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?
[Statement #1] Q = 455 mL
[Statement #2] R = 660 mL
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sugar solution
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j_shreyans
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So that the two statements do not contradict each other, Statement 2 should read as shown below:
Q = 10% sugar.
R = the MIXTURE of P and Q = 25% sugar.
To determine the required ratio of P to Q, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the percentages for P and Q on the ends and the percentage for mixture R in the middle.
P 60%------------25%------------10% Q
Step 2: Calculate the distances between the percentages.
P 60%-----35-----25%-----15-----10% Q
Step 3: Determine the ratio in the mixture.
The required ratio of P to Q is equal to the RECIPROCAL of the distances in red.
P/Q = 15/35 = 3/7.
Since P/Q = 3/7, and 3+7=10, every 10 liters of mixture R is composed of 3 liters of P and 7 liters of Q.
Statement 1: Q=455
Since P/Q = 3/7, P = (3/7)Q.
Thus, P = (3/7)(455) = 195.
SUFFICIENT.
Statement 2: R=650
Since every 10 liters of mixture R includes 3 liters of P, P is equal to 3/10 of mixture R:
P = (3/10)(650) = 195.
SUFFICIENT.
The correct answer is D.
P = 60% sugar.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?
[Statement #1] Q = 455 mL
[Statement #2] R = 650 mL
Q = 10% sugar.
R = the MIXTURE of P and Q = 25% sugar.
To determine the required ratio of P to Q, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the percentages for P and Q on the ends and the percentage for mixture R in the middle.
P 60%------------25%------------10% Q
Step 2: Calculate the distances between the percentages.
P 60%-----35-----25%-----15-----10% Q
Step 3: Determine the ratio in the mixture.
The required ratio of P to Q is equal to the RECIPROCAL of the distances in red.
P/Q = 15/35 = 3/7.
Since P/Q = 3/7, and 3+7=10, every 10 liters of mixture R is composed of 3 liters of P and 7 liters of Q.
Statement 1: Q=455
Since P/Q = 3/7, P = (3/7)Q.
Thus, P = (3/7)(455) = 195.
SUFFICIENT.
Statement 2: R=650
Since every 10 liters of mixture R includes 3 liters of P, P is equal to 3/10 of mixture R:
P = (3/10)(650) = 195.
SUFFICIENT.
The correct answer is D.
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Hi j_shreyans,
This DS question has a great algebra shortcut built into it, but you'll probably have to "set up" the question to see it.
We're told to mix P ounces of a 60% solution with Q ounces of a 10% solution and end up with a 25% solution (the R ounces = P + Q).
This is a reference to the "weighted average" formula and can be written in this way:
(.6P + .1Q)/(P+Q) = .25
This can be simplified (although it's not necessary to do that work to answer this question.
.6P + .1Q = .25P + .25Q
.35P = .15Q
35P = 15Q
7P = 3Q
Looking at this, we can see 2 variables and 1 equation. We don't have enough information here to solve for P or Q just yet (the question asks us to solve for P), but if we had ANOTHER UNIQUE EQUATION with any combination of these variables, then we WOULD have enough information to solve for P.
Fact 1: Q = 455
This is enough information to answer the question and you don't have to do any math to prove it.
Fact 1 is SUFFICIENT
Fact 2: R = 650
With this info, we know the total number of ounces. This tells us (P+Q) = 650. This also serves as a second equation that would help us to answer the question.
P+Q = 650
7P = 3Q
You'd have to do a bit more algebra to find the value of P, but we have 2 variables and 2 unique equations here, so we CAN solve for P.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This DS question has a great algebra shortcut built into it, but you'll probably have to "set up" the question to see it.
We're told to mix P ounces of a 60% solution with Q ounces of a 10% solution and end up with a 25% solution (the R ounces = P + Q).
This is a reference to the "weighted average" formula and can be written in this way:
(.6P + .1Q)/(P+Q) = .25
This can be simplified (although it's not necessary to do that work to answer this question.
.6P + .1Q = .25P + .25Q
.35P = .15Q
35P = 15Q
7P = 3Q
Looking at this, we can see 2 variables and 1 equation. We don't have enough information here to solve for P or Q just yet (the question asks us to solve for P), but if we had ANOTHER UNIQUE EQUATION with any combination of these variables, then we WOULD have enough information to solve for P.
Fact 1: Q = 455
This is enough information to answer the question and you don't have to do any math to prove it.
Fact 1 is SUFFICIENT
Fact 2: R = 650
With this info, we know the total number of ounces. This tells us (P+Q) = 650. This also serves as a second equation that would help us to answer the question.
P+Q = 650
7P = 3Q
You'd have to do a bit more algebra to find the value of P, but we have 2 variables and 2 unique equations here, so we CAN solve for P.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
