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15 Jul 2026, 09:32
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We are given that ratio of T:A :: 3:4
Ratio of T:N = 3/4 of ratio of T:A
= 3/4 * 3:4
= 9:16
So ratio of T:A:N::9:12:16
Again, ratio of A:C = 2 * ratio of T:A
= 2 * 9:12
= 3 : 2
So ratio of T:A:N:C:: 9:12:16:8
If T+C < the smallest three-digit positive integer with distinct number
17x < 102
We need to calculate max. Possible combined no. Of A and N
So we need to calculated max. Value of x which is 5
A+N = 12x + 16x
= 28x
= 28 * 5
= 140
Ratio of T:N = 3/4 of ratio of T:A
= 3/4 * 3:4
= 9:16
So ratio of T:A:N::9:12:16
Again, ratio of A:C = 2 * ratio of T:A
= 2 * 9:12
= 3 : 2
So ratio of T:A:N:C:: 9:12:16:8
If T+C < the smallest three-digit positive integer with distinct number
17x < 102
We need to calculate max. Possible combined no. Of A and N
So we need to calculated max. Value of x which is 5
A+N = 12x + 16x
= 28x
= 28 * 5
= 140
15 Jul 2026, 09:48
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T/A=3/4 =>A = 4T/3
T/N=3/4 * 3/4 = 9/16 =>N = 16T/9
A/C=(3*2)/4 = 3/2 => C=2A/3=8T/9
Let T=9k as only then all of them can be whole numbers.
Then,
A=12k
N=16k
C=8k
T + C <102
17k < 102
k < 6.
There max value of k is 5
A + N = 28k
Therefore, 28 * 5 =140
Answer is C
T/N=3/4 * 3/4 = 9/16 =>N = 16T/9
A/C=(3*2)/4 = 3/2 => C=2A/3=8T/9
Let T=9k as only then all of them can be whole numbers.
Then,
A=12k
N=16k
C=8k
T + C <102
17k < 102
k < 6.
There max value of k is 5
A + N = 28k
Therefore, 28 * 5 =140
Answer is C
15 Jul 2026, 09:53
Kudos
Bookmarks
T-A is 3:4, T/N=3/4*T/A=3/4(3/4)=9/16. Hence T:N -9:16. Hence T=9, A- 12, N -16, c- . Now 102 is the smallest distinct number hence largest possible integer is 5. Assistants and Nurse - 28*5=140. Ans C
Theeldertwin
Joined: 28 Dec 2025
Last visit: 05 Sep 2026
Posts: 163
Given Kudos: 88
Concentration: Strategy
Schools: HEC Sept '27 INSEAD Aug '27 NUS '27
GMAT Focus 1: 655 Q84 V84 DI79 
15 Jul 2026, 09:56
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On simplying the statements, we get,
T:A = 3:4
T:N = 9:16
A:C = 3:2
That further gives us T:A:N:C as 9:12:16:8
Smallest 3 digit number with distinct digits is 102
So T + C is < 102
We know from the proportions that T:C = 9 : 8. Now, assuming T=9x and C=8x, we get 17x<102, or x < 6
To maximise the value of A+N, x should be maximum. Maximum value of x=5
So max value of (A+N) = Max value of (12x+16x) = 28x = 140
T:A = 3:4
T:N = 9:16
A:C = 3:2
That further gives us T:A:N:C as 9:12:16:8
Smallest 3 digit number with distinct digits is 102
So T + C is < 102
We know from the proportions that T:C = 9 : 8. Now, assuming T=9x and C=8x, we get 17x<102, or x < 6
To maximise the value of A+N, x should be maximum. Maximum value of x=5
So max value of (A+N) = Max value of (12x+16x) = 28x = 140
