Work through the questions before checking solutions. Guide question labels stay the same when you shuffle the bank. Use an exact fraction when a decimal would require rounding.
Guide question labels stay the same when the order changes. Check answers when you are ready to review.
Written responses are self-review exercises.
Saved on this browser and device; clearing browser data removes progress.
The drill
Your practice is saved on this device.
Question 1
Guide question E2A
An item costs $96.30 after a 7% sales tax is added. What was its pre-tax price, in dollars?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
Answer: 90
If P is the pre-tax price, then 1.07P = 96.30. Divide by 1.07 to obtain P = 90. Checking: tax is 0.07(90) = 6.30, giving total $96.30.
A quantity rises from 250 to 400. What is its percent increase?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
Answer: 60
The increase is 400 − 250 = 150, measured against the original 250. Thus (150/250)(100) = 60. The new value is 160% of the old value, which is 60% greater.
A participation rate rises from 32% to 40%. What is the relative percent increase in the rate?
Why this answer
Answer: C: 25%
The change is 8 percentage points. Relative to the original rate, it is 8/32 = 0.25, or 25%. The word “relative” rules out the percentage-point answer 8.
A value decreases by 20%. By what percentage must the reduced value increase to return to the original value?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
Answer: 25
Use an original value of 100. After the decrease it is 80. Returning to 100 requires a gain of 20 relative to 80, or (20/80)(100) = 25%. Algebraically, 0.80(1 + r) = 1 gives r = 0.25.
A product’s price decreases by 10%, while the number sold increases by 20%. What is the percent increase in revenue?
Why this answer
Answer: A: 8%
Revenue is price times quantity. Its multiplier is 0.90(1.20) = 1.08, so revenue rises by 8%. Adding the signed percentages gives 10%, but ignores the product relationship.