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20 Dec 2016, 01:24
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B
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At a particular university with 200 students 40% receive loans and 30% receive scholarships. What percent of the students receive neither scholarships nor loans?
(1) At least twenty-five percent of the students do not receive loans.
(2) Twenty-five percent of the students receive both loans and scholarships.
(1) At least twenty-five percent of the students do not receive loans.
(2) Twenty-five percent of the students receive both loans and scholarships.
21 Dec 2016, 04:47
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Hey Everyone,
PFB the detailed solution.
Steps 1 & 2: Understand Question and Draw Inferences
Thus, we can conclude that –
Step 3: Analyze Statement 1 independently
Therefore, statement 1 is not sufficient to arrive at a unique answer.
Step 4: Analyze Statement 2 independently
Therefore, statement 2 is sufficient to arrive at a unique answer.
Hence the correct Answer is B
Thanks,
Saquib
Quant Expert
e-GMAT
PFB the detailed solution.
Steps 1 & 2: Understand Question and Draw Inferences
- • Total number of students in the university \(= 200\).
• Let us consider these \(200\) students in the university as \(100\) %.
- o \(40\)% of the students received loans.
o \(30\)% of the students received scholarships.
• Using the above information, we can draw the Venn diagram as shown –
Thus, we can conclude that –
- • \(X + Z = 40\)%
• \(Y + Z = 30\)%
• \(X + Y + Z + W = 100\)%
• where \(W\) is the percentage of students who received neither loans nor scholarships.
• And we need to find the value of \(W\) = ?
Step 3: Analyze Statement 1 independently
- • It is given that at least twenty-five percent of the students do not receive loans.
• This means that \(Y + W ≥ 25\)%.
• But we cannot find the exact value of \(W\) using the above information.
Therefore, statement 1 is not sufficient to arrive at a unique answer.
Step 4: Analyze Statement 2 independently
- • It is given that twenty-five percent of the students receive both loans and scholarships.
• This means that \(Z = 25\)%
• Using the above information, we can find the value of \(X\) and then subsequently the value of \(W\).
- o \(X + Z = 40\)%
- • \(X = 15\)%
- • \(15\)% \(+ 30\)%\(+ W = 100\)%
• \(W = 55\)%
Therefore, statement 2 is sufficient to arrive at a unique answer.
Hence the correct Answer is B
Thanks,
Saquib
Quant Expert
e-GMAT
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22 Dec 2016, 14:30
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1) No information about overlap between scholarships and loans. INSUFFICIENT.
2) If we know that 25% (50 students) receive both scholarships and loans, we can work out that the number of students that receive scholarships, loans or both is 90. Therefore, the number of students that receives neither is 110, from which we can work out the percentage. SUFFICIENT.
B
2) If we know that 25% (50 students) receive both scholarships and loans, we can work out that the number of students that receive scholarships, loans or both is 90. Therefore, the number of students that receives neither is 110, from which we can work out the percentage. SUFFICIENT.
B
