A rectangular-shaped carpet remnant that measures x feet

[BTGmoderatorLU]

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

[Brent@GMATPrepNow]

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

[fskilnik@GMATH]

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.

[Scott@TargetTestPrep]

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