Jake and Ryan worked together on a job for which they were

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

Jake and Ryan worked together on a job for which they were

by AAPL » Tue Nov 13, 2018 4:41 am

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Princeton Review

Jake and Ryan worked together on a job for which they were each paid a dollars in advance. If Jake spent 20% more time working on the job than Ryan did, and Ryan gave Jake b dollars, so that their hourly wages were equal, then, in terms of b, how much was Jake paid in advance?

A. 0.8b
B. 1.1b
C. 1.2b
D. 10b
E. 11b

OA E.

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Source: Beat The GMAT — Problem Solving | Tue Nov 13, 2018 4:41 am

rrnicky: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Wed Aug 01, 2018 5:21 am

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by rrnicky » Tue Nov 13, 2018 8:45 am

Jake Ryan
advance a a
hours worked 1.2x x
after Ryan gave Jake b $ a+b a-b
hourly rate (a+b)/1.2x = (a-b)/x

on solving the equation :
a+b = 1.2(a-b)
.2a = 2.2b
a = 11b

Hence E

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Tue Nov 13, 2018 10:01 am

AAPL wrote:Princeton Review

Jake and Ryan worked together on a job for which they were each paid a dollars in advance. If Jake spent 20% more time working on the job than Ryan did, and Ryan gave Jake b dollars, so that their hourly wages were equal, then, in terms of b, how much was Jake paid in advance?

A. 0.8b
B. 1.1b
C. 1.2b
D. 10b
E. 11b

Let the hourly wage = $1 per hour.
Let Ryan's time = 10 hours, implying that Jake's time = 10 + (20% of 10) = 10 + 2 = 12 hours.
Thus:
Total number of work hours = 10+12 = 22 hours.
Total pay = (hourly wage)(total number of work hours) = 1*22 = $22.

Since the total pay = 10+12 = $22, and Jake and Ryan each receive the same amount in advance, the amount Jake and Ryan each receive in advance = 22/2 = $11.

Since Ryan works 10 hours at a rate of $1 per hour, Ryan's take-home pay = (hourly wage)(number of work hours) = 1*10 = $10.
Ryan gave Jake b dollars.
Since Ryan receives $11 in advance but takes home only $10, b=1.

In terms of b, how much was Jake paid in advance?
Since Jake and Ryan each receive $11 in advance, the correct answer must yield a value of 11 when b=1.
Only E works:
11b = 11*1 = 11.

The correct answer is E.

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Tue Nov 13, 2018 12:01 pm

AAPL wrote:Princeton Review

Jake and Ryan worked together on a job for which they were each paid a dollars in advance. If Jake spent 20% more time working on the job than Ryan did, and Ryan gave Jake b dollars, so that their hourly wages were equal, then, in terms of b, how much was Jake paid in advance?

A. 0.8b
B. 1.1b
C. 1.2b
D. 10b
E. 11b

$$\left. \matrix{
{\rm{Ryan}}\,\,\left\{ \matrix{
\,\,5t\,\,\,{\rm{hours}} \hfill \cr
\,\,\$ \,\,\left( {a - b} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{{a - b} \over {5t}}\,\,\,{\$ \over {{\rm{hour}}}} \hfill \cr
{\rm{Jake}}\,\,\,\,\left\{ \matrix{
\,\,5t + {1 \over 5}\left( {5t} \right) = 6t\,\,\,{\rm{hours}} \hfill \cr
\,\,\$ \,\,\left( {a + b} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{{a + b} \over {6t}}\,\,\,{\$ \over {{\rm{hour}}}}\,\,\,\,\,\, \hfill \cr} \right\}\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{stem}}} \,\,\,\,\,\,\,\,{{a - b} \over {5t}} = \,\,\,\,{{a + b} \over {6t}}$$
$$?\,\,:\,\,\,a = f\left( b \right)$$
$${{a - b} \over {5t}} = \,\,\,\,{{a + b} \over {6t}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,6\left( {a - b} \right) = 5\left( {a + b} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,?\,\,\,:\,\,\,a = 11b$$

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

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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by Scott@TargetTestPrep » Sun Jan 27, 2019 6:36 pm

AAPL wrote:Princeton Review

Jake and Ryan worked together on a job for which they were each paid a dollars in advance. If Jake spent 20% more time working on the job than Ryan did, and Ryan gave Jake b dollars, so that their hourly wages were equal, then, in terms of b, how much was Jake paid in advance?

A. 0.8b
B. 1.1b
C. 1.2b
D. 10b
E. 11b

OA E.

We can assume each was given 110 dollars for the job. Furthermore, we can assume that Ryan worked 10 hours and Jake worked 12 hours. Thus, the hourly wage, which must be equal for both, should be:

(110 + 110)/(10 + 12) = 220/22 = $10

Therefore, we see that Ryan should give Jake $10 so that Ryan would have $100 (notice that 10 x $10 = $100) and Jake would have $120 (notice that 12 x $10 = $120).

We see that a = 110 and b = 10, so a = 11b.

Answer: E

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