Percents: Percent Change
By what percent did the average cost of a Sleeping Pod Time Unit (SPTU) increase from 2001 to 2002?
>(1) In 2001, the average SPTU was 5 minutes long and cost 65 cents.
>(2) In 2002, the average cost of a SPTU was 2.5 times as much as the average cost of a SPTU in 2001.
Correct.
[[snippet]]
Stat. (1) only gives you the original, so **Stat.(1) → IS → BCE**.
For Stat. (2), while you do not get any specific values, the ratio of the average cost of this year's to last year's SPTU is enough to calculate the percent change. If you call $$x$$ the average cost of a SPTU in 2001, then the average cost of a SPTU in 2002 is $$2.5x$$. That makes the percent change
>$$\displaystyle \mbox{Percent Change}=\frac{\mbox{New} - \mbox{Original}}{\mbox{Original}}\times100\% $$
>>>> $$\displaystyle = \frac{2.5x-x}{x}\times100\%$$
>>>> $$\displaystyle = \frac{1.5x}{x} \times100\%$$
>>>> $$\displaystyle = 1.5\times100\%$$
>>>> $$\displaystyle = 150\%$$.
Therefore, **Stat.(2) → S → B**.
Incorrect.
[[snippet]]
Stat. (1) only gives you the original, so **Stat.(1) → IS → BCE**.
Incorrect.
[[snippet]]
For Stat. (2), while you do not get any specific values, the ratio of the average cost of this year's to last year's SPTU is enough to calculate the percent change. If you call $$x$$ the average cost of a SPTU in 2001, then the average cost of a SPTU in 2002 is $$2.5x$$. That makes the percent change
>$$\displaystyle \mbox{Percent Change}=\frac{\mbox{New} - \mbox{Original}}{\mbox{Original}}\times100\% $$
>>>> $$\displaystyle = \frac{2.5x-x}{x}\times100\%$$
>>>> $$\displaystyle = \frac{1.5x}{x} \times100\%$$
>>>> $$\displaystyle = 1.5\times100\%$$
>>>> $$\displaystyle = 150\%$$.
Therefore, **Stat.(2) → S → BD**.
Incorrect.
[[snippet]]
Stat. (1) only gives you the original, so **Stat.(1) → IS → BCE**.
Incorrect.
[[snippet]]
For Stat. (2), while you do not get any specific values, the ratio of the average cost of this year's to last year's SPTU is enough to calculate the percent change. If you call $$x$$ the average cost of a SPTU in 2001, then the average cost of a SPTU in 2002 is $$2.5x$$. That makes the percent change
>$$\displaystyle \mbox{Percent Change}=\frac{\mbox{New} - \mbox{Original}}{\mbox{Original}}\times100\% $$
>>>> $$\displaystyle = \frac{2.5x-x}{x}\times100\%$$
>>>> $$\displaystyle = \frac{1.5x}{x} \times100\%$$
>>>> $$\displaystyle = 1.5\times100\%$$
>>>> $$\displaystyle = 150\%$$.
Therefore, **Stat.(2) → S → BD**.
Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
EACH statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
