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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8722
GMAT 1: 760 Q51 V42
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A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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Updated on: 06 Dec 2019, 00:30
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45% (medium)

Question Stats:

81% (02:37) correct 19% (02:23) wrong based on 69 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%

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" 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. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 10219 Location: Pune, India Re: A and B are two salt solutions with different concentrations. Mixing [#permalink] ### Show Tags 09 Jan 2020, 07:40 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% Answer (A) _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > DS Forum Moderator Joined: 19 Oct 2018 Posts: 1414 Location: India Re: A and B are two salt solutions with different concentrations. Mixing [#permalink] ### Show Tags 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% Manager Joined: 10 Dec 2017 Posts: 177 Location: India Re: A and B are two salt solutions with different concentrations. Mixing [#permalink] ### Show Tags 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8722 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A and B are two salt solutions with different concentrations. Mixing [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: A and B are two salt solutions with different concentrations. Mixing  [#permalink]

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