Problem Solving

BTGModeratorVI wrote: ↑

Sun Aug 02, 2020 7:01 am

Milk and cream are combined to make a 60-liter mixture that is 50 percent butterfat. If the milk is 5 percent butterfat and the cream is 75 percent butterfat, approximately how many liters of milk are in the mixture?

A. 20.00
B. 21.43
C. 30.00
D. 38.57
E. 42.75

Answer: B
Source: GMAT prep

Use options.
Milk content will have \(5\%\) butter fat.
Total content is \(60\)
So, \(60-\)milk \(=\) cream

Now,
A) 20 is milk
\(40\) will be cream.
\(\Longrightarrow 20\cdot \dfrac{5}{100}= 1\) litre of butterfat
\(\Longrightarrow 40\cdot \dfrac{75}{100} = 30\) litre of butterfat
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Total \(31\) litre of butterfat (greater than \(50\%\) of \(60\) liters of mixture) \(\Large{\color{red}\chi}\)

(So it has to be slighter bigger than \(20\) liters of milk)

B) \(21.43\) is milk
\(60-21.43 = 38.57\) is cream
\(\Longrightarrow 21.43\cdot \dfrac{5}{100}= 1.0715\) liters of butterfat.
\(\Longrightarrow 38.57 \cdot \dfrac{75}{100}= 28.9275\) liters of butterfat.
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Total butterfat is \(1.0715+28.9275=30\) ( desired result, \(50\%\) of \(60\) liters of mixture) \(\Large{\color{green}\checkmark}\)

We can stop here, because we already got the answer.