A newly-opened retail store made $400 profit on the initial

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

A newly-opened retail store made $400 profit on the initial

by BTGmoderatorLU » Tue Nov 06, 2018 2:36 pm

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Source: e-GMAT

A newly-opened retail store made $400 profit on the initial expenditure of $25,000 and then made $1,200 profit on the next $80,000 expenditure. By approximately what percent did the ratio of profit to expenditure change from the first $25,000 expenditure to the next $80,000 expenditure?

A. 6.67% decrease
B. 6.25% decrease
C. 0
D. 6.25% increase
E. 6.67% increase

The OA is B.

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Source: Beat The GMAT — Problem Solving | Tue Nov 06, 2018 2:36 pm

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Tue Nov 06, 2018 5:21 pm

BTGmoderatorLU wrote:Source: e-GMAT

A newly-opened retail store made $400 profit on the initial expenditure of $25,000 and then made $1,200 profit on the next $80,000 expenditure. By approximately what percent did the ratio of profit to expenditure change from the first $25,000 expenditure to the next $80,000 expenditure?

A. 6.67% decrease
B. 6.25% decrease
C. 0
D. 6.25% increase
E. 6.67% increase

\[\left. \begin{gathered}
{\text{I}}{\text{.}}\,\,\,\frac{{400}}{{25000}} = \frac{2}{{125}} \hfill \\
{\text{II}}{\text{.}}\,\,\,\frac{{1200}}{{80000}} = \frac{3}{{200}} \hfill \\
\end{gathered} \right\}\,\,\,\,?\,\, = \Delta \% \left( {\,{\text{I}}\,\,\, \to \,\,\,{\text{II}}\,} \right)\]
\[? = \frac{{\frac{3}{{200}} - \frac{2}{{125}}}}{{\frac{2}{{125}}}} = \frac{{125}}{2}\left( {\frac{{3 \cdot \boxed5}}{{8 \cdot 25 \cdot \boxed5}} - \frac{{2 \cdot \boxed8}}{{5 \cdot 25 \cdot \boxed8}}} \right) = \frac{{5 \cdot 25}}{2}\left( { - \frac{1}{{5 \cdot 25 \cdot 8}}} \right) = - \frac{1}{{16}}\]
\[? = - \frac{1}{4}\left( {\frac{1}{4}} \right) = - \frac{1}{4}\left( {25\% } \right) = - 6\frac{1}{4}\% \,\,\,\,\, \Rightarrow \,\,\,\,\left( B \right)\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Nov 09, 2018 12:20 pm

BTGmoderatorLU wrote:Source: e-GMAT

A newly-opened retail store made $400 profit on the initial expenditure of $25,000 and then made $1,200 profit on the next $80,000 expenditure. By approximately what percent did the ratio of profit to expenditure change from the first $25,000 expenditure to the next $80,000 expenditure?

A. 6.67% decrease
B. 6.25% decrease
C. 0
D. 6.25% increase
E. 6.67% increase

The first profit-to-expenditure ratio is:

400/25000 = 4/250 = 2/125 = 16/1000

The second profit-to-expenditure ratio is:

1200/80,000 = 12/800 = 3/200 = 15/1000

So the percent change is:

(15/1000 - 16/1000)/(16/1000) x 100

-1/1000 x 1000/16 x 100 = -1/16 x 100 = -6.25 percent

The negative coefficient is indicative of a decrease; thus, the change was a 6.25 percent decrease.

Answer: B

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