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28 Jan 2026, 22:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
66% (02:28) correct
34%
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A university offers 3 courses in mathematics: a BS program, an MS program, and a dual degree program. The annual tuition fee for the dual degree program is 20% less than the annual tuition fees for the other 2 programs taken together. If 60% of mathematics students in the upcoming class will attend the BS program and the remaining are equally divided between the other 2 programs, which of the 3 programs will generate the most tuition fees for the university in the coming year?
(1) The annual tuition fee for the MS program is 30% higher than that of the BS program.
(2) The annual tuition fee for the BS program is $30,000.
(1) The annual tuition fee for the MS program is 30% higher than that of the BS program.
(2) The annual tuition fee for the BS program is $30,000.
28 Jan 2026, 23:24
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ExpertsGlobal5
Let the fees for BS be $b and for MS be $m => fees for DG = $0.8(b+m)
Let the number of students be n
=> Enrolments for BS = 0.6n
Remaining students = 0.4n => Enrolments for MS = 0.4n/2 = 0.2n and for DG = 0.2n
=> Revenue for BS = $0.6n×b = $0.6bn, for MS = $0.2n×m = $0.2mn and for DG = $0.8(b+m)×0.2n = $0.16n(b+m)
To compare the values, we only need to compare the values of b and m (in a ratio) since n is present as a multiplier for each course and has no effect on the relative values of the revenues
1: m = 1.3b
=> Revenue for BS = $0.6bn, for MS = 0.2mn = $0.2×1.3b×n = $0.26bn and for DG = 0.16n(b+m) = 0.16n(b+1.3b) = 0.16n×2.3b = $0.368bn
=> Revenue is the greatest from BS - Sufficient
2: The actual value is irrelevant and also insufficient since the comparison between the course prices is not provided - Insufficient
Answer A
01 Feb 2026, 08:45
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ExpertsGlobal5
Explanation:
Let the annual tuition fee for the BS program per student be B.
Let the annual tuition fee for the MS program per student be M.
Let the annual tuition fee for the dual degree program per student be D.
Since the annual tuition fee for the dual degree program is 20% less than the annual tuition fees for the other 2 programs taken together:
D = 0.8(M + B)
Let the total number of mathematics students in the upcoming class be n.
Since 60% of mathematics students in the upcoming class will attend the BS program and the remaining are equally divided between the other 2 programs:
Total number of students attending the BS program = 0.6n.
Total number of students attending the MS program = 0.2n.
Total number of students attending the dual degree program = 0.2n.
Total tuition fees generated from the BS program = B x 0.6n = 0.6Bn.
Total tuition fees generated from the MS program = M x 0.2n = 0.2Mn.
Total tuition fees generated from the dual degree program = D x 0.2n = 0.2Dn.
We need to find which of the 3 programs will generate the most tuition fees, which can also be expressed as:
We need to find whether the maximum value among 0.6Bn, 0.2Mn, and 0.2Dn can be determined.
Statement (1)
M = 1.3B
Total tuition fees generated from the BS program = 0.6Bn.
Total tuition fees generated from the MS program = 0.2Mn = 0.2(1.3B)n = 0.26Bn
Total tuition fees generated from the dual degree program = 0.2Dn = 0.2[0.8(M + B)]n = 0.2[0.8(1.3B + B)]n = 0.2[0.8(2.3B)]n = 0.368Bn
It is possible to determine with certainty which of the 3 programs will generate the most tuition fees for the university. Hence, Statement (1) is sufficient.
Statement (2)
B = 30,000
No information is provided regarding the tuition fees for the MS program or the dual degree program.
It is NOT possible to determine with certainty which of the 3 programs will generate the most tuition fees for the university. Hence, Statement (2) is sufficient.
A is the correct answer choice.
