The combined salaries of three brothers

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

by BTGmoderatorDC » Sun Jan 14, 2018 3:33 am

The combined salaries of three brothers is $90,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?

(A) 20,000
(B) 22,000
(C) 25,000
(D) 30,000
(E) 40,000

Can some experts show me the best solution?

OA A

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Source: Beat The GMAT — Problem Solving | Sun Jan 14, 2018 3:33 am

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

by GMATGuruNY » Sun Jan 14, 2018 4:55 am

lheiannie07 wrote:The combined salaries of three brothers is $90,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?

(A) 20,000
(B) 22,000
(C) 25,000
(D) 30,000
(E) 40,000

We can PLUG IN THE ANSWERS, which represent Mr. Small's salary.
When the correct answer is plugged in, the 3 salaries will sum to 90,000.

B: Mr. Small = 22,000
Since Mr. Big earns twice what Mr. Small earns, Mr. Big = 2 * 22,000 = 44000.
Since Mr. Middle earns 1 1/2 times what Mr. Small earns, Mr. Middle = (3/2)(22,000) = 33,000.
Sum of the 3 salaries = 22,000 + 44,000 + 33,000 = 99,000.
Since the sum is TOO GREAT, Mr. Small's salary must be LESS than 22,000.

The correct answer is A.

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DrMaths: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Mon Jan 15, 2018 2:01 am

by DrMaths » Wed Jan 17, 2018 5:38 am

B : M : S
2 : 1.5 : 1
To change to whole numbers, multiply by 2
4:3.2 which has 4+3+2=9 parts
So Mr Small has 2/9 of 90 000 = 20 000

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by [email protected] » Wed Jan 17, 2018 10:41 am

Hi lheiannie07,

We're told that the combined salaries of three brothers is $90,000; Mr. Big earns TWICE what Mr. Small earns, and Mr. Middle earns 1 1/2 TIMES what Mr. Small earns. We're asked for the smallest salary of the three brothers (re: how much does Mr. Small earn?). This question can be solved rather easily by TESTing THE ANSWERS (the approach Mitch used). It can also be solved Algebraically:

Mr. Small = $X
Mr. Middle = (1.5)($X)
Mr. Big = (2)($X)

Total = X + 1.5X + 2X = $90,000
4.5X = 90,000
9X = 180,000
X = 20,000

Final Answer: A

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Feb 26, 2018 10:32 am

lheiannie07 wrote:The combined salaries of three brothers is $90,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?

(A) 20,000
(B) 22,000
(C) 25,000
(D) 30,000
(E) 40,000

We can let the salaries of Mr. Big, Mr. Small, and Mr. Medium = B, S, and M, respectively, and create the equations:

B + S + M = 90,000

and

B = 2S

and

M = 1.5S

Substituting, we have:

2S + S + 1.5S = 90,000

4.5S = 90,000

S = 20,000

Answer:A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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