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At a particular university with 150 students 70% receive loans and 40%

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At a particular university with 150 students 70% receive loans and 40%  [#permalink]

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New post 05 Feb 2017, 03:26
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E

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Question Stats:

59% (02:17) correct 41% (01:54) wrong based on 88 sessions

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At a particular university with 150 students 70% receive loans and 40% receive scholarships. What percent of the students receive neither scholarships nor loans?

(1) At most 20% of the students received scholarships as well as loans.
(2) No fewer than 30 students that receive loans also receive scholarships.

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Re: At a particular university with 150 students 70% receive loans and 40%  [#permalink]

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New post 05 Feb 2017, 03:58
Bunuel wrote:
At a particular university with 150 students 70% receive loans and 40% receive scholarships. What percent of the students receive neither scholarships nor loans?

(1) At most 20% of the students received scholarships as well as loans.
(2) No fewer than 30 students that receive loans also receive scholarships.



Question is asking how many student received neither Loan(L) nor Scholarship (S) .
It helps to make a 2 X 2 Matrix .

Both statement 1 and 2 give the same information that L + S is greater or equal to 20 % (30 Students) .
There is no unique answer for the asked group .

Answer is E .
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Re: At a particular university with 150 students 70% receive loans and 40%  [#permalink]

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New post 05 Feb 2017, 08:49
(Student with loans) + (Student with Scholarships) + (Student with neither loan nor scholarship) - (Student with both loan and scholarship) = Total Student
Stmt1: 105 + 60 + N - (as per stmt 2 It can be anything between 15 and 30) = 150
so as per above statement value (percentage) of N will change

Stmt2: 105 + 60 + N - (as per stmt 2 It can be anything between 30 and 45) = 150
so as per above statement value (percentage) of N will change

so Ans is E
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Re: At a particular university with 150 students 70% receive loans and 40%  [#permalink]

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New post 05 Feb 2017, 16:11
2
Total Number of University Students: 150

Total Number of University Students who received loans — 70% of 150 = 105
Total Number of University Students who received scholarships — 40% of 150 = 60
Total Number of University Students who received both loans & scholarships = ?
Total Number of University Students who received neither loans or scholarships = ?


Statement 1: At most 20% of the students received scholarships as well as loans.

If 10% students received scholarships as well as loans, then 15 have both,

then 90 students received loans only -15 students received scholarships and loans - 45 students received scholarships only - 0 students received none.

If 20% students received scholarships as well as loans, then 30 have both,

then 75 students received loans only - 30 students received scholarships and loans -15 students received scholarships only - 30 students received none

Since we have two scenarios here, Statement 1 is not sufficient

Statement 2: No fewer than 30 students that receive loans also receive scholarships.

If 30 students received scholarships and loans - then 75 students received loans only - 30 students received scholarships and loans -15 students received scholarships only - 30 students received none

If 45 students received scholarships and loans - then 60 students received loans only - 45 students received scholarships and loans - 0 students received scholarships only - 45 students received none

Since we have two scenarios here, Statement 2 is not sufficient

Combining Statement 1 & 2,

We know that at most 20% received scholarships and loans and No fewer than 30 students that receive loans also receive scholarships, which means that - 30 students received scholarships and loans - then 75 students received loans only - 30 students received scholarships and loans -15 students received scholarships only - 30 students received none.

Therefore answer is C
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Re: At a particular university with 150 students 70% receive loans and 40%  [#permalink]

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New post 05 Feb 2017, 21:21
1
Only Loans: a
Loan and Scholarship intersection: b
Only Scholarship: c
Neither Loan nor Scholarship: x (what we're looking for)

1st statement: max b =30
If b=30, a=75, c=30, so x=15
If b=15, a=90, c=45, so x=0
NS
2nd statement: min b=30
If b=30, a=75, c=30, so x=15
If b=40, a=65, c=20, so x=25
NS

Together, max b = min b = 30. Sufficient to know X.

So C.

