Bar graphs and circle graphs

1. Find the Car bar. Its top sits between the 45 and 50 gridlines; the label above it shows 48.
2. Find the Train bar. Its top is exactly on the 30 gridline, so it is 30.
3. "How many more" means subtract the smaller amount from the larger amount: 48 - 30 = 18

18 more employees drive than take the train.

Check: Add back: 30 + 18 = 48 ✓ — that is the Car bar.

Tip: "How many more" or "how many fewer" always means subtract. "Altogether" or "in all" means add. Always confirm you are reading the two bars the question names.

1. The Transportation section is labeled 12\%.
2. The whole circle stands for the monthly pay, \$3{,}200.
3. Find 12\% of \$3{,}200. Change the percent to a decimal (12\% = 0.12) and multiply: 0.12 \times 3{,}200 = 384

The family spends $384 on transportation.

Check: 10\% of \$3{,}200 is \$320 and 2\% is \$64; 320 + 64 = 384 ✓

Tip: Section amount = percent (as a decimal) × whole. Move the decimal point two places left to turn a percent into a decimal: 12\% \to 0.12.

1. Find the Mystery bar. Its top is exactly on the 80 gridline, so 80 Mystery books were checked out.
2. Find the Biography bar. Its top is on the 20 gridline, so 20 Biography books.
3. "How many fewer" means subtract the smaller value from the larger value: 80 - 20 = 60

60 fewer Biography books were checked out.

Check: 20 + 60 = 80 ✓, which is the Mystery bar.

Tip: "Fewer" and "more" both mean subtract. Before you subtract, point at the two bars the question names so you do not grab a neighboring bar by mistake.

1. Find the Charting section: it is 25\% of the shift.
2. The whole shift is 12 hours.
3. Change the percent to a decimal: 25\% = 0.25.
4. Multiply by the whole: 0.25 \times 12 = 3

The nurse spends 3 hours charting.

Check: 25\% is one-fourth, and one-fourth of 12 hours is 12 \div 4 = 3 ✓.

Tip: A circle graph section × the total gives the amount. Benchmark percents help you check fast: 50% is half, 25% is a fourth, 10% is a tenth.

1. Rent is 35\% and Transportation is 12\% of the same whole.
2. Because both are parts of the same whole, subtract the percents: 35\% - 12\% = 23\%
3. Find 23\% of \$3{,}200: 0.23 \times 3{,}200 = 736

The family spends $736 more on rent than on transportation.

Check (the long way): Rent = 0.35 \times 3{,}200 = \$1{,}120; Transportation = 0.12 \times 3{,}200 = \$384; 1{,}120 - 384 = \$736 ✓

Tip: When two sections share the same whole, you may add or subtract their percents first and convert to dollars once. This saves time and avoids rounding errors.

1. A whole circle is 360^\circ, which stands for 100\% of the data.
2. The Football section is 40\% of the circle, so its angle is 40\% of 360^\circ: 0.40 \times 360^\circ = 144^\circ

The central angle is 144°.

Check: Another way: football is \dfrac{96}{240} = \dfrac{2}{5} of the people, and \dfrac{2}{5} of 360^\circ is 144^\circ ✓

Tip: Central angle = \text{percent} \times 360^\circ, or \dfrac{\text{part}}{\text{whole}} \times 360^\circ. All the central angles of a circle graph add to 360^\circ.

1. Read Store A's bars: Q1 = 40 (thousand dollars), Q3 = 70.
2. Find the amount of increase: 70 - 40 = 30
3. Divide by the original (Q1) value and convert to a percent: \frac{30}{40} = 0.75 = 75\%

Store A's sales increased by 75%.

Check: 40 + 75\% of 40 = 40 + 30 = 70 ✓

Tip: The units (thousands of dollars) cancel when you find a percent change, so you can work with the numbers on the scale directly. Always divide by the starting value.

1. Read the Plastic bar. It ends between the 80 and 100 labels, on the gridline for 90 pounds.
2. The whole is the total collected: 400 pounds.
3. Percent = part ÷ whole × 100: \frac{90}{400} = 0.225 0.225 \times 100 = 22.5\%

22.5% of the weight was plastic.

Check: 22.5\% of 400 is 0.225 \times 400 = 90 ✓. Also, 90 is a little less than one-fourth of 400 (which is 100), and 22.5% is a little less than 25% ✓.

Tip: Divide by the whole, never by "everything else." Ask yourself: what is the total the question is talking about?

