A rectangular-shaped carpet remnant that measures x feet by

Question

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)

gmatsaga · Accepted Answer

x feet y feet total price = $50 find: cost of carpet ($/yd^2) now the trap here would be for you to convert x feet and y feet using the given conversion in the question. see, the conversion states that 9 square feet = 1 yard -->> if you analyze this statement it means square feet! SQUARE! this means that two units have already been multiplied (hope you're catching my drift) this means that we should multiply x by y first, we have xy (area in square feet; this makes the conversion consistent) (xy square feet) x (1 square yard)/(9 square feet) = xy square yard / 9 -->> see we want to cancel out square feet in numerator and square feet in denominator now we want to get the cost of carpet per square yard, this means we just divide the total cost by what we got earlier; we have.. 50/(xy/9) = 50 * 9 / xy = 450/xy Answer is (E) I think the main takeaway here is the trap that I said earlier. You have to think like the test maker.

That being said, this question is very GMAT-esque, and I'm not surprised since the source is GMATPrep. Anyway, can I get a kudos?

Thanks!

KarishmaB · Answer

Area of the carpet = xy square feet
Cost per square foot = $50/xy square feet

Cost per square yard = $50/(xy/9) = $450/xy square yard

tusharacc · Answer

xy sq ft = $50
1 sq ft = $50/xy
multiplying by 9 on both side
9 sq ft = $450/xy
or 1 sq yard = $450/xy
Hence E.

LavetaLocklin · Answer

Could you elaborate the cost?

KarishmaB · Answer

Cost = $50

Area of rug = x feet * y feet = xy square feet

We need cost in dollars per square yard

We are given that 9 square feet = 1 square yard
1 square foot = 1/9 square yard
So xy square feet = (1/9)*xy square yard = xy/9 square yard

Cost in dollars/square yard = $50 / (xy/9) square yard = (450/xy) dollars per square yard

ScottTargetTestPrep · Answer

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

CLIMBTHELADDER · Answer

Step 1:  We know that the rectangular shaped carper is xy square feet and is price at 50. 
 Step 2 : So the price per square feet is 50/xy. 
 Step 3:  Let’s convert xy square feet into xy square yards. 
 Step 4:  xy sq feet * 1 square yard / 9 square feet = xy/9. 
 Step 5:  We now have 50 / xy/ 9. Divide means multiplying times its reciprocal. 
 Step 6:  450 / xy. 
Key takeaway: 
When benig asked for price per square feet/yard, calculate price per square feet/yard first to simplify calculation and maintain an overview.

fskilnik · Answer

Excellent opportunity to use UNITS CONTROL, one of the most powerful tools of our course!

9\,\,{	ext{f}}{{	ext{t}}^2}\,\,\, \leftrightarrow \,\,\,1\,\,{	ext{yar}}{{	ext{d}}^2}

\left( {{	ext{carpet}}} ight)\,\,xy\,\,{	ext{f}}{{	ext{t}}^2}\,\,\,\, \leftrightarrow \,\,\,\$ 50

\left( {{	ext{carpet}}} ight)\,\,\,\,\frac{{\$ \,\,\,?}}{{1\,\,\,{	ext{yar}}{{	ext{d}}^2}\,\,}}

?\,\, = \,\,\,\left( {\frac{{\$ 50}}{{xy\,\,{	ext{f}}{{	ext{t}}^2}}}\begin{array}{*{20}{c}}
 
earrow \ 
 
earrow 
\end{array}} ight)\,\,\,\left( {\frac{{9\,\,{	ext{f}}{{	ext{t}}^2}}}{{1\,\,{	ext{yar}}{{	ext{d}}^2}}}\begin{array}{*{20}{c}}
 
earrow \ 
 
earrow 
\end{array}} ight)\,\,\,\, = \,\,\,\,\frac{{\$ \,\,450}}{{xy\,\,{	ext{yar}}{{	ext{d}}^2}\,}}\,\,\,\,\mathop = \limits^{{	ext{FOCUS}}!} \,\,\,\,\frac{{\$ \left( {\frac{{450}}{{xy}}} ight)}}{{1\,\,{	ext{yar}}{{	ext{d}}^2}\,\,}}

Obs.: arrows indicate licit converters.

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

Regards, 
Fabio.

Pro123 · Answer

I noticed one thing that the unit ($/square yard) is correct only in option E.

However, one should solve the problem by proper conversion method to avoid any mistake.

Regards

ArindamLucky · Answer

X*Y =$50
Sq ft to sqyard conversion
Xy/9
Dollar per square yd =50/(xy/9)

Posted from my mobile device

Paras96 · Answer

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)

Cost of carpet in dollars per square yard = Total cost/Area of carpet in square yard = 50/(xy/9) = 450/xy

Hence E

RitwikAgrawal · Answer

>30 Sec Solution:

dollar/size
~ constant / xy

Hence E

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A rectangular-shaped carpet remnant that measures x feet by

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