Ratios, Rates, and Percents: Chapter Test

Solution

Correct answer: C

You chose A: Divides both parts by the common factor $3$ and stops, though $15$ and $21$ still share a factor of $3$.

You chose B: Divides the first part by $9$ and the second by $7$, using a different factor on each part.

You chose D: Subtracts $9$ from each part instead of dividing, which changes the comparison.

Solution

Correct answer: A

You chose B: Shifts the decimal point one place to the right instead of two.

You chose C: Shifts the point three places, as though the percent sign asked for a factor of $1000$.

You chose D: Attaches the percent sign without multiplying by $100$ at all.

Solution

Correct answer: D

You chose A: Divides the minutes by the kilograms, which answers minutes per kilogram rather than the rate asked for.

You chose B: Subtracts the minutes from the kilograms rather than dividing.

You chose C: Multiplies the two quantities, which gives kilogram-minutes and not a rate.

Solution

Correct answer: B

You chose A: Multiplies by the bare $45$, leaving the division by $100$ that the percent sign asks for undone.

You chose C: Divides by the percent instead of multiplying, which answers what number $180$ is $45\%$ of.

You chose D: Works out the share left over, $55\%$, rather than the share asked for.

Solution

Correct answer: C

You chose A: Adds the gap between the denominators, $88 - 11 = 77$, to the numerator, holding the ratio by addition.

You chose B: Divides the known diagonal product by a number it has just used rather than by the one diagonally opposite the blank.

You chose D: Multiplies straight across, $6 \times 11$, instead of along a diagonal.

Solution

Correct answer: D

You chose A: Reports the drop of $35$ members as though a count were already a percent.

You chose B: Divides the drop by the new membership $215$ rather than by the membership it started from.

You chose C: Reports what share of the original remains rather than the size of the fall.

Solution

Correct answer: A

You chose B: Gives the sand alone, which is the other part rather than the whole batch.

You chose C: Matches the $42$ kilograms to the first ratio number, reading the mix as cement to sand.

You chose D: Multiplies the cement by the total number of parts instead of by the value of one part.

Solution

Correct answer: B

You chose A: Takes the piece with the smaller ticket price, though the two pieces hold different amounts of cheese.

You chose C: Divides the ounces by the dollars, which counts ounces per dollar, then labels the result in dollars.

You chose D: Works in ounces per dollar and picks the smaller number, as though a smaller figure always meant the better deal.

Solution

Correct answer: D

You chose A: Divides the whole by the part, which answers what percent $80$ is of $46$.

You chose B: Reports the gap $80 - 46$ as though a count of the difference were already a percent.

You chose C: Divides the part by the whole correctly but attaches the percent sign without multiplying by $100$.

Solution

Correct answer: C

You chose A: Adds $15\%$ of the reduced price back on, though the reduction was $15\%$ of the larger earlier price.

You chose B: Applies the reduction a second time instead of undoing it.

You chose D: Treats the $15$ as $15$ dollars rather than as a percent, and adds it on.

Solution

Correct answer: A

You chose B: Tests only the small factors $2$, $3$ and $5$ and stops, missing the factor of $23$ that both parts carry.

You chose C: Multiplies top by top and bottom by bottom instead of along the two diagonals.

You chose D: Looks for a matching difference between corresponding parts, though what makes two ratios equal is a matching factor.

Solution

Correct answer: B

You chose A: Scales the wrong way, by $\frac{45}{60}$ rather than by $\frac{60}{45}$, so the answer covers less than a minute.

You chose C: Multiplies the volume by the full $60$ seconds, as though $54$ cubic meters arrived every second.

You chose D: Adds the extra $15$ seconds on as $15$ cubic meters instead of scaling both quantities by one factor.

Solution

Correct answer: C

You chose A: Subtracts one percent from the other, as though both had been taken of the same amount.

You chose B: Attaches the rise and the fall to the wrong changes, working out $0.75 \times 1.16$.

You chose D: Treats stacked percent changes as depending on the starting amount, though the two multipliers combine to one factor for every original.

Solution

Correct answer: D

You chose A: Multiplies the part by the percent, which finds $36\%$ of $117$ rather than the whole $117$ came from.

You chose B: Subtracts $36$ from $117$, treating the percent as a count of exhibits.

You chose C: Divides by $0.64$, the share that is not on loan, rather than by the share the $117$ represents.

Solution

Correct answer: B

You chose A: Lists the two quantities in opposite orders on the two sides, so the line answers a different question.

You chose C: Adds the gap $26 - 4 = 22$ to the $7$, holding the relationship by a difference rather than by a factor.

You chose D: Multiplies the known diagonal and stops, never dividing by the number diagonally opposite the blank.

Solution

Correct answer: A

You chose B: Counts how many times $17$ tonnes fit into $102$ and reports that count as the time, leaving the $4$ minutes out.

You chose C: Multiplies the load by $4$, as though each tonne took $4$ minutes.

You chose D: Reports the tonnes moved in one minute as though that number were a time.

Solution

Correct answer: D

You chose A: Adds the extra $110$ cream tiles to the $84$ blue, holding the ratio by addition rather than by a factor.

You chose B: Reads the ratio as fixing the counts themselves, so the larger mosaic keeps the smaller one's blue count.

You chose C: Multiplies the known diagonal and never divides by the number diagonally opposite the blank.

Solution

Correct answer: C

You chose A: Nets the two percents into a single $18\%$ rise, as though both had been taken of the same amount.

You chose B: Runs the two changes forward a second time instead of undoing them.

You chose D: Undoes the cut and leaves the earlier rise in place, so one of the two changes is never reversed.

Solution

Correct answer: A

You chose B: Reports the first week's sales, leaving the second week's fall unapplied.

You chose C: Applies the $20\%$ as a rise rather than a fall.

You chose D: Multiplies by the $0.20$ that is removed rather than by the $0.80$ that remains.

Solution

Correct answer: B

You chose A: Assumes the order of two multipliers changes the result, though multiplication gives the same product either way.

You chose C: Expects a $p\%$ rise and a $p\%$ fall to undo each other, though the fall is taken of the larger amount.

You chose D: Notices that one order discounts a larger amount but overlooks that the same order also charges a smaller one.