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Kate ate 1/3 of a cake, Fritz ate 1/5 of the remaining cake,
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02 Apr 2019, 09:34
02 Apr 2019, 09:34
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Question Stats:
88% (00:47) correct
11% (00:43) wrong based on 36 sessions
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Kate ate \(\frac{1}{3}\) of a cake, Fritz ate \(\frac{1}{5}\) of the remaining cake, and what was left was eaten by Emily.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
Fraction of the cake eaten by Emily |
\(\frac{5}{7}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Re: Kate ate 1/3 of a cake, Fritz ate 1/5 of the remaining cake,
[#permalink]
03 Apr 2019, 01:45
03 Apr 2019, 01:45
1
Expert Reply
First, Kate ate \(\frac{1}{3}\) of the cake. So \(\frac{2}{3}\) of the cake remains.
Then, Fritz ate \(\frac{1}{5}\) of the remaining cake, which is \(\frac{2}{3}\) of the original cake. Fritz, then, ate \(\frac{1}{5}\) of \(\frac{2}{3}\) of the cake.
In word problems, "of" means multiply, so Fritz ate \(\frac{1}{5} \times \frac{2}{3} = \frac{2}{15}\) of the cake.
So \(\frac{1}{3} + \frac{2}{15} = \frac{5}{15} + \frac{2}{15} = \frac{7}{15}\) of the cake was eaten. This means \(\frac{8}{15}\) of the cake remains for Emily to eat.
\(\frac{8}{15}\) is pretty close to \(\frac{1}{2}\). But \(\frac{5}{7}\) is much greater than \(\frac{1}{2}\). So Quantity B is definitely greater.
Then, Fritz ate \(\frac{1}{5}\) of the remaining cake, which is \(\frac{2}{3}\) of the original cake. Fritz, then, ate \(\frac{1}{5}\) of \(\frac{2}{3}\) of the cake.
In word problems, "of" means multiply, so Fritz ate \(\frac{1}{5} \times \frac{2}{3} = \frac{2}{15}\) of the cake.
So \(\frac{1}{3} + \frac{2}{15} = \frac{5}{15} + \frac{2}{15} = \frac{7}{15}\) of the cake was eaten. This means \(\frac{8}{15}\) of the cake remains for Emily to eat.
\(\frac{8}{15}\) is pretty close to \(\frac{1}{2}\). But \(\frac{5}{7}\) is much greater than \(\frac{1}{2}\). So Quantity B is definitely greater.
gmatclubot
Re: Kate ate 1/3 of a cake, Fritz ate 1/5 of the remaining cake, [#permalink]
03 Apr 2019, 01:45
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