GED Math Mastery: How to Solve Average Problems (

GED Math Mastery: How to Solve Average Problems (

Hook (10 seconds on camera): "Average problems show up 3-5 times on every GED Math test—master them, and you’ll bank 10-15 extra points, pushing you into the next scoring tier (150+ to 165+)."

What This Question Type Is Actually Testing

The GED isn’t testing whether you can calculate an average—it’s testing: 1. Reading precision: Did you extract the exact numbers from the problem, or did you misread "total" vs. "average"? 2. Equation setup: Can you translate words into the formula Total = Average × Number of items without mixing up variables? 3. Trap detection: Will you fall for answer choices that swap totals and averages or ignore hidden conditions (e.g., "excluding one value")?

Anatomy of the Question

Every average problem on the GED follows this structure:

1. The Stem (The Scenario)

• Describes a real-world situation (e.g., test scores, sales, temperatures).
• Key words: "average," "mean," "total," "combined," "per," "excluding."
• Example stem: "A student has taken 5 math tests. The average score on the first 4 tests is 82. What score does the student need on the 5th test to have an overall average of 85?"

2. The Conditions (Hidden Rules)

• Explicit: Numbers given directly (e.g., "average of 82 on 4 tests").
• Implicit: What’s not stated but required (e.g., "5th test score must be a whole number").
• Traps:
• "Excluding one value" (you must subtract it from the total).
• "Weighted averages" (e.g., "two tests count double").

3. The Answer Choices (Distractors)

• Correct answer: Matches the calculated value.
• Wrong answers:
• Swaps totals and averages (e.g., 82 × 5 = 410 instead of 85 × 5 = 425).
• Ignores a condition (e.g., forgets to subtract the excluded value).
• Off-by-one errors (e.g., uses 4 tests instead of 5).

4. What to Ignore

• Fluff words: "A student," "in a class," "over the semester" (unless they specify a condition).
• Red herrings: Extra numbers not needed for the calculation (e.g., "the student’s highest score was 90").

The Decision Framework (Step-by-Step)

Run this process for every average problem:

1. Identify the unknown.
2. What are you solving for? (e.g., "5th test score," "total sales," "number of items").

3. Circle or underline it in the question.

4. Write the average formula.

5. Average = Total ÷ Number of items

6. Rearrange to solve for the unknown:

   • Total = Average × Number of items
   • Number of items = Total ÷ Average

7. Extract all given numbers.

8. List them with labels (e.g., "Avg of 4 tests = 82," "Desired avg = 85," "5 tests total").

9. Cross out irrelevant numbers.

10. Calculate the required total.

11. Use the formula to find the total needed for the desired average.

12. Example: 85 (desired avg) × 5 (tests) = 425 (total points needed).

13. Calculate the current total.

14. Use given averages to find the sum of known values.

15. Example: 82 (avg of 4 tests) × 4 = 328 (current total).

16. Find the missing value.

17. Subtract the current total from the required total.

18. Example: 425 – 328 = 97 (5th test score needed).

19. Check for traps.

20. Did you account for all conditions? (e.g., "excluding one value," "weighted scores").

21. Does the answer make sense? (e.g., a test score can’t be negative).

22. Match to answer choices.

23. Eliminate wrong answers first (see "Wrong Answer Patterns" below).
24. Pick the remaining choice.

Worked Examples

Example 1: Straightforward (GED Easy-Medium)

Question: "A basketball team has played 6 games. Their average score is 78 points. How many total points have they scored?"

Step-by-Step: 1. Unknown: Total points scored. 2. Formula: Total = Average × Number of items 3. Given:
- Average = 78
- Number of games = 6 4. Calculate: 78 × 6 = 468 5. No traps: No excluded values or weights. 6. Answer: 468

Answer Choices (Hypothetical): A) 72 B) 468 C) 474 D) 528

Elimination: - A) 72 is too small (78 × 1). - C) 474 is 79 × 6 (off by 1). - D) 528 is 88 × 6 (wrong average).

Example 2: Common Trap (GED Medium)

Question: "A student has an average of 88 on 4 quizzes. If the lowest quiz score is dropped, the average of the remaining 3 quizzes is 92. What was the lowest quiz score?"

Step-by-Step: 1. Unknown: Lowest quiz score. 2. Formula: Total = Average × Number of items 3. Given:
- Avg of 4 quizzes = 88 → Total = 88 × 4 = 352
- Avg of 3 quizzes (after dropping lowest) = 92 → Total = 92 × 3 = 276 4. Find missing value: 352 (total of 4) – 276 (total of 3) = 76 (lowest score) 5. Trap: Forgetting to subtract the dropped score. 6. Answer: 76

Answer Choices (Hypothetical): A) 76 B) 80 C) 84 D) 88

Elimination: - B) 80: Would make the new total 272 (352 – 80), but 272 ÷ 3 = 89.33 (not 92). - C) 84: New total = 268 → 268 ÷ 3 ≈ 89.33. - D) 88: New total = 264 → 264 ÷ 3 = 88 (wrong).

