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

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

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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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).

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..

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

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!!!

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?