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# A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug

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Math Expert
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Posts: 56269
A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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03 Mar 2015, 07:03
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27
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:27) correct 41% (01:34) wrong based on 641 sessions

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A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sugar solution to produce R ounces of a 25% sugar solution. What is the value of P?

(1) Q = 455 mL
(2) R = 650 mL

Kudos for a correct solution.

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Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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03 Mar 2015, 23:13
2
5
Hi All,

You have to be very careful about your assumptions with this question. You will likely find that doing a little bit of extra work will help you to be sure that you have the correct answer.

From the prompt, we know that we're mixing P ounces of a 60% sugar solution with Q ounces of a 10% sugar solution to form R ounces of a 25% sugar solution. We're asked for the value of P....

Before dealing with the two Facts, I'm going to set up a "weighted average" equation using the above information....

(.6P + .1Q)/(P+Q) = .25

.6P + .1Q = .25P + .25Q
.35P = .15Q
35P = 15Q

P/Q = 15/35 = 3/7 This means that for every 3 ounces of P, we have 7 ounces of Q. However, we don't yet know the exact number of ounces of each we have....

We also know that R = P+Q

Looking at this from an algebraic standpoint, we have 3 variables and 2 equations.....

Fact 1: Q = 455

With this value, and the given ratio for P/Q, we CAN answer the question.
Fact 1 is SUFFICIENT

Fact 2: R = 660

Since we know that R = P+Q and the ratio of P/Q = 3/7, we CAN answer the question. Here's how...

With the given ratio, for every 3 ounces of P, we have 7 ounces of Q. In basic terms, that means that every 10 ounces is 3 ounces of P and 7 ounces of Q. With a total of 660 ounces, we have 66(3) = 198 ounces of P and 66(7) = 462 ounces of Q.
Fact 2 is SUFFICIENT

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##### General Discussion
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Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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03 Mar 2015, 10:05

1)statement 1 :-q=455
Let x amount of P is added then , sugar and water are(0.6x and 0.4x respectively

amount of sugar in q is known 10 percent of 455
amount of sugar in p is 0.6x

total in R:- 45.5+0.6x
also total fluid is :-455+x

ratio of sugar is given:-25%
so 45.5+0.6x=(455+x) *0.25
x can be found out hence sufficeint

2) statment 2 says amount of sugar is known but p and q can be any ratio , hence not sufficient
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Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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03 Mar 2015, 13:25
Forming equation based on the question stem-

0.60P + 0.10Q = 0.25R (eqn1)

OR, 0.60P + 0.10Q = 0.25(P+Q) (As, R=P+Q) (eqn2)

We need to find the value of "P"

1) Q=455ml
Hence, using eqn (2), we can find the value of P.
Therefore, 1 sufficient.

2) R=660ml
Even by substituting the value of R in any of the above equations, we cannot get the value of P or Q.
Therefore 2, insufficient

Math Expert
Joined: 02 Sep 2009
Posts: 56269
Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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08 Mar 2015, 16:08
1
2
Bunuel wrote:
A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sugar solution to produce R ounces of a 25% sugar solution. What is the value of P?

(1) Q = 455 mL
(2) R = 660 mL

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

This one is very elegant. We have three variables — the amount of 60% sugar solution, the amount of 15% sugar solution, and the amount of the resultant 25% sugar solution. Three variables. We have two equations: the volume equation and the concentration equation. Right now, three variables and two equations: we can’t solve.

Now, look at the statements. Each statement gives us the value of one of the variables. If we get the value of one variable, that’s no longer a variable, and thus we are down to two variables with two equations: that’s a situation in which we can find a full solution. Thus, given the value of either Q or R, we enter a situation in which we can solve for everything, and thus we would know P. Therefore, each statement, by itself, is sufficient.

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Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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09 Mar 2015, 22:25
1
60%---------------------25%----------10%

35p=15q

p/q=15/35=3/7

what is the value of P?

St.1 Q=455, so P=(3/7)*455. SUFF

St.2 R=660, so P=(3/10)*660. SUFF

D

one notice is that to be consistent, R in the second statement should be 650
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Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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10 Mar 2015, 05:33
0.6P + 0.10Q = 0.25(P+Q)

Statement i tell Q hence sufficient

Now Statement ii tells P+Q = 660

Now we have two equations and two variable. can be solved Sufficient
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Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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06 Oct 2016, 07:01
Bunuel wrote:
A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sugar solution to produce R ounces of a 25% sugar solution. What is the value of P?

(1) Q = 455 mL
(2) R = 660 mL

Kudos for a correct solution.

I started with a matrix chart...
P=0.6P(sugar) + 0.4P(other stuff)
Q=0.1Q(sugar) + 0.9Q(other stuff)
now:
0.6P+0.1Q=0.25R
and
0.4P+0.9Q=0.75R

multiply first one by 3:
1.8P+0.3Q=0.4P+0.9Q
or
1.2P=0.6Q -> multiply everything by 10
12P=6Q -> divide by 6
2P=Q
so to find P, we need either value of Q, or value of R.

1. we have value for Q - sufficient
2. we have value for R - sufficient.

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Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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13 Sep 2017, 01:30
1
Bunuel, There is a mistake in the Question.

For both statements to give a consistent solution, R should be 650 and not 660.

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Posts: 56269
Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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13 Sep 2017, 01:36
gumnamibaba wrote:
Bunuel, There is a mistake in the Question.

For both statements to give a consistent solution, R should be 650 and not 660.

Yes, you are right. Edited. Thank you.
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Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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04 Jan 2018, 13:00
Given: P + Q = R
0.6P + 0.1Q = 0.25R

Three unknown variables, 2 eqns

Statement 1: Q = 455 mL => reduces unknown variables to 2, so 2 equations and 2 unknown variables -> sufficient to solve
Statement 2: R = 660 mL => reduces unknown variables to 2, so 2 equations and 2 unknown variables -> sufficient to solve

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Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug  [#permalink]

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07 Jan 2019, 06:27
Bunuel wrote:
A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sugar solution to produce R ounces of a 25% sugar solution. What is the value of P?

(1) Q = 455 mL
(2) R = 650 mL

Kudos for a correct solution.

From the Rule of Alligations :

$$\frac{Q}{P}$$ =$$\frac{60-25}{25-10}$$

$$\frac{Q}{P}$$ = $$\frac{7}{3}$$

St 1 : Q is Given

P can be found

Sufficient

St 2 : R is Given

R = P + Q

Two Equations, Two unknowns

P can be found

Sufficient

Choice D
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Re: A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sug   [#permalink] 07 Jan 2019, 06:27
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