BTGmoderatorDC 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

OA D

Source: Magoosh

From the given information, we have R = P + Q

From the first solution, we have

Sugar content = 60% of P = 0.6P; and
Water content = 40% of P = 0.4P

From the second solution, we have

Sugar content = 10% of Q = 0.1Q; and
Water content = 90% of Q = 0.9Q

Total sugar content = 0.6P + 0.1Q;
Total water content = 0.4P + 0.9Q

Since is given that the combined solution of R ounces a solution of a 25% sugar solution, we have sugar content in the final solution = 25% of R = 0.25R = 0.25(P + Q)

=> 0.6P + 0.1Q = 0.25(P + Q)

=> P = 3Q/7 ---(1)

We have to get the value of P.

Let's take each statement one by one.

(1) Q = 455 ml

Sufficient. P = 3Q/7 = 3*(455/7) = 195 ml

(2) R = 650 ml

=> R = P + Q = 650

=> Q = 650 - P ---(2)

From (1) and (2), we have

P = 3Q/7 = 3(650 - P)/7

=> 7P = 650*3 - 3P

10P = 650*3

P = 195 ml

The correct answer: D

Hope this helps!

-Jay
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