How many sophomore students attend the college?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Jan 30, 2009 3:21 am

Of all sophomore students attending a certain college, 20% are enrolled in an English course while 10% are enrolled in a psychology course. How many sophomore students attend the college?

1. 5% of the sophomore students at the college are enrolled in both an English course and a psychology course.

2. A total of 210 sophomore students at the college are enrolled in neither an English course nor a psychology course.

What is the OA?

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Source: Beat The GMAT — Data Sufficiency | Fri Jan 30, 2009 3:21 am

shulapa: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Thu Nov 13, 2008 8:05 am; Thanked: 6 times

by shulapa » Fri Jan 30, 2009 4:10 am

Clearly a Van diagram problem so we should base our calculations on the following equation:
Total = Eng + Psy - Both + Non.

The information provided is the percentage of students enrolled in each class, therefore, the Total is equal to 100 percent. However, it is important to note that the question is about the NUMBER of student attending the college. The question can actually be answered without doing the calculations but I will show them in order to prove my point.

(1) provides the percentage of students enrolled in both Eng and Psy classes. From this information we can calculate the percentage of people who are not enrolled in either of the classes.

100% = 20% + 10% - 5% + None
None = 75%

Now we have the percentage but not the actual amounts. Therefore, insufficient.

(2) provides us with the number of student who are not enrolled to neither of the classes. However, as we lack the how much is this from the total number of students, we cannot answer the question - therefore, insufficient.

(1) + (2)

As we know the proportion of the student not enrolled in those classes to the number of students in the college, and also the number of them, we can calculate the total amount of students.

210/0.75 = 280. Therefore C

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Jan 30, 2009 4:30 am

shulapa wrote:Clearly a Van diagram problem so we should base our calculations on the following equation:
Total = Eng + Psy - Both + Non.

The information provided is the percentage of students enrolled in each class, therefore, the Total is equal to 100 percent. However, it is important to note that the question is about the NUMBER of student attending the college. The question can actually be answered without doing the calculations but I will show them in order to prove my point.

(1) provides the percentage of students enrolled in both Eng and Psy classes. From this information we can calculate the percentage of people who are not enrolled in either of the classes.

100% = 20% + 10% - 5% + None
None = 75%

Now we have the percentage but not the actual amounts. Therefore, insufficient.

(2) provides us with the number of student who are not enrolled to neither of the classes. However, as we lack the how much is this from the total number of students, we cannot answer the question - therefore, insufficient.

(1) + (2)

As we know the proportion of the student not enrolled in those classes to the number of students in the college, and also the number of them, we can calculate the total amount of students.

210/0.75 = 280. Therefore C

OA is? IMO C.

The OE is

Answering the question requires some information about the numbers of students, not just percentages. Statement (1) alone provides no numerical information and is therefore insufficient to answer the question. Statement (2) provides some numerical information but is nevertheless insufficient alone to answer the question, because we donï¿½t know how many sophomores are enrolled in both an English course and a psychology course. If there is no overlap, then the 210 sophomores enrolled in neither type of course would account for 70% (100% ï¿½ 20% ï¿½ 10%) of the total number, and the answer to the question would be 300 (210 is 70% of 300). But if there is an overlap, the total number would be smaller. Considering statements (1) and (2) together, however, we can determine the total number of sophomore students. Given that 20% of sophomore students are enrolled in an English course and that 10% are enrolled in a psychology course, and given the 5% overlap indicated in statement (1), 25% (30% ï¿½ 5%) of sophomore students are enrolled in either or both types of courses. It follows that 75% are enrolled in neither type of course. Statement (2) indicates that this number is 210, which is 75% of 280 (the total number of sophomore students).

Source: https://www.west.net/~stewart/gmat

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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