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Mixed skills
10 original practice questions · Untimed · Fractions and exact decimals accepted
1. A bag has 4 green and 8 purple tokens. Each token is equally likely to be chosen. What is the probability of green?
ged-single-draw-12. A tool priced at $100 is discounted by 15%. What is the sale price before tax, in dollars?
ged-sale-price-13. 4 workers average 8 completed jobs. Another group averages 5 jobs. Together they average 6 jobs per worker. How many workers are in the second group?
Answer: __________________
Optional written extension · self-assessment only
Show the model and intermediate calculations, then refute one competing method. This written extension is not automatically scored.
Show your reasoning for each part. This task is not automatically scored.
4. A repair bill is $46, including an $18 visit fee and $7 per hour. How many hours were billed?
ged-hourly-invoice-15. A board measures 30 inches. Using 12 inches = 1 foot, what is its length in feet?
ged-length-conversion-26. A calculator shows 7 × (12 − 6) + 8. What value should it display?
ged-grouped-operations-47. A scale drawing uses 3 centimeters for every 8 meters. A wall is 24 meters long. How many centimeters represent it?
ged-proportion-unknown-18. The greatest common factor of 16x³ + 24x² is kx², where k is positive. Find k.
ged-x2-shared-polynomial-factor-39. A community garden grows from 60 plots to 75 plots. What is the percent increase?
ged-relative-change-110. 5 identical boxes each contain x notebooks and 3 folders. There are 55 items altogether. What is x?
ged-equal-bundles-3Answers & reasoning
1. 1/3 · Choice A
Count all tokens to define the equally likely outcomes. Divide the green-token count by the total. The requested value is 1/3. Check its units and meaning against the original question.
ged-single-draw-12. 85 · Choice C
A 15% discount leaves 85% of the original price. Apply the multiplier to the original price, not to the discount amount. The requested value is 85. Check its units and meaning against the original question.
ged-sale-price-13. 8
Let n be the second group size: 32+5n=6(4+n). Rearranging gives 8=n. There are 8 workers in the second group; the weighted mean checks as 6.
Optional written extension · self-assessment only
Show the model and intermediate calculations, then refute one competing method. This written extension is not automatically scored.
- Select the operation and explain the relevant condition. (1 points)
- Show correct substituted arithmetic and the requested value or units. (1 points)
- Evaluate a competing operation and explain why it answers the wrong question. (1 points)
Let n be the second group size: 32+5n=6(4+n).
Rearranging gives 8=n.
There are 8 workers in the second group; the weighted mean checks as 6.
If both groups had 4 workers, their mean would be (32+20)/8=13/2, not 6 jobs. Equal group sizes therefore contradict the given combined mean.
4. 4 · Choice B
Subtract the fixed visit fee from the total. Divide the remaining labor charge by dollars per hour. The requested value is 4. Check its units and meaning against the original question.
ged-hourly-invoice-15. 5/2 · Choice B
Use a conversion factor of 1 foot per 12 inches. A measurement in feet should be numerically smaller than the same length in inches. The requested value is 5/2. Check its units and meaning against the original question.
ged-length-conversion-26. 50 · Choice B
Evaluate the difference in parentheses first. Multiply the resulting 6 before adding the final term. The requested value is 50. Check its units and meaning against the original question.
ged-grouped-operations-47. 9 · Choice B
Write the scale as 3 centimeters per 8 meters. Multiply the actual length by the scale, canceling meters. The requested value is 9. Check its units and meaning against the original question.
ged-proportion-unknown-18. 8 · Choice C
Use the smaller variable power and the greatest common divisor of the coefficients. The coefficient GCF is gcd(16,24)=8. The full common factor is 8x², leaving 2x+3.
ged-x2-shared-polynomial-factor-39. 25 · Choice B
Subtract the original count from the new count. Divide the increase by the original count, then multiply by 100. The requested value is 25. Check its units and meaning against the original question.
ged-relative-change-110. 8 · Choice D
Divide the total item count by the number of identical boxes. Subtract the three folders from the item count in one box. The requested value is 8. Check its units and meaning against the original question.
ged-equal-bundles-3Original parameterized practice, independently checked by computation. Educator review pending. Not an official exam paper.