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# A certain business school has a student body of 2,000 students, 45% of

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Math Expert
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A certain business school has a student body of 2,000 students, 45% of  [#permalink]

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17 Feb 2015, 09:21
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Difficulty:

35% (medium)

Question Stats:

78% (02:04) correct 22% (02:03) wrong based on 134 sessions

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A certain business school has a student body of 2,000 students, 45% of whom are male. What percent of the students are international students?

(1) The number of male international students in the business school is twice the number of female students who are not international students.
(2) The number of male students who are not international students is twice the number of male students who are international students.

Kudos for a correct solution.

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A certain business school has a student body of 2,000 students, 45% of  [#permalink]

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Updated on: 18 Feb 2015, 17:43
1
Male students = 900
Female students = 1100
Total students = 2000
Question: International students x% of 2000.

(1) Not sufficient. Knowing that a certain number of male students who are international students is twice the number of female students who are not international does not help us to find x%. It could be that out of all 900 male students 400 are international, which would mean that there are 200 female students who are not international. But it could be that there 600 male international students and 300 not international female students.

(2) Not sufficient. That helps find the number of international male students and not international male students, 300 and 600 respectively. We still don't know how many international female students there are.

(1)+(2) Sufficient. From the statement (2) we find that there are 300 international male students and 600 not international male students. And from statement (1) we find that there are 150 not international female students and 950 international female students. 1250/2000=62.5%

Originally posted by viktorija on 17 Feb 2015, 21:51.
Last edited by viktorija on 18 Feb 2015, 17:43, edited 1 time in total.
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Re: A certain business school has a student body of 2,000 students, 45% of  [#permalink]

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17 Feb 2015, 23:14
1
Bunuel wrote:
A certain business school has a student body of 2,000 students, 45% of whom are male. What percent of the students are international students?

(1) The number of male international students in the business school is twice the number of female students who are not international students.
(2) The number of male students who are not international students is twice the number of male students who are international students.

Kudos for a correct solution.

2000 total students. 45% i.e. 900 male so 1100 female. We need the total of International students.

Statement 1:

Make the table:

.......................Regular................International...........Total

Male...................................................2x......................900

Female..................x......................................................1100

Total...............................................................................

There is no way to know the total number of international students.

Statement 2:

.......................Regular................International...........Total

Male......................4x.............................2x....................900

Female..........................................................................1100

Total...............................................................................

We get that 6x = 900 so x = 150. But there is no way to know the number of female international students.

Both together:

.......................Regular................International...........Total

Male......................600.............................300....................900

Female...................150...............................y.......................1100

Total...............................................................................

Female international students = 1100 - 150 = 950 = y
Total number of international students = 300+950
We can find the desired % now.

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Re: A certain business school has a student body of 2,000 students, 45% of  [#permalink]

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19 Feb 2015, 06:59
ans C..

we have a number, which is further subdivided into four groups $$m_l$$, $$m_i$$, $$f_l$$and $$f_i$$. we know m and f...
and we are to find sum of two of these groups $$m_i$$ and $$f_i$$..
1)statement one tells us a relation between $$m_l$$ and $$f_i$$... insufficient
2) statement two tells us a relation between $$m_l$$ and $$m_i$$...here we get values of both these quantities... value of $$f_i$$ still required..insufficient

combined .. value of $$m_l$$ found from statement2, we can get $$f_i$$ from statement 1....sufficient
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Re: A certain business school has a student body of 2,000 students, 45% of  [#permalink]

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19 Feb 2015, 12:52
2

Here is my best explanation (refer to print screen);
1) we are looking for "x" and they are mutually exclusive (you can't be male and female at the same time).
2) In red is statement one
3) In blue is statement two

Clearly we do not know x so by itself none is useful, however if we use both statements, we can see that the males cleanly divide up in the same amount (x).

So, you would just need to divide 45% of 2000 in 2 to get x, hence SUFFICIENT.
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Re: A certain business school has a student body of 2,000 students, 45% of  [#permalink]

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22 Feb 2015, 11:37
Bunuel wrote:
A certain business school has a student body of 2,000 students, 45% of whom are male. What percent of the students are international students?

(1) The number of male international students in the business school is twice the number of female students who are not international students.
(2) The number of male students who are not international students is twice the number of male students who are international students.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Think of this as a 2x2 table. Before we begin, we know the total number of students (2000) and the total number of male students (45% of 2000, or 900). Statement (1) only tells us only the relationship between male international students and female non-international students, so we don't know the total number of international students; not sufficient. Statement (2) tells us there are twice as many non-international male students (600) as there are international male students (300). This doesn't tell us anything about the female student body, however, so it too is insufficient. Combining the two statements, we know that the number of male international students (300) is twice the number of female non-international students (150). Since we know there are 1100 female students (2000 total - 900 male = 1100 female), we now know the number of female international students (950). We now know that of the 2000 students at the school, 1250 of them are internationals: 5/8 or 62.5%. Both statements together are sufficient.
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Re: A certain business school has a student body of 2,000 students, 45% of  [#permalink]

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19 Nov 2017, 16:29
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Re: A certain business school has a student body of 2,000 students, 45% of &nbs [#permalink] 19 Nov 2017, 16:29
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