Magoosh
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
OA D.
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
A chef mixes P ounces of 60% sugar solution with Q ounces of
This topic has expert replies
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Hi All,
To start, 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.....
1) Q = 455
With this equation, we now have 3 variables and 3 equations. P/Q = 3/7 = P/455. We can solve for the value of P.
Fact 1 is SUFFICIENT
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 = 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
To start, 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.....
1) Q = 455
With this equation, we now have 3 variables and 3 equations. P/Q = 3/7 = P/455. We can solve for the value of P.
Fact 1 is SUFFICIENT
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 = 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
