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# At a particular university with 200 students 30% only receive loans an

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Math Expert
Joined: 02 Sep 2009
Posts: 52108
At a particular university with 200 students 30% only receive loans an  [#permalink]

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24 Jan 2017, 08:52
00:00

Difficulty:

15% (low)

Question Stats:

91% (01:59) correct 9% (01:43) wrong based on 74 sessions

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At a particular university with 200 students 30% only receive loans and 40% only receive scholarships. What percent of the students receive neither scholarships nor loans?

(1) At least 5% of the students do not receive loans.
(2) More than 15% of the students receive both loans and scholarships.

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Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 669
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: At a particular university with 200 students 30% only receive loans an  [#permalink]

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05 Mar 2017, 12:12
2
Original information:

Statement (1):

This statement gives you no new information. You already know that there are more than 10 students who get loans, because you know there are 80 students who get no loans (and do get scholarships). Since it gives you no new info, it's insufficient.

Statement (2):

This statement gives you a lot of information, but it still doesn't let you solve the problem. We know that there are at least 30 people in the top left. So, there are at least 110 scholarship recipients, and at least 90 loan recipients. That means there are no more than 90 people without scholarships, and no more than 110 people without loans, in total. Both of those facts tell you there are at most 30 people who get neither. However, you don't know if there are 30 or 0 or anything in between.

(1+2)

Since you get no new info from Statement 1, and statement 2 is insufficient, 1+2 are insufficient together.
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Re: At a particular university with 200 students 30% only receive loans an &nbs [#permalink] 05 Mar 2017, 12:12
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