100 students appeared for two tests-Physics and Chemistry. 60 students

Question

100 students appeared for two tests-Physics and Chemistry. 60 students passed the Physics test and 33 students passed the Chemistry test. The school had announced a cash prize of $1,000 for every student who passed in at least one test. What is the difference between the maximum and minimum possible values of the cash disbursal done by the school?

A. $7,000
B. $33,000
C. $40,000
D. $60,000
E. $67,000

A. $7,000
B. $33,000
C. $40,000
D. $60,000
E. $67,000

jatinmittal91 · Answer

Max will be if all the student passed in 1 subject only and if their total is less than 100, then the sum of the passed student will be taken and if the sum is more than 100 then 100 will be taken.

Max = 60 + 33 = 93*1000 = 93000
Min = 60 = 60*1000 = 60000

Diff = 93000-60000 = 33000

chetan2u · Answer

So we have to find the max and min number of students who have passed at least one exam...
 MAX number.... When there is NO overlap, so none have cleared both and have cleared just one .. hence number = 60+33=93
 MIN number.... When there is maximum overlap, so 33 who have cleared chemistry have also cleared physics.. hence number = 60

Difference = 93-60=33..
Hence the difference in money disbursed = 33*1000=33000

B

GMATWhizTeam · Answer

Solution:  
 • Total number of students = 100
 o Number students passed in physics = 60 
o Number of students passed in chemistry = 33 
• The maximum cash disbursal will happen, when the maximum number of students are given the prize and that is only possible, when each student pass in exactly one subject.
 o So, there are 60 unique students who pass only physics and 33 unique students who pass only Chemistry.
o Thus, total students eligible for the prize money = 60 + 33 = 93 
• The minimum cash disbursal will happen when the minimum number of students are given the cash prize, and that is only possible when we maximize the number of students who pass in both subjects.
 o Out of 33 and 60.. we can assume that 33 of those who pass in Chemistry, pass in Physics also.
o So out of 60, 33 are repetitive cases and 27 students (60 - 33) pass only Physics.
o Thus, total students eligible for the prize money = 33 + 27 = 60 
• Difference = (93-60)*1000 =$ 33000 
Hence, the correct answer is  Option B.

ScottTargetTestPrep · Answer

The maximum number of cash prizes awarded would occur if none of the students passed both exams. Thus, there would be 60 + 33 = 93 students who would earn the cash prize.

The minimum number of students to earn the cash prize would occur if all of the students who passed Chemistry also passed Physics. In this case, a total of 60 students (the number of those who passed Physics) would earn the cash prize.

The difference between the maximum and minimum possible values of the cash disbursal is $93,000 - $60,000 = $33,000.

Answer: B

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100 students appeared for two tests-Physics and Chemistry. 60 students

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