Example 3: Hard Variant (GED Hard)

Question: "A class has 20 students. The average score on a test is 75. If the average score of the 12 girls is 80, what is the average score of the 8 boys?"

Step-by-Step: 1. Unknown: Average score of the boys. 2. Formula: Total = Average × Number of items 3. Given:
- Total students = 20, avg = 75 → Total class score = 75 × 20 = 1500
- Girls = 12, avg = 80 → Total girls’ score = 80 × 12 = 960 4. Find boys’ total: 1500 – 960 = 540 5. Find boys’ average: 540 ÷ 8 = 67.5 6. Trap: Forgetting to subtract girls’ total from class total. 7. Answer: 67.5

Answer Choices (Hypothetical): A) 65 B) 67.5 C) 70 D) 72

Elimination: - A) 65: Would make boys’ total = 520 → class total = 1480 (not 1500). - C) 70: Boys’ total = 560 → class total = 1520 (wrong). - D) 72: Boys’ total = 576 → class total = 1536 (wrong).

Wrong Answer Patterns

1. Swaps totals and averages.
- Why it looks right: Uses the given average but multiplies by the wrong number of items.
- Why it’s wrong: Example: For 5 tests with avg 85, picks 85 × 4 = 340 (ignores the 5th test).

2. Ignores a condition.
- Why it looks right: Calculates the average correctly but forgets to exclude a value.
- Why it’s wrong: Example: Drops the lowest score but doesn’t subtract it from the total.

3. Off-by-one errors.
- Why it looks right: Uses the right formula but miscounts the number of items.
- Why it’s wrong: Example: For 6 games, uses 5 in the calculation.

4. Misapplies weights.
- Why it looks right: Treats all values equally when some are weighted.
- Why it’s wrong: Example: Two tests count double but are treated as single tests.

Common Mistakes

1. Misreading "average" vs. "total."
- Why it happens: Rushing and seeing numbers without context.
- Correct approach: Circle the unknown and label all given numbers.

2. Forgetting to rearrange the formula.
- Why it happens: Memorizing Average = Total ÷ N but not Total = Average × N.
- Correct approach: Write the formula first, then solve for the unknown.

3. Skipping the "current total" step.
- Why it happens: Assuming the given average is the final answer.
- Correct approach: Always calculate the total needed and the current total.

4. Not checking units.
- Why it happens: Mixing up "per student" vs. "per class."
- Correct approach: Label all numbers (e.g., "80 avg for 12 girls").

5. Falling for "excluding" traps.
- Why it happens: Overlooking words like "dropped," "excluding," or "remaining."
- Correct approach: Underline these words and adjust totals accordingly.

Time Strategy

• Target time: 45–60 seconds per question.
• When to skip:
• If you’re stuck after 30 seconds, flag it and move on.
• If the question has multiple conditions (e.g., weighted averages + excluding values), come back later.
• Minimum work to answer confidently:
• Write the formula.
• Calculate the required total.
• Calculate the current total.
• Subtract to find the missing value.
• Eliminate 2 wrong answers.

Backsolving and Shortcuts

1. Plug in answer choices (backsolving).
- Start with the middle choice (B or C) and work backward.
- Example: For the 5-test problem, test choice C (90):
- 82 × 4 = 328
- 328 + 90 = 418
- 418 ÷ 5 = 83.6 (not 85) → too low.
- Test choice D (97):
- 328 + 97 = 425
- 425 ÷ 5 = 85 → correct.

2. Use the "difference" shortcut for missing values.
- Example: To raise an average from 82 to 85 over 5 tests:
- Difference per test: 85 – 82 = 3
- Total difference needed: 3 × 5 = 15
- Current total: 82 × 4 = 328
- Missing value: 328 + 15 = 343? No!
- Correction: The 5th test must cover the 15-point gap plus its own 85-point share:
- 328 + x = 425 → x = 97.

3. Eliminate first.
- Cross out answers that are clearly too high/low (e.g., negative scores, averages higher than all given values).

1-Minute Recap

"Here’s your 30-second cheat sheet for average problems on the GED:

1. Circle the unknown. What are you solving for? A score? A total? A number of items?
2. Write the formula: Total = Average × Number of items. Rearrange it to solve for your unknown.
3. Calculate the required total. Multiply the desired average by the total number of items.
4. Calculate the current total. Multiply the given average by the number of known items.
5. Find the missing value. Subtract the current total from the required total.
6. Check for traps. Did you exclude a value? Are some scores weighted? Does the answer make sense?
7. Eliminate wrong answers. Swap totals and averages? Off-by-one errors? Cross them out.

Average problems are free points if you follow the steps. Slow down, write the formula, and you’ll get them right every time. Now go practice—your 165+ score is waiting!

Final Notes for Test Day

• Always write the formula first. It takes 2 seconds and prevents mistakes.
• Label your numbers. "Avg = 82, N = 4" is clearer than scribbles.
• Trust the process. Even if the question looks hard, the framework works.

Next Steps: 1. Drill 10 average problems using this framework. 2. Time yourself: Aim for 45 seconds per question. 3. Review mistakes using the "Common Mistakes" list above.

You’ve got this! ?