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Marcia has 2 liters (L) of a 60% concentrated solution of ph

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Marcia has 2 liters (L) of a 60% concentrated solution of ph [#permalink] New post 23 Nov 2018, 05:55
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Marcia has 2 liters (L) of a 60% concentrated solution of phosphoric acid. She wants to add 3L of less concentrated phosphoric acid solutions, so that she has 5L of a solution with a concentration less than 50%. Which could she add?

Indicate all possible combinations of solutions.

A. 3L of a 40% concentrated solution

B. 3L of a 42% concentrated solution

C. 3L of a 44% concentrated solution

D. 3L of a 46% concentrated solution

E. 3L of a 48% concentrated solution

F. 2L of a 40% solution and 1L of a 45% solution

G. 1L of a 40% solution and 2L of a 45% solution
[Reveal] Spoiler: OA

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Re: Marcia has 2 liters (L) of a 60% concentrated solution of ph [#permalink] New post 14 Dec 2018, 15:02
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First, note that the amount of phosphoric acid is 1.2L because it said 2 L at 60% concentration; hence 2(.6)=1.2

Next, we translate the sentence into an equation that is implicated on the amount of phosporic solution

2(.6) + 3x < .5(5)
1.2 + 3x < 2.5
x<.433

That means, 3 L of any solution with concentration less than .4333 works. Therefore A, B.

Next look at option F. Before doing that, note that the amount of phosphoric acid is NO more than 3(.4333) = 1.29 L

F. 2L of a 40% solution and 1L of a 45% solution
This means we have 2(.4) + .45(1) < 1.29 L of phosphoric acid, so F.

G. 1L of a 40% solution and 2L of a 45% solution
This means we have 1(.4) + .45(2) > 1.29 L of phosphoric acid so eliminate it.

So A, B, F
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Re: Marcia has 2 liters (L) of a 60% concentrated solution of ph [#permalink] New post 24 Jun 2020, 21:26
QuantumWonder wrote:
First, note that the amount of phosphoric acid is 1.2L because it said 2 L at 60% concentration; hence 2(.6)=1.2

Next, we translate the sentence into an equation that is implicated on the amount of phosporic solution

2(.6) + 3x < .5(5)
1.2 + 3x < 2.5
x<.433

That means, 3 L of any solution with concentration less than .4333 works. Therefore A, B.

Next look at option F. Before doing that, note that the amount of phosphoric acid is NO more than 3(.4333) = 1.29 L

F. 2L of a 40% solution and 1L of a 45% solution
This means we have 2(.4) + .45(1) < 1.29 L of phosphoric acid, so F.

G. 1L of a 40% solution and 2L of a 45% solution
This means we have 1(.4) + .45(2) > 1.29 L of phosphoric acid so eliminate it.

So A, B, F


I think there is some problem with calculation of G. Plus as per your explanation x should be less than 43% so I am unable to understand your explanation with point F and G :(
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Re: Marcia has 2 liters (L) of a 60% concentrated solution of ph [#permalink] New post 26 Jun 2020, 03:34
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Farina wrote:
QuantumWonder wrote:
First, note that the amount of phosphoric acid is 1.2L because it said 2 L at 60% concentration; hence 2(.6)=1.2

Next, we translate the sentence into an equation that is implicated on the amount of phosporic solution

2(.6) + 3x < .5(5)
1.2 + 3x < 2.5
x<.433

That means, 3 L of any solution with concentration less than .4333 works. Therefore A, B.

Next look at option F. Before doing that, note that the amount of phosphoric acid is NO more than 3(.4333) = 1.29 L

F. 2L of a 40% solution and 1L of a 45% solution
This means we have 2(.4) + .45(1) < 1.29 L of phosphoric acid, so F.

G. 1L of a 40% solution and 2L of a 45% solution
This means we have 1(.4) + .45(2) > 1.29 L of phosphoric acid so eliminate it.

So A, B, F


I think there is some problem with calculation of G. Plus as per your explanation x should be less than 43% so I am unable to understand your explanation with point F and G :(


You can consider the sum as:

60% of 2L + Extra < 50% of 5L

Therefore, 1.2 + y < 2.5

Now you just have to see that 1.2 + y does not exceed and does not equate to 2.5, So

Option A: y = 40% of 3L = 1.2 (correct)

Option B: y = 42% of 3L = 1.26 (correct)

Option C: y = 44% of 3L = 1.32 (incorrect)

Option D: y = 46% of 3L = 1.38 (incorrect)

Option E: y = 48% of 3L = 1.44 (incorrect)

Option F: y = 40% of 2L + 45% of 1L = 1.25 (correct)

Option G: y = 40% of 1L + 45% of 2L = 1.3 (incorrect)
Re: Marcia has 2 liters (L) of a 60% concentrated solution of ph   [#permalink] 26 Jun 2020, 03:34
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Marcia has 2 liters (L) of a 60% concentrated solution of ph

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