, which mixes a count with dollars. And 30.10t charges the whole $30.10 for every single text.

What is the median of the data set 7, 3, 9, 5, 11?

• a.35
• b.5
• c.9
• d.7✓

First order the numbers: 3, 5, 7, 9, 11; the middle value is 7. The median is the center of an ordered list. With five values, the third number is the median.

If a triangle has angles measuring 40° and 75°, what is the third angle?

• a.75°
• b.55°
• c.65°✓
• d.115°

The angles of a triangle sum to 180°, so 180 − 40 − 75 = 65°. This triangle-angle-sum rule holds for every triangle. The missing angle measures 65 degrees.

Expand the expression 4(2x + 3).

• a.6x + 7
• b.8x + 12✓
• c.8x + 7
• d.8x + 3

Use the distributive property to multiply 4 by each term: 4 × 2x = 8x and 4 × 3 = 12. The result is 8x + 12. Distribution multiplies the outside factor across everything inside the parentheses.

A worker earns $18 per hour and works 35 hours in a week. What are the weekly earnings?

• a.$720
• b.$53
• c.$530
• d.$630✓

Multiply the hourly rate by hours worked: 18 × 35 = 630 dollars. Total pay equals rate times time. The worker earns $630 that week.

What is the square root of 144?

• a.11
• b.72
• c.12✓
• d.14

The square root of 144 is the number that, multiplied by itself, gives 144; that number is 12 because 12 × 12 = 144. Square roots reverse the squaring operation. Note that 72 is half of 144, not its root.

A number increased by 20% becomes 60. What was the original number?

• a.48
• b.50✓
• c.40
• d.72

If the original number is x, then 1.20x = 60, so x = 60 ÷ 1.20 = 50. Increasing by 20% multiplies by 1.20. Reversing the increase means dividing by 1.20.

Two angles are complementary. If one measures 35°, what is the other?

• a.45°
• b.145°
• c.55°✓
• d.65°

Complementary angles add up to 90°, so the other angle is 90 − 35 = 55°. Complementary differs from supplementary, which sums to 180°. The missing angle is 55 degrees.

What is 3/8 + 1/4?

• a.4/12
• b.3/4
• c.5/8✓
• d.1/2

Rewrite 1/4 as 2/8 so the denominators match, then add the numerators: 3/8 + 2/8 = 5/8. Adding numerators and denominators straight across gives 4/12, which is what makes fractions look harder than they are. One half is 4/8 and falls just short. And 3/4 is 6/8, one eighth too much.

What is 2/3 × 3/5?

• a.5/8
• b.2/5✓
• c.6/5
• d.1/5

Multiply straight across to get 6/15, then divide both parts by 3 for 2/5. Adding across instead of multiplying produces 5/8. Inverting the second fraction gives 6/5, which is what division would call for. And 1/5 drops a factor somewhere in the reduction.

What is 5/6 ÷ 1/3?

• a.2 1/2✓
• b.5/18
• c.2/9
• d.1 1/2

Dividing by a fraction means multiplying by its reciprocal: 5/6 × 3/1 = 15/6, which reduces to 5/2, or 2 1/2. Multiplying by 1/3 instead of dividing gives 5/18. The answer 1 1/2 would come from a different dividend altogether. And 2/9 does not arise from any correct step here.

Write 0.45 as a fraction in lowest terms.

• a.45/10
• b.4/5
• c.1/45
• d.9/20✓

The digits end in the hundredths place, so 0.45 is 45/100, and dividing both parts by 5 gives 9/20. Writing 45/10 misplaces the decimal by a factor of ten. Four fifths is 0.8, nearly twice as large. And 1/45 inverts the number entirely.

Which list puts 5/8, 0.6 and 58% in order from least to greatest?

• a.58%, 5/8, 0.6
• b.5/8, 0.6, 58%
• c.0.6, 58%, 5/8
• d.58%, 0.6, 5/8✓

Convert everything to decimals: 58% is 0.58, 0.6 stays as it is, and 5/8 is 0.625, so the order runs 0.58, 0.60, 0.625. Reversing that order puts the largest first. Placing 0.6 below 58% mistakes 0.6 for 0.06. And putting 5/8 before 0.6 treats eight parts as smaller than they are.

