Quentin's income is 60% less than Rex's income, and Sam's

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

Quentin's income is 60% less than Rex's income, and Sam's

by BTGmoderatorDC » Thu Oct 25, 2018 4:01 am

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Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

A. 8/9
B. 11/12
C. 8/13
D. 11/13
E. 12/13

OA A

Source: Manhattan Prep

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Source: Beat The GMAT — Problem Solving | Thu Oct 25, 2018 4:01 am

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 » Thu Oct 25, 2018 4:23 am

BTGmoderatorDC wrote:Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

A. 8/9
B. 11/12
C. 8/13
D. 11/13
E. 12/13

Let Rex's income = 100.
Since Quentin's income is 60% less than Rex's, Quentin's income = 100 - (60% of 100) = 100-60 = 40.
Since Sam's income is 25% less than Quentin's, Sam's income = 40 - (25% of 40) = 40-10 = 30.
After Rex gives 60% of his income to Sam, Sam's new income = 30 + (60% of 100) = 30+60 = 90.
After Rex gives 40% of his income to Quentin, Quentin's new income = 40 + (40% of 100) = 40+40 = 80.
Resulting fraction:
(Quentin's new income)/(Sam's new income) =80/90 = 8/9.

The correct answer is A.

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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 » Thu Oct 25, 2018 6:29 am

BTGmoderatorDC wrote:Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

A. 8/9
B. 11/12
C. 8/13
D. 11/13
E. 12/13
Source: Manhattan Prep

$$? = {Q \over S}$$
$$\left. \matrix{
Q = {2 \over 5}R\,\,\,\,\left( {40\% R} \right)\,\,\,\,\,\,\,\,\,\,\, + \,\,\,\,\,\,{2 \over 5}R\,\,\,\,\left( {40\% R} \right)\,\,\,\,\, = \,\,\,{4 \over 5}R \hfill \cr
S = {3 \over 4}Q\,\,\,\left( {75\% Q} \right) = \,\,{3 \over 4}\left( {{2 \over 5}R} \right) = {3 \over {10}}R\,\,\,\,\,\,\,\,\,\,\, + \,\,\,\,\,\,{3 \over 5}R\,\,\,\,\left( {60\% R} \right)\,\,\,\,\, = \,\,\,{9 \over {10}}R\,\,\,\, \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\,\, = \,\,{4 \over 5} \cdot {{10} \over 9} = {8 \over 9}$$

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
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Oct 28, 2018 5:22 pm

BTGmoderatorDC wrote:Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

A. 8/9
B. 11/12
C. 8/13
D. 11/13
E. 12/13

If we let Rex's income be $10, then Quentin's income is $4 and Sam's income is $3. If Rex gives $6 to Sam and $4 to Quentin, then Quentin's new income is $8 and Sam's is $9. Therefore, Quentin's new income is 8/9 of Sam's new income.

Answer: A

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