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24 Feb 2025, 01:30
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C
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Difficulty:
35%
(medium)
Question Stats:
68% (02:06) correct
32%
(01:59)
wrong
based on 69
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.
(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.
24 Feb 2025, 02:00
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T = 150 or 100%
L = 70%
S = 40%
T = L+S - B+N
100 = 70+40-B+N
N=B-10 - (1)
We need B to solve this
Statement 1
B<= 20
Using eqn 1 we know a relation b/w B and N
But we don't know how much B can vary b/w 10 and 20, since N cannot be negative. N can be b/w 0 and 10
Insufficient
Statement 2
Bmin = 30
Bmin = 30*100/150 =20%
This tells me N is at-least 10, but we don't know the N max
Insufficient
Combining we know N = 10
Sufficient
L = 70%
S = 40%
T = L+S - B+N
100 = 70+40-B+N
N=B-10 - (1)
We need B to solve this
Statement 1
B<= 20
Using eqn 1 we know a relation b/w B and N
But we don't know how much B can vary b/w 10 and 20, since N cannot be negative. N can be b/w 0 and 10
Insufficient
Statement 2
Bmin = 30
Bmin = 30*100/150 =20%
This tells me N is at-least 10, but we don't know the N max
Insufficient
Combining we know N = 10
Sufficient
Bunuel
24 Feb 2025, 04:34
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We need to determine what percentage of the 150 students receive neither scholarships nor loans.
Given:
- 70% receive loans → 0.7 × 150 = 105 students
- 40% receive scholarships → 0.4 × 150 = 60 students
- Let x be the number of students who receive both scholarships and loans.
- Students receiving either a scholarship or a loan = (105 + 60 - x).
- Students receiving neither = 150 - (105 + 60 - x) = 150 - 165 + x = x - 15.
- We need to determine x to find the percentage of students who receive neither.
Evaluating the Statements
(1) At most 20% of the students received both scholarships and loans.
- 20% of 150 = 30, so x ≤ 30.
- If x is at most 30, then students receiving neither = x - 15 ≤ 30 - 15 = 15.
- However, we don’t know the exact value of x, so we cannot determine a specific percentage.
- Not sufficient.
(2) No fewer than 30 students that receive loans also receive scholarships.
- This means x ≥ 30.
- If x is at least 30, then students receiving neither = x - 15 ≥ 30 - 15 = 15.
- Again, we don’t have an exact value for x, so we cannot determine a specific percentage.
- Not sufficient.
Evaluating Both Statements Together
- Statement (1) says x ≤ 30, and Statement (2) says x ≥ 30.
- This means x = 30.
- Students receiving neither = 30 - 15 = 15.
- Percentage of students receiving neither = (15 / 150) × 100 = 10%.
- Since we can now determine a specific percentage, the statements together are sufficient.
Conclusion
Answer: C (Statements 1 and 2 together are sufficient, but neither alone is sufficient).
Given:
- 70% receive loans → 0.7 × 150 = 105 students
- 40% receive scholarships → 0.4 × 150 = 60 students
- Let x be the number of students who receive both scholarships and loans.
- Students receiving either a scholarship or a loan = (105 + 60 - x).
- Students receiving neither = 150 - (105 + 60 - x) = 150 - 165 + x = x - 15.
- We need to determine x to find the percentage of students who receive neither.
Evaluating the Statements
(1) At most 20% of the students received both scholarships and loans.
- 20% of 150 = 30, so x ≤ 30.
- If x is at most 30, then students receiving neither = x - 15 ≤ 30 - 15 = 15.
- However, we don’t know the exact value of x, so we cannot determine a specific percentage.
- Not sufficient.
(2) No fewer than 30 students that receive loans also receive scholarships.
- This means x ≥ 30.
- If x is at least 30, then students receiving neither = x - 15 ≥ 30 - 15 = 15.
- Again, we don’t have an exact value for x, so we cannot determine a specific percentage.
- Not sufficient.
Evaluating Both Statements Together
- Statement (1) says x ≤ 30, and Statement (2) says x ≥ 30.
- This means x = 30.
- Students receiving neither = 30 - 15 = 15.
- Percentage of students receiving neither = (15 / 150) × 100 = 10%.
- Since we can now determine a specific percentage, the statements together are sufficient.
Conclusion
Answer: C (Statements 1 and 2 together are sufficient, but neither alone is sufficient).
