Ratios, Percents, and Proportion: Chapter Test

Solution

Correct answer: B

You chose A: Places yards in the numerator, leaving $\text{yd}^2/\text{ft}$ instead of cancelling the yards.

You chose C: Inverts the true equality itself, writing $1\text{ ft} = 3\text{ yd}$ rather than $1\text{ yd} = 3\text{ ft}$.

You chose D: Builds the factor from the quantity being converted, $9$, rather than from the conversion fact itself.

Solution

Correct answer: D

You chose A: Reports the smaller number ($4k$) instead of the larger one asked for.

You chose B: Treats the ratio's own number as the amount, rather than multiplying it by $k$.

You chose C: Reports the number of parts $4 + 5$ instead of an actual amount.

Solution

Correct answer: A

You chose B: Reports the total amount $A$ instead of the interest $I$ alone.

You chose C: Computes one year's interest and forgets to multiply by the $5$ years.

You chose D: Forgets to convert the percent to a decimal rate before multiplying.

Solution

Correct answer: C

You chose A: Multiplies by the rate instead of dividing, as if $63$ were the missing PART rather than the known one.

You chose B: Divides by $35$ instead of $0.35$, forgetting to convert the percent to a decimal.

You chose D: Misplaces the decimal point, dividing by $0.035$ instead of $0.35$.

Solution

Correct answer: B

You chose A: Takes $A$ and $B$ from the first ratio and $C$ from the second without scaling so that $B$ agrees in both.

You chose C: Scales $A:B$ correctly to $6:10$, then reuses that same multiplier $2$ on the second ratio to get $C=14$, instead of the $5$ that ratio needs to bring its own $B$ to $10$.

You chose D: Scales $B$ to $10$ but forgets to scale $A$ by that same factor.

Solution

Correct answer: A

You chose B: Tests only the first pair's ratio $y/x = 10$ and assumes it holds for the rest without checking the others.

You chose C: Correctly senses the product is constant, but reports the first pair's ratio $y/x$ instead of the product $xy$.

You chose D: Finds the correct constant product $40$ but misnames the relationship as direct instead of inverse.

Solution

Correct answer: D

You chose A: Stops after converting to hours only, never applying the second factor to reach minutes.

You chose B: Computes the minutes in a single day and forgets to account for both days.

You chose C: Adds the two conversion numbers, $2\times(24+60)$, instead of multiplying through the chain.

Solution

Correct answer: C

You chose A: Reports the ratio's own number $5$ as a percent, instead of computing green's share of the total.

You chose B: Compares the green tickets to the other two colors combined, not to the full total of $400$.

You chose D: Reports the green ticket COUNT as if it were already the percent.

Solution

Correct answer: A

You chose B: Adds $15\%$ of the sale price back on, instead of dividing by the retained factor $0.85$.

You chose C: Divides by the removed rate $0.15$ instead of the retained factor $0.85$.

You chose D: Multiplies by the retained factor $0.85$ instead of dividing by it.

Solution

Correct answer: D

You chose A: Adds the drain's rate to the pipe's rate instead of subtracting it, as if the drain were a second pipe.

You chose B: Subtracts the two TIMES directly ($10-6$) instead of subtracting their rates.

You chose C: Reports the net RATE itself as if it were already the time, without taking the reciprocal.

Solution

Correct answer: B

You chose A: Divides the whole by the part instead of the part by the whole.

You chose C: Forgets to multiply the decimal rate by $100$ to express it as a percent.

You chose D: Reports the percent that is NOT $160$ (the complement) instead of the percent that is.

Solution

Correct answer: C

You chose A: Averages the two speeds directly instead of using total distance over total time.

You chose B: Divides total distance by the SUM of the two speeds instead of by total time.

You chose D: Uses only the time of the slower leg as if it were the total time for the whole ride.

Solution

Correct answer: D

You chose A: Computes the time in HOURS ($\frac{1}{18}$ h) and reports the number as if it were already in seconds.

You chose B: Multiplies the speed $18$ by $3{,}600$ instead of dividing $3{,}600$ by $18$, converting the rate the wrong way round.

You chose C: Reports the number of seconds in one hour, the time unit itself, rather than the time to cover one meter.

Solution

Correct answer: B

You chose A: Adds the two rates ($10\% + 10\%$) instead of multiplying the factors.

You chose C: Confuses this with a rise-then-fall pair, computing $1.10\times0.90$ instead of $1.10\times1.10$.

You chose D: Assumes two percent changes of equal size must cancel out exactly, without multiplying the two factors to check.

Solution

Correct answer: A

You chose B: Scales by the weight ratio only, ignoring that the distance also changed.

You chose C: Scales by the distance ratio only, ignoring that the weight also changed.

You chose D: Adds the weight and distance scale factors, $1.5+1.6$, instead of multiplying them.

Solution

Correct answer: A

You chose B: Reports the new nonfiction count rather than the fiction count the question asks for.

You chose C: Reports the ORIGINAL nonfiction count, before the $8$ books were added, instead of the fiction count.

You chose D: Cross-multiplies without distributing across $(3k+8)$, solving $20k=15k+8$ instead of $20k=15k+40$.

Solution

Correct answer: C

You chose A: Adds $0.20$ to the price per meter instead of multiplying by the growth factor $1.2$.

You chose B: Reports the original $4$-meter cost, applying neither the new length nor the price rise.

You chose D: Uses the new price per meter but the OLD length of $4$ meters instead of $6$.

Solution

Correct answer: B

You chose A: Treats the relationship as direct variation ($y=kx$) instead of inverse ($y=k/x$).

You chose C: Uses $x=8$ directly without converting inches to feet, mixing two different units in the same equation.

You chose D: Converts inches to feet by multiplying by $12$ instead of dividing.

Solution

Correct answer: D

You chose A: Averages the two speeds directly ($\frac{50+60}{2}$) instead of weighting by how the total time actually splits.

You chose B: Swaps which speed goes with which leg, driving the shorter-time leg at $60$ mph instead of $50$.

You chose C: Divides total distance by the number of legs ($2$) instead of by the total time.

Solution

Correct answer: C

You chose A: Divides by $1.25$ incorrectly, computing $5\times0.25$ instead of $5\div1.25$.

You chose B: Assumes the time falls by the same $25\%$ that the speed rises, treating time and speed as changing by equal percentages.

You chose D: Multiplies the time by the speed's growth factor $1.25$ instead of dividing by it.