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28 May 2019, 21:35
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
68% (02:24) correct
32%
(02:24)
wrong
based on 251
sessions
History
Date
Time
Result
Not Attempted Yet
A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?
A. 10
B. 12
C. 15
D. 18
E. 20
A. 10
B. 12
C. 15
D. 18
E. 20
05 Jul 2020, 14:55
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nick1816
Solution:
We see that the rate of each person is 1/120. We also see that the rate of each day starting with the first day is 1/120, 2/120, 3/120, etc. Therefore, let n be the number of days needed to complete the job. We can create the equation:
1/120 + 2/120 + 3/120 + … + n/120 = 1
1/120 + 2/120 + 3/120 + … + n/120 = 120/120
1 + 2 + 3 + … + n = 120
Using the formula for the sum of n consecutive integers, we have:
n(n + 1)/2 = 120
n(n + 1) = 240
We see that when n = 15, we have 15(16) = 240. So n = 15.
Answer: C
General Discussion
wizmaverick
Joined: 22 May 2019
Last visit: 30 Mar 2021
Posts: 16
Given Kudos: 19
Location: India
Schools: Darden '23 (A) ISB'22 (A) IESE'23 (D) Haas '23 (WL) Anderson '23 (I) Tepper '23 (A$) McCombs '23 (A$) Fuqua '23 (D)
GMAT 1: 760 Q50 V42
Schools: Darden '23 (A) ISB'22 (A) IESE'23 (D) Haas '23 (WL) Anderson '23 (I) Tepper '23 (A$) McCombs '23 (A$) Fuqua '23 (D)
GMAT 1: 760 Q50 V42
Posts: 16
28 May 2019, 22:02
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The answer should be C IMO
The series reduced to an Arithmetic Progression with the first term as 1/120 and difference of 1/120.
The sum of the Arithmetic Progression should equal 1
On solving the quadratic equation obtained, you get two values of n : 15 and -16
As the number of workers can't be negative, the answer should be 15
Posted from my mobile device
The series reduced to an Arithmetic Progression with the first term as 1/120 and difference of 1/120.
The sum of the Arithmetic Progression should equal 1
On solving the quadratic equation obtained, you get two values of n : 15 and -16
As the number of workers can't be negative, the answer should be 15
Posted from my mobile device
