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A rectangular-shaped carpet remnant that measures x feet

This topic has 3 expert replies and 0 member replies

A rectangular-shaped carpet remnant that measures x feet

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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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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 :: www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 30/Sep with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 70% discount!

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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

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Brent Hanneson – Creator of GMATPrepNow.com
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Post
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

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