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The combined salaries of three brothers is $90,000. Mr. Big earns twic

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The combined salaries of three brothers is $90,000. Mr. Big earns twic  [#permalink]

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New post 03 Mar 2014, 04:30
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Question Stats:

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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

Source- NOVA

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Re: The combined salaries of three brothers is $90,000. Mr. Big earns twic  [#permalink]

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New post 03 Mar 2014, 04:51
rango 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

Source- NOVA


Mr. Small = x;
Mr. Middle = 3/2*x;
Mr. Big = 2x.

x + 3/2*x + 2x = 90 --> x=20.

Answer: A.

Or plug in answer choices:
C. If S=25, then M=37.5, and B=50 --> the sum is more than 90. Try smaller numbers.
B. If S=22, then M=33, and B=44 --> the sum is more than 90. Try smaller numbers.
A. If S=20, then M=30, and B=40 --> the sum is 90.

Answer: A.

Hope it helps.
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Re: The combined salaries of three brothers is $90,000. Mr. Big earns twic  [#permalink]

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New post 03 Mar 2014, 23:04
rango 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

Source- NOVA


My brain processed it as follows:

$90,000 = B + M + S
B = 2S
M = (3/2)S
S = S

Thus --> 90,000 = 2S + (3/2)S + S

Thus --> 90,000 = (4/2)S + (3/2)S + (2/2)S (found lowest common denominator)

Thus --> 90,000 = (9/2)S

Thus --> 90,000 * (2/9) = S (took the reciprocal of 9/2 when dividing)

Thus --> 180,000/9 = S

Thus --> S = 20,000

Might be slower but helps me to get terms I can combine.
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Re: The combined salaries of three brothers is $90,000. Mr. Big earns twic  [#permalink]

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New post 23 Jul 2014, 23:59
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?

Let assume Mr Small= X
Now Mr big Earns Twice Which Means= 2X
Now For Middle one= X*1/2

X+2x+x*1/2=90

Answer B is correct.
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Re: The combined salaries of three brothers is $90,000. Mr. Big earns twic  [#permalink]

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New post 25 Jun 2017, 10:59
B + S + M = $90,000

B = 2S
M = 3S/2

2S + S + 3S/2 = $90,000
4S + 2S + 3S = $180,000
S = $180,000/9 = $20,000. Ans - A.
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Re: The combined salaries of three brothers is $90,000. Mr. Big earns twic  [#permalink]

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New post 26 Jun 2017, 06:13
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?

Let the salary for Mr. Small be \(x\)

\(2x + 1.5x + x = 90,000\)

\(4.5x = 90,000\)

\(x = 20,000\)

Hence, Answer is A
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Re: The combined salaries of three brothers is $90,000. Mr. Big earns twic  [#permalink]

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New post 26 Feb 2018, 11:21
rango 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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Re: The combined salaries of three brothers is $90,000. Mr. Big earns twic   [#permalink] 26 Feb 2018, 11:21
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