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Re: At a particular university with 150 students 70% receive loans and 40%  [#permalink]

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New post 05 Feb 2017, 21:50
Using the double set matrix,

------------- -------Loans-------NoLoans----|
| | |
| | |
Scholarship | | 60
|----------------------------- |-------------------|
| | |
No Scholarship | |90
------------------------------ |------------------- |---
105 45 | 150

(1) At most 30 students got both. So try placing 30 comes in first quadrant (Loans + scholarship). We can get the MAX no.of students who receive neither scholarships nor loans, but not the exact value. So, insufficient.

------------- -------Loans-------NoLoans----|
| | |
| | |
Scholarship 30 | | 60
|----------------------------- |-------------------|
| | |
No Scholarship | |90
------------------------------ |------------------- |-
105 45 | 150


(2) St. 2 repeats the same thing as St1. So, insufficient.
Also, as (1) is same as (2), combining them also does no good.
So, (E).


Bunuel wrote:
At a particular university with 150 students 70% receive loans and 40% receive scholarships. What percent of the students receive neither scholarships nor loans?

(1) At most 20% of the students received scholarships as well as loans.
(2) No fewer than 30 students that receive loans also receive scholarships.
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Re: At a particular university with 150 students 70% receive loans and 40%  [#permalink]

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New post 06 Feb 2017, 03:04
ajay2121988 wrote:
Using the double set matrix,

------------- -------Loans-------NoLoans----|
| | |
| | |
Scholarship | | 60
|----------------------------- |-------------------|
| | |
No Scholarship | |90
------------------------------ |------------------- |---
105 45 | 150

(1) At most 30 students got both. So try placing 30 comes in first quadrant (Loans + scholarship). We can get the MAX no.of students who receive neither scholarships nor loans, but not the exact value. So, insufficient.

------------- -------Loans-------NoLoans----|
| | |
| | |
Scholarship 30 | | 60
|----------------------------- |-------------------|
| | |
No Scholarship | |90
------------------------------ |------------------- |-
105 45 | 150


(2) St. 2 repeats the same thing as St1. So, insufficient.
Also, as (1) is same as (2), combining them also does no good.
So, (E).


Bunuel wrote:
At a particular university with 150 students 70% receive loans and 40% receive scholarships. What percent of the students receive neither scholarships nor loans?

(1) At most 20% of the students received scholarships as well as loans.
(2) No fewer than 30 students that receive loans also receive scholarships.



The answer is clearly C as both the statements can be combined in a double-set matrix to solve for the percentage of students who receive neither scholarship nor loans..
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Re: At a particular university with 150 students 70% receive loans and 40%  [#permalink]

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New post 07 Feb 2017, 07:12
From 1), we get that 30 students is the maximum no. of students who received loans and scholarships. The number varies from 1 to 30. >> INSUFFICIENT
From 2), we get that 30 students is the minimum no. of such the same case above. The number varies from 30 to 60. >> INSUFFICIENT

From 1) and 2), the only possible number is 30. Since we know that there are 30 students who received both L and S, we are able to acquire the rest of numbers. >>> SUFFICIENT

ANS C
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Re: At a particular university with 150 students 70% receive loans and 40%  [#permalink]

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New post 07 Feb 2017, 23:18
stat 1: not suff
stat 2 : Not suff

Both combined: Atmost 30% and not fewer than 30 means both loan and scholarship is 30.

hence number of students who neither received loan or scholarship can be calculated..
hence answer C

Many thanks!!!
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Re: At a particular university with 150 students 70% receive loans and 40%  [#permalink]

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New post 23 Mar 2017, 15:13
Bunuel wrote:
At a particular university with 150 students 70% receive loans and 40% receive scholarships. What percent of the students receive neither scholarships nor loans?

(1) At most 20% of the students received scholarships as well as loans.
(2) No fewer than 30 students that receive loans also receive scholarships.


The answer should be C- using the minimum and maximum given in both statements we can arrive at a unique value that satisfies the equation?
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Re: At a particular university with 150 students 70% receive loans and 40% &nbs [#permalink] 23 Mar 2017, 15:13
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