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A and B are two salt solutions with different concentrations. Mixing

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A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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New post Updated on: 06 Dec 2019, 00:30
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[GMAT math practice question]

A and B are two salt solutions with different concentrations. Mixing 200g of A and 100g of B makes a 4% salt solution, and mixing 100g of A and 200g of B makes a 3% salt solution. What are the concentrations of A and B?

A. 5%, 2%
B. 6%, 4%
C. 5%, 1%
D. 6%, 2%
E. 7%, 3%

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Originally posted by MathRevolution on 04 Dec 2019, 01:18.
Last edited by MathRevolution on 06 Dec 2019, 00:30, edited 1 time in total.
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Re: A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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New post 09 Jan 2020, 07:40
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1
MathRevolution wrote:
[GMAT math practice question]

A and B are two salt solutions with different concentrations. Mixing 200g of A and 100g of B makes a 4% salt solution, and mixing 100g of A and 200g of B makes a 3% salt solution. What are the concentrations of A and B?

A. 5%, 2%
B. 6%, 4%
C. 5%, 1%
D. 6%, 2%
E. 7%, 3%


Responding to a pm:

Using WA formula

w1/w2 = (A2 - Aavg)/(Aavg - A1)

200/100 = (A2 - 4)/(4 - A1)
8 - 2*A1 = A2 - 4

100/200 = (A2 - 3)/(3 - A1)
3 - A1 = 2*A2 - 6

Solving the two equations, we get A1 = 5% and A2 = 2%

Answer (A)
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Re: A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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New post 04 Dec 2019, 04:13
\(\frac{200a+100b}{300}= 4\)

2a+b=12.....(1)

Also, \(\frac{100a+200b}{300}= 3\)

a+2b=9.....(2)


a= 5 and b =2



MathRevolution wrote:
[GMAT math practice question]

A and B are two salt solutions with different concentrations. Mixing 200g of A and 100g of B makes a 4% salt solution, and mixing 100g of A and 200g of B makes a 3% salt solution. What are the concentrations of A and B?

A. 5%, 2%
B. 6%, 4%
C. 5%, 1%
D. 6%, 2%
E. 7%, 3%
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Re: A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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New post 04 Dec 2019, 05:54
MathRevolution wrote:
[GMAT math practice question]

A and B are two salt solutions with different concentrations. Mixing 200g of A and 100g of B makes a 4% salt solution, and mixing 100g of A and 200g of B makes a 3% salt solution. What are the concentrations of A and B?

A. 5%, 2%
B. 6%, 4%
C. 5%, 1%
D. 6%, 2%
E. 7%, 3%

Wa/Wb=2/1=B-4/4-A
8-2A=B-4
B+2A=12-(1)
and
Wa/Wb=1/2=B-3/3-A
3-A=2B-6
2B+A=9-(2)
From 1 and 2
A=5, B=2
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Re: A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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New post 06 Dec 2019, 00:32
=>

Assume the percentages of the two salt solutions \(A\) and \(B\) are \(a%\) and \(b%\), respectively. We need to figure out the amount of salt for salt solution questions.

The amount of salt in \(200g\) of solution \(A\) is \(200*(\frac{a}{100}) = 2a\). The amount of salt in \(100g\) of solution \(B\) is \(100*(\frac{b}{100}) = b.\)

After mixing the \(2\) solutions, the new solution is \(\frac{(2a + b) }{ 300} = \frac{4}{100}\), \(100(2a + b) = 4(300),\) and \(200a + 100b = 1200\). Dividing everything by \(100\) gives us \(2a + b = 12.\)

Then, the amount of salt in \(100g\) of solution \(A\) is \(100*(\frac{a}{100}) = a\) and \(200*(\frac{b}{100}) = 2b.\)

After mixing the \(2\) solution, the new solution is \(\frac{(a + 2b) }{ 300} = \frac{3}{100,} 100(a + 2b) = 3(300),\) and \(100a + 200b = 900\). Dividing everything by \(100\) gives us \(a + 2b = 9.\)

When we add two equations, we have \((2a + b) + (a + 2b) = 12 + 9, 3a + 3b = 21\) or \(a + b = 7.\)

Then we have \(a = (2a + b) - (a + b) = 12 – 7 = 5\) and \(b = (a + 2b) – (a + b) = 9 – 7 = 2.\)

Therefore, A is the answer
Answer: A
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Re: A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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New post 09 Jan 2020, 07:55
MathRevolution wrote:
[GMAT math practice question]

A and B are two salt solutions with different concentrations. Mixing 200g of A and 100g of B makes a 4% salt solution, and mixing 100g of A and 200g of B makes a 3% salt solution. What are the concentrations of A and B?

A. 5%, 2%
B. 6%, 4%
C. 5%, 1%
D. 6%, 2%
E. 7%, 3%


Let the concentration of A & B be a & b respectively

(200a + 100b)/300 = 4
(100a + 200b)/300 = 3

giving
a = 5 & b = 2

IMO A
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Re: A and B are two salt solutions with different concentrations. Mixing   [#permalink] 09 Jan 2020, 07:55
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