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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)$7000
- b)$33000
- c)$40000
- d)$60000
- e)$67000
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
100 students appeared for two tests-Physics and Chemistry. 60 students...
Step 1: Question statement and Inferences
We are given that a total of 100 students appeared in the two tests. Out of these 100 students, 60 passed in Physics and 33 passed in Chemistry. The point to note here is that the question statement doesn’t say “60 students passed ONLY in Physics” or “33 students passed ONLY in Chemistry”. Therefore, the numbers given here are for the total number of students who passed in Physics and Chemistry respectively.
If a student passes in at least one test, the school gives him a cash prize of $1,000. We have to find the difference in the maximum and minimum possible values of the prize money that the school disbursed to the students.
Let’s say,
P = the number of students who passed only in Physics
C = the number of students who passed only in Chemistry
X = the number of students who passed both the tests
Given that,
Number of students who passed in Physics = 60
This means, P + X = 60
Or, P = 60 – X
Similarly, C + X = 33
This means, C = 33 – X
Let the number of students who qualify for money disbursement be Z.
Thus
Z = P + C + X
That is, Z = (60 -X) + (33 – X) + X
Z = 93 -X
As we can see, the value of Z depends on the value of X.
Case 1: Maximum value of Z
Z will be maximum when the value of X is the least. The lowest possible value of X is zero (X cannot be negative because it denotes the number of students)
Thus, Zmax = 93
Case 2: Minimum value of Z
Z will be minimum when the value of X is the maximum.
Since there are only 33 students who passed in Chemistry, X cannot exceed 33. Thus, the maximum value of X can be 33.
(Logically speaking: the number of students who passed BOTH Physics and Chemistry cannot be greater than the total number of students who passed Chemistry)
Thus, Zmin = 93 – 33 = 60
Step 2: Finding required values
Maximum possible amount of disbursement by the school = 1000* Zmax = 1000*93 = $93,000
Minimum possible amount of disbursement by the school = 1000* Zmin = 1000*60 = $60,000
Step 3: Calculating the final answer
The difference in the maximum and the minimum possible amounts of disbursement
= $93,000 -$60,000
= $33,000
Answer: Option (B)
Most Upvoted Answer
100 students appeared for two tests-Physics and Chemistry. 60 students...
To find the difference between the maximum and minimum possible values of the cash disbursal done by the school, we need to consider different scenarios based on the number of students who passed in both Physics and Chemistry tests.
Let's analyze the different possibilities:
1. Students who passed in both Physics and Chemistry:
- The number of students who passed in both tests can range from 0 to 33 (as there are 33 students who passed the Chemistry test).
- For each student who passed in both tests, the cash prize is given only once. Therefore, the cash disbursal for this scenario would be 1000 * (0 to 33).
- The maximum cash disbursal for this scenario would be 1000 * 33 = 33000.
2. Students who passed in only one test:
- The number of students who passed in only one test can range from 60 (all students who passed Physics) to 67 (33 who passed Chemistry but failed Physics).
- For each student who passed in only one test, the cash prize is given once.
- The cash disbursal for this scenario would be 1000 * (60 to 67).
- The minimum cash disbursal for this scenario would be 1000 * 60 = 60000.
3. Students who passed in neither test:
- The number of students who passed in neither test can range from 0 to 7 (100 - 60 - 33).
- As per the given condition, the cash prize is given to every student who passed in at least one test. Therefore, the cash disbursal for this scenario would be 0.
Thus, the difference between the maximum and minimum possible values of the cash disbursal done by the school is 60000 - 33000 = 27000, which is closest to option B ($33000).
Let's analyze the different possibilities:
1. Students who passed in both Physics and Chemistry:
- The number of students who passed in both tests can range from 0 to 33 (as there are 33 students who passed the Chemistry test).
- For each student who passed in both tests, the cash prize is given only once. Therefore, the cash disbursal for this scenario would be 1000 * (0 to 33).
- The maximum cash disbursal for this scenario would be 1000 * 33 = 33000.
2. Students who passed in only one test:
- The number of students who passed in only one test can range from 60 (all students who passed Physics) to 67 (33 who passed Chemistry but failed Physics).
- For each student who passed in only one test, the cash prize is given once.
- The cash disbursal for this scenario would be 1000 * (60 to 67).
- The minimum cash disbursal for this scenario would be 1000 * 60 = 60000.
3. Students who passed in neither test:
- The number of students who passed in neither test can range from 0 to 7 (100 - 60 - 33).
- As per the given condition, the cash prize is given to every student who passed in at least one test. Therefore, the cash disbursal for this scenario would be 0.
Thus, the difference between the maximum and minimum possible values of the cash disbursal done by the school is 60000 - 33000 = 27000, which is closest to option B ($33000).
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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)$7000b)$33000c)$40000d)$60000e)$67000Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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)$7000b)$33000c)$40000d)$60000e)$67000Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)$7000b)$33000c)$40000d)$60000e)$67000Correct answer is option 'B'. Can you explain this answer?.
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