1. Read the two sections: Patient care is 45\% and Medication is 15\%.
2. Find the difference in percent: 45\% - 15\% = 30\%.
3. Find 30% of the 12-hour shift: 0.30 \times 12 = 3.6 \text{ hours}
4. Convert hours to minutes (1 hour = 60 minutes): 3.6 \times 60 = 216 \text{ minutes}

The nurse spends 216 more minutes on patient care.

Check: Patient care: 0.45 \times 12 = 5.4 h = 324 min. Medication: 0.15 \times 12 = 1.8 h = 108 min. 324 - 108 = 216 ✓.

Tip: Circle the unit the question asks for. Graph data often comes in one unit (hours) while the answer must be in another (minutes).

1. Read the sections: Heating/cooling = 42\%, Water heating = 18\%.
2. Difference in percent: 42\% - 18\% = 24\%.
3. Take 24% of the monthly total of 1,200 kWh: 0.24 \times 1{,}200 = 288

Heating and cooling uses 288 kWh more per month.

Check: Do each part separately. Heating/cooling: 0.42 \times 1{,}200 = 504 kWh. Water heating: 0.18 \times 1{,}200 = 216 kWh. 504 - 216 = 288 ✓.

Tip: When both sections come from the same whole, you can subtract the percents first and multiply once. It saves a step and reduces calculator errors.

1. Use the legend: blue = 2024, orange = 2025.
2. Find the change (2025 − 2024) for each group:
   • 18–29: 150 - 120 = +30
   • 30–44: 130 - 140 = -10 (a decrease)
   • 45–59: 110 - 90 = +20
   • 60+: 80 - 40 = +40
3. The largest increase is +40.

The 60+ age group had the greatest increase.

Check: 60+ grew by 40 members, more than the 30 members in the 18–29 group ✓. The 30–44 group actually lost members.

Tip: "Greatest increase" is about the gap between paired bars, not the tallest bar. Small bars can have the biggest change.

1. Notice the vertical axis starts at 400, not 0 (see the break mark). So bar heights do not show true sizes.
2. Read the actual values: Friday = 450, Saturday = 600.
3. "How many times as many" means divide: \frac{600}{450} = \frac{4}{3} = 1\tfrac{1}{3}

Saturday's sales were only 1\tfrac{1}{3} times Friday's.

Check: 450 \times 1\tfrac{1}{3} = 450 + 150 = 600 ✓. The picture shows 4 times because the visible parts of the bars are 600 - 400 = 200 and 450 - 400 = 50, and 200 \div 50 = 4.

Tip: Always check where the vertical axis starts. If it does not start at 0, compare the numbers, never the bar lengths.

1. Read the key: a full circle = 8 trees, a half circle = 4 trees.
2. Group C has 6 full circles: 6 \times 8 = 48 trees.
3. Group D has 2 full circles and 1 half circle: 2 \times 8 + 4 = 20 trees.
4. "How many more" means subtract: 48 - 20 = 28

Group C planted 28 more trees.

Check: Count symbols: C has 6, D has 2.5, a difference of 3.5 symbols. 3.5 \times 8 = 28 ✓.

Tip: In a pictograph, every symbol stands for a number given in the key. Always multiply by the key value — and remember half symbols.

1. All sections of a circle graph add to 100\%. Find the Fish percent: 100\% - 45\% - 30\% - 10\% = 15\%
2. So 54 customers are 15\% of the total T: 0.15 \times T = 54
3. Divide both sides by 0.15: T = \frac{54}{0.15} = 360

360 customers were surveyed.

Check: 15\% of 360 = 0.15 \times 360 = 54 ✓

Tip: This is a "work backwards" percent problem: part ÷ percent = whole. Before dividing, make sure you found the correct missing percent — use every labeled section, including "Other".

1. Read the 60+ bars: 2024 (original) = 40, 2025 (new) = 80.
2. Find the change: 80 - 40 = 40 members.
3. Divide by the original value: \frac{40}{40} = 1
4. Change to a percent: 1 \times 100 = 100\%.

Membership in the 60+ group rose by 100%.

Check: A 100% increase means the group gained as many members as it started with: 40 + 40 = 80 ✓. In other words, it doubled.

Tip: "Doubled" = a 100% increase, not 200%. The new amount is 200% of the old, but the increase is 100%.

