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Question Stats:
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80%
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wrong
based on 93
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A takes thrice as much time as B to complete a piece of work.
B takes thrice as much time as C to complete the work.
C takes thrice as much time as D to complete the work.
One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days. Which is the group that takes 13 days and which is the group that takes 31 days?
A. 13 days group = (A, B, C); 31 days group = (A, B, D)
B. 13 days group = (A, B, D); 31 days group = (A, B, C)
C. 13 days group = (B, C, D); 31 days group = (A, B, C)
D. 13 days group = (A, C, D); 31 days group = (A, B, C)
E. 13 days group = (A, B, D); 31 days group = (A, B, D)
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B takes thrice as much time as C to complete the work.
C takes thrice as much time as D to complete the work.
One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days. Which is the group that takes 13 days and which is the group that takes 31 days?
A. 13 days group = (A, B, C); 31 days group = (A, B, D)
B. 13 days group = (A, B, D); 31 days group = (A, B, C)
C. 13 days group = (B, C, D); 31 days group = (A, B, C)
D. 13 days group = (A, C, D); 31 days group = (A, B, C)
E. 13 days group = (A, B, D); 31 days group = (A, B, D)
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sujoykrdatta
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Tutor
Joined: 26 Jun 2014
Last visit: 23 Aug 2026
Posts: 598
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
GMAT 1: 750 Q51 V39
Expert reply
GMAT 1: 750 Q51 V39
Posts: 598
Bunuel
A takes thrice as much time as B to complete the work. => Efficiency of A = 1/3rd of the efficiency of B
Assuming efficiency of A = 1 unit per day, we have:
Efficiency of B = 3 units per day
B takes thrice as much time as C to complete the work. => Efficiency of B = 1/3rd of the efficiency of C
Efficiency of C = 9 units per day
C takes thrice as much time as D to complete the work. => Efficiency of C = 1/3rd of the efficiency of D
Efficiency of D = 27 units per day
Note that a group of 3 of them take 13 days and another group of 3 take 31 days
Thus, ratio of efficiencies of these 2 groups = 31 : 13 respectively
We have the efficiencies: A = 1, B = 3, C = 9 and D = 27
Observe that A+B+C = 13 and A+B+D = 31 (efficiencies)
Thus, A, B and C take 31 days and A, B and D take 13 days
Answer B
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2. Live sessions for GMAT & GRE
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Email: sujoy.datta@gmail | WhatsApp: +919433063089
Posts: 34
Hi seniors,
can anyone please explain this question using the common approach of w = r*t ? I am unable to comprehend the solution
provided above by Sujoy. Thank you a lot in advance!
can anyone please explain this question using the common approach of w = r*t ? I am unable to comprehend the solution
provided above by Sujoy. Thank you a lot in advance!
Kinshook
Major Poster
Joined: 03 Jun 2019
Last visit: 15 Sep 2026
Posts: 6,129
Location: India
Schools: HBS '28 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
A takes thrice as much time as B to complete a piece of work.
B takes thrice as much time as C to complete the work.
C takes thrice as much time as D to complete the work.
One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days.
Which is the group that takes 13 days and which is the group that takes 31 days?
Let us assume that D takes x days to complete the work
C takes 3x days to complete the work
B takes 9x days to complete the work
A takes 27x days to complete the work
D is fastest and A is slowest.
Therefore, the group of (B,C,D) will take lowest time and the group of (A,B,C) will take highest time
Time taken by (B,C,D) to complete the work = 1/(1/9x + 1/3x + 1/x) = 9x/13
Time taken by (A,B,C) to complete the work = 1/(1/27x + 1/9x + 1/3x) = 27x/13
Time taken by (A,B,D) to complete the work = 1/(1/27x + 1/9x + 1/x) = 27x/31
If 27x/31 = 13; x = 13*31/27
27x/13 = 31
A. 13 days group = (A, B, C); 31 days group = (A, B, D)
B. 13 days group = (A, B, D); 31 days group = (A, B, C)
C. 13 days group = (B, C, D); 31 days group = (A, B, C)
D. 13 days group = (A, C, D); 31 days group = (A, B, C)
E. 13 days group = (A, B, D); 31 days group = (A, B, D)
IMO B
B takes thrice as much time as C to complete the work.
C takes thrice as much time as D to complete the work.
One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days.
Which is the group that takes 13 days and which is the group that takes 31 days?
Let us assume that D takes x days to complete the work
C takes 3x days to complete the work
B takes 9x days to complete the work
A takes 27x days to complete the work
D is fastest and A is slowest.
Therefore, the group of (B,C,D) will take lowest time and the group of (A,B,C) will take highest time
Time taken by (B,C,D) to complete the work = 1/(1/9x + 1/3x + 1/x) = 9x/13
Time taken by (A,B,C) to complete the work = 1/(1/27x + 1/9x + 1/3x) = 27x/13
Time taken by (A,B,D) to complete the work = 1/(1/27x + 1/9x + 1/x) = 27x/31
If 27x/31 = 13; x = 13*31/27
27x/13 = 31
A. 13 days group = (A, B, C); 31 days group = (A, B, D)
B. 13 days group = (A, B, D); 31 days group = (A, B, C)
C. 13 days group = (B, C, D); 31 days group = (A, B, C)
D. 13 days group = (A, C, D); 31 days group = (A, B, C)
E. 13 days group = (A, B, D); 31 days group = (A, B, D)
IMO B
Rakshit25
Joined: 15 Jun 2020
Last visit: 23 Mar 2026
Posts: 120
Location: India
Schools: INSEAD Aug '26 (A) LBS '26 (D) IESE '26 (A)
GPA: 8.4
Schools: INSEAD Aug '26 (A) LBS '26 (D) IESE '26 (A)
Posts: 120
Hey,
Can you please explain how are you getting an integer by equating the days worked by A, B and D to 13 days. Even if I go by trial and error, this option is not equal to 13
\(27(x)/31=13\)
\(x=(31*13)/27\)
x= 14.92 days which is not an integer
The logic for equating the option is not clear and even if you are trying to find an integer value of x, B does not match.
Thank you in advance:)
Can you please explain how are you getting an integer by equating the days worked by A, B and D to 13 days. Even if I go by trial and error, this option is not equal to 13
\(27(x)/31=13\)
\(x=(31*13)/27\)
x= 14.92 days which is not an integer
The logic for equating the option is not clear and even if you are trying to find an integer value of x, B does not match.
Thank you in advance:)
Kinshook
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