Let
Trainees = T
Assistant = A
Nurse = N
Coordinator = C
Then As per question stem,
T/A = 3/4
T/N = (3/4)*T/A = 3/4 * 3/4 = 9/16=9x/16x
A/C = 2*T/A = 2*3/4 = 3/2
Then taking common factors,
T/A = 3/4 = 9/12 = 9x/12x (T should be divisible by 9 also)
Then A/C = 3/2 = 12/8 = 12x/8x
Hence,
T = 9x
N = 16x
A = 12x
C = 8x
Minimum 3 digit number is 102. Then T+C <102
9x + 8x = 17 x < 102 then maximum value of x is 5.
Then A+N = 12x + 16x = 28x.
Max value A+N will be achieved when max x is taken
Hence,
Max. A+N = 28x = 28*5 = 140 = AnsBunuel
At a volunteer clinic, every volunteer is assigned exactly one of four roles: trainee, assistant, nurse, or coordinator. The ratio of trainees to assistants is 3 : 4. The ratio of trainees to nurses is 3/4 of the ratio of trainees to assistants and the ratio of assistants to coordinators is twice the ratio of trainees to assistants. If the combined number of trainees and coordinators is less than the smallest three-digit positive integer with distinct digits, what is the maximum possible combined number of assistants and nurses?
A. 112
B. 128
C. 140
D. 168
E. 196
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