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24 Apr 2026, 01:05
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
80% (03:24) correct
20%
(02:54)
wrong
based on 5
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In a certain course on financial math, there are three times as many lawyers as scientists and twice as many lawyers as doctors. Seventeen students are neither doctors, lawyers, nor scientists. If more than half of the students are lawyers, what is the smallest possible number of lawyers in the class?
A. 96
B. 102
C. 103
D. 108
E. 120
A. 96
B. 102
C. 103
D. 108
E. 120
24 Apr 2026, 02:20
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Setting up the ratios:
3 times as many lawyers as scientists → Scientists = L/3
Twice as many lawyers as doctors → Doctors = L/2
For these to be whole numbers,L must be divisible by both 2 and 3, so divisible by 6
Total students:
Total = L + L/3 + L/2 + 17
= (6L + 2L + 3L)/{6} + 17
= 11 L/6 + 17
The condition — MORE than half are lawyers:
L > 1/2 * {Total}
L > 1/2 * (11L/6 + 17)
L/12 > 17/2
L > 102
Remember L must be divisible by 6
102 ÷ 6 = 17 but L must be more than 102
Next multiple of 6 = 108
Hence the answer is D. 108
3 times as many lawyers as scientists → Scientists = L/3
Twice as many lawyers as doctors → Doctors = L/2
For these to be whole numbers,L must be divisible by both 2 and 3, so divisible by 6
Total students:
Total = L + L/3 + L/2 + 17
= (6L + 2L + 3L)/{6} + 17
= 11 L/6 + 17
The condition — MORE than half are lawyers:
L > 1/2 * {Total}
L > 1/2 * (11L/6 + 17)
L/12 > 17/2
L > 102
Remember L must be divisible by 6
102 ÷ 6 = 17 but L must be more than 102
Next multiple of 6 = 108
Hence the answer is D. 108
24 Apr 2026, 02:56
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The hard part of this type of question is usually the wording. Then while it's possible to set up equations, testing is also a quick and dirty way to go about it once you set up the test well.
First, make sure that the number of lawyers is three times the number of scientists: L = 3s, not the other way around (easily done). Double-check this! "Three times as many lawyers as scientists" means that, for example, for 4 scientists you have 12 lawyers and so on.
Similarly, L = 2d, not vice-versa.
If we put everything in terms of L, then we get L/3 + L/2 + L + 17 is total. We know that L is more than half of these, but let's hold off for a second. It's a number of people, which must be an integer. It must also divide by 2 and by 3, which means it is divisible by 6. (C) 103 is prime so this answer is garbage. Ignore.
Working our way up, we can see that:
96: L/3 + L/2 + L + 17 = 32 + 48 + 96 + 17, so the non-L are 97 while L are 96. Too low.
102: this is the balance point -- L/3 + L/2 + L + 17 = 34 + 51 + 102 + 17, where non-L are 102 and L are 102. It's not more than 50%, it's exactly 50%.
From here, the answer has to be the next multiple of 6 up: 108 (D).
To verify, L/3 + L/2 + L + 17 = 36 + 54 + 108 + 17, where non-L are 107 and L are 108. Answer confirmed (D).
First, make sure that the number of lawyers is three times the number of scientists: L = 3s, not the other way around (easily done). Double-check this! "Three times as many lawyers as scientists" means that, for example, for 4 scientists you have 12 lawyers and so on.
Similarly, L = 2d, not vice-versa.
If we put everything in terms of L, then we get L/3 + L/2 + L + 17 is total. We know that L is more than half of these, but let's hold off for a second. It's a number of people, which must be an integer. It must also divide by 2 and by 3, which means it is divisible by 6. (C) 103 is prime so this answer is garbage. Ignore.
Working our way up, we can see that:
96: L/3 + L/2 + L + 17 = 32 + 48 + 96 + 17, so the non-L are 97 while L are 96. Too low.
102: this is the balance point -- L/3 + L/2 + L + 17 = 34 + 51 + 102 + 17, where non-L are 102 and L are 102. It's not more than 50%, it's exactly 50%.
From here, the answer has to be the next multiple of 6 up: 108 (D).
To verify, L/3 + L/2 + L + 17 = 36 + 54 + 108 + 17, where non-L are 107 and L are 108. Answer confirmed (D).
kevincan