What is −7 − (−3)?

• a.4
• b.−10
• c.−4✓
• d.10

Subtracting a negative is the same as adding its opposite, so −7 − (−3) becomes −7 + 3, which is −4. Treating the two minus signs as one gives −10. Changing the sign of the first number as well gives 10. And 4 has the right size but the wrong sign, since the result stays below zero.

What is the product of −3 and −5?

• a.8
• b.15✓
• c.−15
• d.−8

Two negative factors give a positive product, so (−3)(−5) = 15. Keeping the answer negative ignores that rule. The value −8 comes from adding rather than multiplying. And 8 is that same sum with the sign dropped.

Evaluate |−9| − |4|.

• a.13
• b.5✓
• c.−13
• d.−5

Absolute value strips the sign, so this is 9 − 4, which equals 5. Adding the two values after stripping the signs gives 13. Keeping the first number negative and then subtracting gives −13. And −5 reverses the order of the subtraction.

A 12-ounce bottle of juice costs $3.60. What is the price per ounce?

• a.$0.30✓
• b.$3.33
• c.$0.33
• d.$4.32

A unit rate divides cost by quantity: $3.60 ÷ 12 = $0.30 per ounce. Dividing the ounces by the dollars gives 3.33 and answers a question nobody asked. The figure $0.33 comes from dividing by 11 or from a slip in the decimal. And multiplying rather than dividing gives $4.32.

A price rises from $40 to $50. What is the percent increase?

• a.25%✓
• b.20%
• c.125%
• d.10%

Percent change divides the increase by the original amount: 10 ÷ 40 = 0.25, or 25%. Dividing by the new price instead gives 20%, which is the classic trap in these problems. The raw increase of 10 dollars is not itself 10 percent. And 125% is the new price as a share of the old, not the increase.

8 is what percent of 32?

• a.4%
• b.40%
• c.400%
• d.25%✓

Divide the part by the whole and convert: 8 ÷ 32 = 0.25, which is 25%. The value 4 is the result of dividing 32 by 8, the reverse comparison. Forty percent of 32 would be 12.8. And 400% would make 8 four times the whole rather than a quarter of it.

An item costs $24 and sales tax is 7%. What is the total?

• a.$24.07
• b.$25.68✓
• c.$1.68
• d.$31.00

The tax is 0.07 × $24 = $1.68, and adding it to the price gives $25.68; multiplying $24 by 1.07 does both steps at once. Adding seven cents treats the percent as a flat amount. Adding seven dollars treats it as dollars rather than percent. And $1.68 is the tax alone, not the total.

A meal costs $45 and the diner leaves an 18% tip. How much is the tip?

• a.$81.00
• b.$0.81
• c.$5.31
• d.$8.10✓

Eighteen percent of $45 is 0.18 × 45 = $8.10. Moving the decimal one place too far left gives $0.81. Moving it the other way gives $81, which is more than the meal. And $5.31 would be about 11.8 percent, a rate the question did not give.

How much simple interest does $500 earn at 4% per year for 3 years?

• a.$60✓
• b.$600
• c.$20
• d.$540

Simple interest is principal times rate times time: 500 × 0.04 × 3 = $60. Leaving out the three years gives $20, the first year only. The figure $600 misplaces a decimal. And $540 is the balance after interest rather than the interest itself, and even then only if the interest were $40.

Write 3.2 × 10⁴ in standard form.

• a.320,000
• b.3,200
• c.32,000✓
• d.12.8

An exponent of 4 moves the decimal point four places to the right, turning 3.2 into 32,000. Moving it three places gives 3,200. Moving it five gives 320,000. And 12.8 is 3.2 multiplied by 4 rather than by ten to the fourth.

What is the value of (2³)²?

• a.512
• b.12
• c.32
• d.64✓

Work from the inside out: 2³ is 8, and 8² is 64; multiplying the exponents to get 2⁶ gives the same result. Multiplying the base by the exponents gives 12. Adding the exponents gives 2⁵, or 32. And 512 is 2⁹, which would come from raising 8 to the third power.