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In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.
(1) 20 women can do the same job in 10 days.
(2) 24 men and 5 women can complete the same job in 40/11 days.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In how many days can 12 men and 15 women complete a job, if 8 men can ...
The question is asking how long it would take 12 men and 15 women to complete a certain job. It tells you that 8 men complete this job in 12 days.
Let the total amount of work involved in completing the job be W.
Work done by 8 men in 12 days = W
Work done by 8 men in 1 day = W/12
Work done by 1 man in 1 day = W/96 . . . Equation 1
So, work done by 12 men in 1 day = 12W/96 = W/8
Let one woman working alone complete the job in d days.
So, work done by 1 woman in 1 day =W/d . . . Equation 2
So, work done by 15 women in 1 day = 15W/d
Work done by 12 men and 15 women working together in 1 day = W/8 + 15W/d=(1/8+15/d)W
Once we know the value of d, we will be able to know the value of the coefficient of w in the above equation.
The reciprocal of this coefficient will be equal to the total time taken by 12 men and 15 women to complete the task.
So, we need to find the value of d.
Step 3: Analyze Statement 1
20 women can do the same job in 10 days.
Work done by 20 women in 10 days = W
Work done by 20 women in 1 day = W/10
Work done by 1 woman in 1 day =W/200 . . . Equation 3
Comparing Equation 3 with Equation 2:
d=200
Thus, Statement 1 is sufficient to arrive at a unique value of the time taken by 12 men and 15 women
to complete the job
Step 4: Analyze Statement 2
24 men and 5 women can complete the same job in 40/11 days.
Work done by 24 men and 5 women in 40/11 days = W
Work done by 24 men and 5 women in 1 day =
Using Equations 1 and 2 we can write:
Thus, we have a linear equation in d.
By solving this equation, we will be able to find the value of d
Thus, Statement 2 too is sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
You get unique answers in steps 3 and 4, so this step is not required
Answer: Option (D)
Most Upvoted Answer
In how many days can 12 men and 15 women complete a job, if 8 men can ...
Given information:
- 8 men can complete a job in 12 days.
- 12 men and 15 women need to complete the same job.
- All men work at the same rate and all women work at the same rate.
To find:
- The number of days required for 12 men and 15 women to complete the job.
Statement 1: 20 women can do the same job in 10 days.
- Let the rate of work of one woman be w.
- Then, 20 women working together can complete the job in 10 days, so their combined rate of work is 2w (since rate x time = work).
- We don't know the rate of work of one man, so we can't use this statement to find the number of days required for 12 men and 15 women to complete the job.
- Statement 1 alone is not sufficient.
Statement 2: 24 men and 5 women can complete the same job in 40/11 days.
- Let the rate of work of one man be m.
- Let the rate of work of one woman be w.
- Then, 24 men working together can complete the job in d days, where d is given by:
m x 24 x d = 1 (since 24 men can complete the job in 1 day)
- Simplifying, we get:
d = 1 / (24m)
- Similarly, 5 women working together can complete the job in d days, where d is given by:
w x 5 x d = 1 (since 5 women can complete the job in 1 day)
- Simplifying, we get:
d = 1 / (5w)
- From the given information, we know that 12 men and 15 women need to complete the job. Let the number of days required for them to complete the job be x.
- Then, their combined rate of work is:
12m + 15w = 1 / x
- We can use this equation to solve for x. Substituting the values of d from the equations above, we get:
12m + 15w = 1 / x = (1 / (24m)) + (1 / (5w))
- Simplifying, we get:
12m^2 + 15mw = (1 / 24) + (3 / 5)
- We have two equations with two variables (m and w), so we can solve for them.
- Once we know m and w, we can use the equation 12m + 15w = 1 / x to find x.
- Therefore, statement 2 alone is sufficient.
Answer:
- Statement 1 alone is not sufficient.
- Statement 2 alone is sufficient.
- The correct answer is option D.
- 8 men can complete a job in 12 days.
- 12 men and 15 women need to complete the same job.
- All men work at the same rate and all women work at the same rate.
To find:
- The number of days required for 12 men and 15 women to complete the job.
Statement 1: 20 women can do the same job in 10 days.
- Let the rate of work of one woman be w.
- Then, 20 women working together can complete the job in 10 days, so their combined rate of work is 2w (since rate x time = work).
- We don't know the rate of work of one man, so we can't use this statement to find the number of days required for 12 men and 15 women to complete the job.
- Statement 1 alone is not sufficient.
Statement 2: 24 men and 5 women can complete the same job in 40/11 days.
- Let the rate of work of one man be m.
- Let the rate of work of one woman be w.
- Then, 24 men working together can complete the job in d days, where d is given by:
m x 24 x d = 1 (since 24 men can complete the job in 1 day)
- Simplifying, we get:
d = 1 / (24m)
- Similarly, 5 women working together can complete the job in d days, where d is given by:
w x 5 x d = 1 (since 5 women can complete the job in 1 day)
- Simplifying, we get:
d = 1 / (5w)
- From the given information, we know that 12 men and 15 women need to complete the job. Let the number of days required for them to complete the job be x.
- Then, their combined rate of work is:
12m + 15w = 1 / x
- We can use this equation to solve for x. Substituting the values of d from the equations above, we get:
12m + 15w = 1 / x = (1 / (24m)) + (1 / (5w))
- Simplifying, we get:
12m^2 + 15mw = (1 / 24) + (3 / 5)
- We have two equations with two variables (m and w), so we can solve for them.
- Once we know m and w, we can use the equation 12m + 15w = 1 / x to find x.
- Therefore, statement 2 alone is sufficient.
Answer:
- Statement 1 alone is not sufficient.
- Statement 2 alone is sufficient.
- The correct answer is option D.
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In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.(1) 20 women can do the same job in 10 days.(2) 24 men and 5 women can complete the same job in 40/11 days.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?
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In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.(1) 20 women can do the same job in 10 days.(2) 24 men and 5 women can complete the same job in 40/11 days.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.(1) 20 women can do the same job in 10 days.(2) 24 men and 5 women can complete the same job in 40/11 days.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.(1) 20 women can do the same job in 10 days.(2) 24 men and 5 women can complete the same job in 40/11 days.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?.
In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.(1) 20 women can do the same job in 10 days.(2) 24 men and 5 women can complete the same job in 40/11 days.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.(1) 20 women can do the same job in 10 days.(2) 24 men and 5 women can complete the same job in 40/11 days.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.(1) 20 women can do the same job in 10 days.(2) 24 men and 5 women can complete the same job in 40/11 days.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?.
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In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.(1) 20 women can do the same job in 10 days.(2) 24 men and 5 women can complete the same job in 40/11 days.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.(1) 20 women can do the same job in 10 days.(2) 24 men and 5 women can complete the same job in 40/11 days.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.(1) 20 women can do the same job in 10 days.(2) 24 men and 5 women can complete the same job in 40/11 days.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In how many days can 12 men and 15 women complete a job, if 8 men can do the same job in 12 days? Assume the rate of working of all men is same and rate of working of all women is same.(1) 20 women can do the same job in 10 days.(2) 24 men and 5 women can complete the same job in 40/11 days.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
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