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In 1997, N people graduated from college. If 1/3 of them rec
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22 Sep 2016, 11:32
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64% (01:52) correct
35% (02:34) wrong based on 70 sessions
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In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?
Re: In 1997, N people graduated from college. If 1/3 of them rec
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22 Sep 2016, 11:34
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GreenlightTestPrep wrote:
In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?
(A) 11N/12 (B) 7N/12 (C) 5N/12 (D) 6N/7 (E) N/7
Source: Grockit
Here's the Double Matrix Method with step-by-step details:
Note: This technique can be used for most questions featuring a population in which each member has two criteria associated with it. Here, the criteria are: - degree(applied sciences or not) - school location(north eastern state or not)
In 1997, N people graduated from college.
1/3 of them received a degree in the applied sciences
Of those (1/3)N students, 1/4 graduated from a school in one of six northeastern states. In other words, (1/12)N students have a degree in applied sciences and graduated from a northeastern school.
Which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states? If the box that has (1/12)N students in it represents the students with a degree in applied sciences and graduated from a northeastern school, then the remaining boxes (shaded in blue) must represent the students who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.
Since all 4 boxes must add to N (the total number of students), the 3 shaded boxes must add to (11/12)N.
Re: In 1997, N people graduated from college. If 1/3 of them rec
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16 Dec 2018, 21:22
GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
How did you simply add all three boxes when they only asked for the number of people who did not graduate with an applied science degree and did not graduate from one of the six northeastern states?
Re: In 1997, N people graduated from college. If 1/3 of them rec
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17 Dec 2018, 06:57
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QuantumWonder wrote:
GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
How did you simply add all three boxes when they only asked for the number of people who did not graduate with an applied science degree and did not graduate from one of the six northeastern states?
Be careful, the question asks "which of the following expressions represents the number of people who graduated from college in 1997 who did notBOTH receive a degree in the applied sciences and graduate from a school in one of six northeastern states?"
The top-left box represents the people who BOTH received a degree in the applied sciences AND graduated from a school in one of six northeastern states"
So, the other 3 boxes must represent the people who did notBOTH receive a degree in the applied sciences and graduate from a school in one of six northeastern states.
Re: In 1997, N people graduated from college. If 1/3 of them rec
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17 Dec 2018, 07:12
GreenlightTestPrep wrote:
Be careful, the question asks "which of the following expressions represents the number of people who graduated from college in 1997 who did notBOTH receive a degree in the applied sciences and graduate from a school in one of six northeastern states?"
The top-left box represents the people who BOTH received a degree in the applied sciences AND graduated from a school in one of six northeastern states"
So, the other 3 boxes must represent the people who did notBOTH receive a degree in the applied sciences and graduate from a school in one of six northeastern states.
Does that help?
Cheers, Brent
Yes, thank you kind sir!
Now, if it said either instead of both, would that mean we only add the two corresponding boxes?
Re: In 1997, N people graduated from college. If 1/3 of them rec
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07 Apr 2019, 17:14
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Expert Reply
GreenlightTestPrep wrote:
In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?
(A) 11N/12 (B) 7N/12 (C) 5N/12 (D) 6N/7 (E) N/7
Source: Grockit
We see that N x ⅓ x ¼ = N/12 people both received a degree in the applied sciences and graduated from a school in one of six northeastern states. Thus, 1 - N/12 = 11N/12 people did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.
Note: The wording of this question is confusing. The question asks the number of people who DID NOT DO BOTH. If we let A = degree in applied science and N = graduated from a school in one of six northeastern states, then we see there are 4 possible events: [A,N] [A, not N] [not A, N] [not A, not N]. This question asks the number of people who were NOT [A, N], which means that we count the number of people in the three remaining events as the correct answer.
It is a common error to misinterpret the question as asking the number who were (only) [not A, not N], but in this case the question would be “How many people neither received a degree in applied science nor graduated from a school in one of six northeastern states.?
Re: In 1997, N people graduated from college. If 1/3 of them rec
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16 Oct 2023, 06:03
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Re: In 1997, N people graduated from college. If 1/3 of them rec [#permalink]
22 Sep 2016, 11:32
64% (01:52) correct
