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

Question

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 .

EMPOWERgmatRichC · Accepted Answer

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

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

Temurkhon · Answer

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

utkgogia2003 · Answer

IMO answer should be A

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

Aksh19 · Answer

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

Hence, Answer "A"

Bunuel · Answer

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.

Answer = D

iamdp · Answer

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

mvictor · Answer

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.

D is the answer.

gumnamibaba · Answer

Bunuel , There is a  mistake in the Question .

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

Please edit.

Bunuel · Answer

Yes, you are right. Edited. Thank you.

hellosanthosh2k2 · Answer

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

(D)

ksrutisagar · Answer

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

QuantMadeEasy · Answer

P ounces of 60% sugar solution is mixed with Q ounces of a 10% sugar solution to produce R ounces of a 25% sugar solution
Weighted average concept states that the total difference above the average is equal to the total difference below the average
Here,
(60-25)% * P = (25-10)% * Q
35%* P = 15% * Q
7P = 3Q -------(i)

To find: Value of P

(1) using Q = 455, P can be calculated. Sufficient

(2) P+Q = R = 650------(ii)
from (i) Q = (7/3)*P and substituting in (ii)
P can be calculated
Sufficient

D is correct

Advait01 · Answer

Damn i made such a silly mistake of not converting R =P+Q
Really felt stupid while seeing the solution

Rohit_842 · Answer

Are we assuming both solutions to be equally dense? because how can we derive the number of P ounces if the statements only give us information on volume and from question we just have a ratio 3/7.

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