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

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by BTGmoderatorDC » Wed Aug 21, 2019 5:19 pm

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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

OA D

Source: Magoosh
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Aug 21, 2019 9:07 pm
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 60% of P + 10% of Q = 25% of R

We know that R = P + Q

Thus, from 60% of P + 10% of Q = 25% of R, we have 0.6P + 0.1Q = 0.25R

Let's take each statement one by one.

(1) Q = 455 mL

From 0.6P + 0.1Q = 0.25R, we have 0.6P + 0.1Q = 0.25(P + Q) => 0.6P + 0.1*455 = 0.25(P + 455). This is a linear equation; we can get the unique value of P. Sufficient.

(2) R = 650 mL

From 0.6P + 0.1Q = 0.25R, we have 0.6P + 0.1(R - P) = 0.25R => 0.6P + 0.1(660 - P) = 0.25*660. This is a linear equation; we can get the unique value of P. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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by swerve » Sat Aug 24, 2019 3:00 pm
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

60%-----------------25%----------10%

\(35p=15q\)

\(\frac{p}{q}=\frac{15}{35}=\frac{3}{7}\)

what is the value of P?

Statement 1.
\(Q=455\), so \(P=\frac{3}{7}\cdot 455\). Sufficient \(\color{green}\checkmark\)

Satement 2.
\(R=660\), so \(P=\frac{3}{10}\cdot 660\). Sufficient \(\color{green}\checkmark\)

Therefore, __D__
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