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A rectangular-shaped carpet remnant that measures x feet by

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A rectangular-shaped carpet remnant that measures x feet by  [#permalink]

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New post 28 Jun 2012, 14:09
2
15
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (01:56) correct 34% (01:57) wrong based on 499 sessions

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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)

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Re: A rectangular-shaped carpet remnant that measures  [#permalink]

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New post 28 Jun 2012, 17:41
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Stiv 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)
1)\(50xy\)
2) \(450xy\)
3) \(\frac {xy}{9}\)
4)\(\frac {xy}{50}\)
5) \(\frac {450}{xy}\)



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!
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Re: A rectangular-shaped carpet remnant that measures  [#permalink]

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New post 28 Jun 2012, 16:37
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.
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Re: A rectangular-shaped carpet remnant that measures  [#permalink]

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New post 28 Jun 2012, 22:58
2
Stiv 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)
1)\(50xy\)
2) \(450xy\)
3) \(\frac {xy}{9}\)
4)\(\frac {xy}{50}\)
5) \(\frac {450}{xy}\)


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

To learn how to quickly convert units, check: http://www.veritasprep.com/blog/2011/01 ... nd-ounces/
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Re: A rectangular-shaped carpet remnant that measures x feet by  [#permalink]

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New post 13 Oct 2016, 02:22
Could you elaborate the cost?
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Re: A rectangular-shaped carpet remnant that measures x feet by  [#permalink]

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New post 13 Oct 2016, 04:08
LavetaLocklin wrote:
Could you elaborate the cost?


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
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Re: A rectangular-shaped carpet remnant that measures x feet by  [#permalink]

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New post 14 Oct 2016, 04:45
1
Stiv 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
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Re: A rectangular-shaped carpet remnant that measures x feet by  [#permalink]

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New post 19 Apr 2018, 05:47
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.
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Re: A rectangular-shaped carpet remnant that measures x feet by  [#permalink]

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New post 16 Sep 2018, 17:41
1
Stiv 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)

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.
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Re: A rectangular-shaped carpet remnant that measures x feet by &nbs [#permalink] 16 Sep 2018, 17:41
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