A rectangular-shaped carpet remnant that measures x feet

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BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Sun Sep 16, 2018 7:51 am

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A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $50. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)

A. 50xy
B. 450xy
C. xy / 9
D. xy / 50
E. 450 / (xy)

The OA is E.

Source: GMAT Prep

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Sep 16, 2018 8:00 am

BTGmoderatorLU wrote:A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $50. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)

A. 50xy
B. 450xy
C. xy / 9
D. xy / 50
E. 450 / (xy)

The OA is E.

Source: GMAT Prep

Area of rectangle = (base)(height) = (x feet)(y feet) = xy square feet

GIVEN: 9 square feet = 1 square yard
So, we can also say that 1 square foot = 1/9 square yards

So, xy square feet = xy/9 square YARDS

So, if xy/9 square YARDS cost $50, then each square YARD = $50/(xy/9)
= ($50)(9/xy)
= 45/xy

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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

by fskilnik@GMATH » Sun Sep 16, 2018 5:37 pm

BTGmoderatorLU wrote:A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $50. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)

A. 50xy
B. 450xy
C. xy / 9
D. xy / 50
E. 450 / (xy)

Source: GMAT Prep

Excellent opportunity to use UNITS CONTROL, one of the most powerful tools of our course!
\[9\,\,{\text{f}}{{\text{t}}^2}\,\,\, \leftrightarrow \,\,\,1\,\,{\text{yar}}{{\text{d}}^2}\]
\[\left( {{\text{carpet}}} \right)\,\,xy\,\,{\text{f}}{{\text{t}}^2}\,\,\,\, \leftrightarrow \,\,\,\$ 50\]
\[\left( {{\text{carpet}}} \right)\,\,\,\,\frac{{\$ \,\,\,?}}{{1\,\,\,{\text{yar}}{{\text{d}}^2}\,\,}}\,\,\,\,\,\]
\[?\,\, = \,\,\,\left( {\frac{{\$ 50}}{{xy\,\,{\text{f}}{{\text{t}}^2}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\left( {\frac{{9\,\,{\text{f}}{{\text{t}}^2}}}{{1\,\,{\text{yar}}{{\text{d}}^2}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\, = \,\,\,\,\frac{{\$ \,\,450}}{{xy\,\,{\text{yar}}{{\text{d}}^2}\,}}\,\,\,\,\mathop = \limits^{{\text{FOCUS}}!} \,\,\,\,\frac{{\$ \left( {\frac{{450}}{{xy}}} \right)}}{{1\,\,{\text{yar}}{{\text{d}}^2}\,\,}}\]
Obs.: arrows indicate licit converters.

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: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Sep 18, 2018 5:51 pm

BTGmoderatorLU wrote:A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $50. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)

A. 50xy
B. 450xy
C. xy / 9
D. xy / 50
E. 450 / (xy)

We are given that a rectangular-shaped carpet remnant that measures x feet by y feet is priced at $50. We need to determine the cost, in dollars per square yard.

The area of the carpet is xy square feet, and we have to convert that value to square yards.

(xy square feet) x (1 square yard/9 square feet) = xy/9 square yards

The cost of the carpet, in dollars per square yard, is 50/(xy/9) = 450/(xy).

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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