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The combined salaries of three brothers

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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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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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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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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

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