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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8566
GMAT 1: 760 Q51 V42
GPA: 3.82
A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 81% (02:37) correct 19% (02:23) wrong based on 67 sessions

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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%

_________________

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.
VP  V
Joined: 19 Oct 2018
Posts: 1301
Location: India
Re: A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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$$\frac{200a+100b}{300}= 4$$

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%
Manager  G
Joined: 10 Dec 2017
Posts: 178
Location: India
Re: A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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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
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8566
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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=>

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 $$b = (a + 2b) – (a + b) = 9 – 7 = 2.$$

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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10105
Location: Pune, India
Re: A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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1
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%

_________________
Karishma
Veritas Prep GMAT Instructor

SVP  D
Joined: 03 Jun 2019
Posts: 2004
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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