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Last year, 3/8 of the 440 juniors at Central High Sc
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27 Jul 2017, 10:44
27 Jul 2017, 10:44
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Last year, 3/8 of the 440 juniors at Central High School took French, 2/5 took Geography, and 1/4 took both. Which of the following statements must be true?
Indicate all statements that apply.
A. More students took French than Geography.
B. More students took both French and Geography than took neither.
C. The number of students that took Geography but not French was greater than 50.
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Last year, 3/8 of the 440 juniors at Central High Sc
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23 Feb 2019, 06:21
23 Feb 2019, 06:21
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Carcass wrote:
Last year, 3/8 of the 440 juniors at Central High School took French, 2/5 took Geography, and 1/4 took both. Which of the following statements must be true?
Indicate all statements that apply.
A. More students took French than Geography.
B. More students took both French and Geography than took neither.
C. The number of students that took Geography but not French was greater than 50.
We can solve this with a technique called the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions)..
Here, we have a population of juniors , and the two characteristics are:
- took French or did not take French
- took Geography or did not take Geography
This question type is VERY COMMON on the GRE, so be sure to master the technique.
3/8 of 440 = 165, so 165 students took French
2/5 of 440 = 176, so 176 students took Geography
1/4 of 440 = 110, so 110 students took BOTH
We can take this information and set up the Matrix as follows:
If 165 of the 440 students took French, then the remaining 275 students did NOT take French
If 176 of the 440 students took Geography, then the remaining 264 students did NOT take Geography
Once we know the sums of the rows and columns, we can complete the Matrix as follows:
Now check the answer choices . . .
A. More students took French than Geography.
165 took French, and 176 took Geography
Not true!
B. More students took both French and Geography than took neither.
110 took BOTH, and 209 took NEITHER
Not true!
C. The number of students that took Geography but not French was greater than 50.
66 took Geography but not French
TRUE!
Answer: C
Cheers,
Brent
To learn more about the Double Matrix Method, watch this video:
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Re: Last year, 3/8 of the 440 juniors at Central High Sc
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12 Mar 2021, 00:05
12 Mar 2021, 00:05
Carcass wrote:
Last year, 3/8 of the 440 juniors at Central High School took French, 2/5 took Geography, and 1/4 took both. Which of the following statements must be true?
Indicate all statements that apply.
A. More students took French than Geography.
B. More students took both French and Geography than took neither.
C. The number of students that took Geography but not French was greater than 50.
French = \(\frac{3}{8}(440) = 165\)
Geography = \(\frac{2}{5}(440) = 176\)
Both = \(\frac{1}{4}(440) = 110\)
None = Total - French - Geography + Both
None = \(440 - 165 - 176 + 110\)
None = \(209\)
A. More students took French than Geography - NO
\(165\) is not greater than \(176\)
B. More students took both French and Geography than took neither - NO
\(110\) is not greater than \(209\)
C. The number of students that took Geography but not French was greater than 50 - YES
Only Geography = Geography - Both = \(165 - 110 = 55\)
\(55\) is greater than \(50\)
Hence, option C
