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T:A = 3/4 = 9/12
T:N = 3/4 * 3/4 = 9/16
A:C = 2*3/4 = 3/2 = 12/8

If T=9, A=12, N=16, C=8

T=9i, A=12i, N=16i, C=8i with i=integer

The 3-digit number is 102
9i+8i = 17i < 102
i < 6
maximum if i=5

12i+16i = 28i = 28*5 = 140

The correct answer is C
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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 = Ans


Bunuel
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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Ans is 168 by ratio N is near to 98 And c is near to 70 so 168 is max by approximation
Bunuel
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


 


This question was provided by GMAT Club
for the GMAT World Cup Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 


⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
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