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Tracy and Lee are installing tile on the floor of a shopping center

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MasteringGMAT
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Tracy and Lee are installing tile on the floor of a shopping center [#permalink] New post   02 Jul 2023, 05:27
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Tracy and Lee are installing tile on the floor of a shopping center. Tracy installs 200 tiles per hour and Lee installs 160 tiles per hour. If their hourly pay is proportional to the rate at which they install tiles, Tracy's hourly pay is what percent greater than Lee's hourly pay?

A. 20%
B. 25%
C. 40%
D. 80%
E. 125%
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B
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Re: Tracy and Lee are installing tile on the floor of a shopping center [#permalink] New post   02 Jul 2023, 06:48
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MasteringGMAT wrote:
Tracy and Lee are installing tile on the floor of a shopping center. Tracy installs 200 tiles per hour and Lee installs 160 tiles per hour. If their hourly pay is proportional to the rate at which they install tiles, Tracy's hourly pay is what percent greater than Lee's hourly pay?

A. 20%
B. 25%
C. 40%
D. 80%
E. 125%


Let's assume the pay for installing one tile = $1. Tracy and Lee works for one hour.

Pay received by Tracy = $\(200\)
Pay recieved by Lee = $\(160\)

Difference = $\((200 - 160)\) = $\(40\)

Required percentage = \(\frac{40}{160} * 100 = 25\)%

Option B
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Re: Tracy and Lee are installing tile on the floor of a shopping center [#permalink] New post   04 Jul 2023, 04:52
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MasteringGMAT wrote:
Tracy and Lee are installing tile on the floor of a shopping center. Tracy installs 200 tiles per hour and Lee installs 160 tiles per hour. If their hourly pay is proportional to the rate at which they install tiles, Tracy's hourly pay is what percent greater than Lee's hourly pay?

A. 20%
B. 25%
C. 40%
D. 80%
E. 125%


Since their hourly wage is proportional to the rate at which they install tiles, we have:

w_T/w_L = 200/160 = 5/4 = 1.25

w_T = (1.25)w_L

A factor of 1.25 corresponds to “25% greater.”

Answer: B
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Re: Tracy and Lee are installing tile on the floor of a shopping center [#permalink] New post   28 Feb 2024, 13:06
­Let the pay be $1 . Tracy and Lee works for one hour.

Tracy's payment = $200
Lee's payment = $160

Difference = $(200−160) = $40

Required percentage = 40/160∗100= 25%(160 in denominator because we have to tell increase percentage with respet to lee)
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Re: Tracy and Lee are installing tile on the floor of a shopping center [#permalink] New post   31 Mar 2024, 14:13
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MasteringGMAT wrote:
Tracy and Lee are installing tile on the floor of a shopping center. Tracy installs 200 tiles per hour and Lee installs 160 tiles per hour. If their hourly pay is proportional to the rate at which they install tiles, Tracy's hourly pay is what percent greater than Lee's hourly pay?

A. 20%
B. 25%
C. 40%
D. 80%
E. 125%

­Since the hourly pay is proprortional to the rate (tiles per hour), the question simplifies to: "200 is what percent greater than 160?".

Our formula for % Change, in general, is \(\frac{New - Old }{ Old} * 100%\), or it's often easier to use this version of the formula: (\(\frac{New }{ Old} - 1)\) * 100%

When we have the wording "X is what percent greater than Y", Y represents the baseline, "Old", and X represents the "New".

(200/160 - 1) * 100% = (5/4 - 1) * 100% = 25%­
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Re: Tracy and Lee are installing tile on the floor of a shopping center [#permalink]
31 Mar 2024, 14:13
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