1. The axis begins at $1,450, so the bars are cut off and bar heights mislead.
2. Read the values: 2022 = $1,500, 2024 = $1,650.
3. Change: 1{,}650 - 1{,}500 = 150 dollars.
4. Percent increase = \dfrac{\text{change}}{\text{original}} \times 100: \frac{150}{1{,}500} \times 100 = 10\%

Rent actually rose by 10%.

Check: 10\% of $1,500 is $150, and 1{,}500 + 150 = 1{,}650 ✓. The reader's 300% comes from the visible bar parts: 50 and 200, a 4-times jump that looks like +300%.

Tip: On the GED, a graph with a broken axis is often paired with a claim. Test the claim with the actual numbers.

Test each choice with the percents: Heating/cooling 42%, Appliances 22%, Water heating 18%, Lighting 10%, Electronics 8%.

1. A: Appliances + water heating = 22\% + 18\% = 40\%, which is less than heating/cooling's 42%. False.
2. B: Lighting + electronics = 10\% + 8\% = 18\% of 1,200: 0.18 \times 1{,}200 = 216 kWh. True.
3. C: Appliances use 22\% \div 10\% = 2.2 times the lighting, not 12 times. False.
4. D: Heating/cooling is 42%, which is less than half (50%). False.

The supported statement is B.

Check: Lighting alone is 0.10 \times 1{,}200 = 120 kWh and electronics is 0.08 \times 1{,}200 = 96 kWh; 120 + 96 = 216 ✓.

Tip: In "which statement is true" items, test every option. A statement can sound right because one part is true while the numbers are wrong.

1. The sections must add to 100\%. Car wash percent: 100\% - 35\% - 30\% - 25\% = 10\%
2. So $450 is 10\% of the total T: 0.10 \times T = 450
3. Divide both sides by 0.10: T = \frac{450}{0.10} = 4{,}500

The fundraiser raised $4,500 in all.

Check: 10\% of $4,500 is $450 ✓. The other sections: donations 0.35 \times 4{,}500 = 1{,}575, bake sale 1{,}350, raffle 1{,}125; 1{,}575 + 1{,}350 + 1{,}125 + 450 = 4{,}500 ✓.

Tip: Working backwards: part ÷ percent = whole. If your "whole" comes out smaller than the part, you multiplied when you should have divided.

1. Current savings: 10\% of \$3{,}200: 0.10 \times 3{,}200 = 320
2. Add the \$160 moved from Other: 320 + 160 = 480
3. New share of the pay (the whole is still \$3{,}200): \frac{480}{3{,}200} = 0.15 = 15\%
4. New central angle: 0.15 \times 360^\circ = 54^\circ

The Savings section will be 54°.

Check: The old angle was 0.10 \times 360^\circ = 36^\circ. The \$160 is \tfrac{160}{3{,}200} = 5\% of the pay, which is 0.05 \times 360^\circ = 18^\circ. 36^\circ + 18^\circ = 54^\circ ✓

Tip: When money moves between sections but the total stays the same, the change in angle equals the moved amount's share of 360^\circ. Keep track of what the whole is at every step.

1. Old charting time: 25\% of 12 h = 0.25 \times 12 = 3 hours.
2. Convert 36 minutes to hours: 36 \div 60 = 0.6 hours.
3. New charting time: 3 + 0.6 = 3.6 hours. The shift is still 12 hours.
4. New fraction of the shift: \dfrac{3.6}{12} = 0.30 = 30\%.
5. Central angle: 0.30 \times 360^\circ = 108^\circ

The Charting section will measure 108°.

Check: The old angle was 0.25 \times 360 = 90^\circ. The extra 0.6 h is \tfrac{0.6}{12} = 5\% of the shift, which adds 0.05 \times 360 = 18^\circ. 90 + 18 = 108 ✓.

Tip: When time or money moves between sections but the total stays the same, find the new amount, divide by the (unchanged) total, then multiply by 360°.

1. This year's metal (from the bar): 40 pounds. That is \frac{40}{400} = 10\% of the total.
2. Next year's metal: 15\% of 400 = 0.15 \times 400 = 60 pounds.
3. Change: 60 - 40 = 20 pounds.
4. Percent increase (divide by the original): \frac{20}{40} \times 100 = 50\%

The weight of metal increased by 50%.

Check: 40 \times 1.50 = 60 ✓. Note that metal's share went from 10% to 15%, which is 5 percentage points, but a 50% increase in weight.

Tip: "Percentage points" (15% − 10% = 5 points) and "percent change" (50%) are different. The GED asks for percent change unless it says points.