Mike, Mark and Matt can individually build a house in 12, 16 and 24 days respectively. If Mark starts building the house and receives help from Mike and Matt every second day, in how many days will they complete building the house?
A) 2 B) 4 C) 6 D) 8 E) 10
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chaitanya.bhansali
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Let the house = 48 units.chaitanya.bhansali wrote:Mike, Mark and Matt can individually build a house in 12, 16 and 24 days respectively. If Mark starts building the house and receives help from Mike and Matt every second day, in how many days will they complete building the house?
A) 2 B) 4 C) 6 D) 8 E) 10
Since Mike takes 12 days to build a house, Mike's rate = 48/12 = 4 units per day.
Since Mark takes 16 days to build a house, Mark's rate = 48/16 = 3 units per day.
Since Matt takes 24 days to build a hours, Matt's rate = 48/24 = 2 units.
When all 3 work together, their combined rate = 4+3+2 = 9 units per day.
Every 2 days:
Work produced by Mark alone on the first day = 3 units.
Work produced by all 3 on the second day = 9 units.
Thus:
Amount of work produced every 2 days = 3+9 = 12 units.
Since 12 units are produced every 2 days, the AVERAGE amount of work produced per day = 12/2 = 6 units.
At an average rate of 6 units per day, the time required to produce all 48 units = 48/6 = 8 days.
The correct answer is D.
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Hi cahitanya.bhansali,
I'm a big fan of Mitch's approach to this question (converting the data and TESTing a Value). Since this is essentially just a "rate" question, you can organize the information in other ways and TEST THE ANSWERS.
We're given the length of time that it would take each person to build a house. I'm going to convert that information into the "fraction of a house" that each person could build per day:
Mike: 12 days = 1/12 of a house per day
Mark: 16 days = 1/16 of a house per day
Matt: 24 days = 1/24 of a house per day
We're told that MARK work every day, but that Mike and Matt only work every second day.
Looking at the answers (which are relatively small), and considering how little work each person does per day (or every second day, in the cases of Mike and Matt), to get 1 complete house, the answer has to be one of the larger options.
Let's TEST THE ANSWERS by starting with D. How much house would be built in 8 days?
Mark does 1/16 per day, so in 8 days he would complete 8/16 of the house.
Mike does 1/12 per day, so in 4 days he would complete 4/12 of the house.
Matt does 1/24 per day, so in 4 days he would complete 4/24 of the house.
8/16 + 4/12 + 4/24 =
1/2 + 1/3 + 1/6 =
3/6 + 2/6 + 1/6 = 1 complete house.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
I'm a big fan of Mitch's approach to this question (converting the data and TESTing a Value). Since this is essentially just a "rate" question, you can organize the information in other ways and TEST THE ANSWERS.
We're given the length of time that it would take each person to build a house. I'm going to convert that information into the "fraction of a house" that each person could build per day:
Mike: 12 days = 1/12 of a house per day
Mark: 16 days = 1/16 of a house per day
Matt: 24 days = 1/24 of a house per day
We're told that MARK work every day, but that Mike and Matt only work every second day.
Looking at the answers (which are relatively small), and considering how little work each person does per day (or every second day, in the cases of Mike and Matt), to get 1 complete house, the answer has to be one of the larger options.
Let's TEST THE ANSWERS by starting with D. How much house would be built in 8 days?
Mark does 1/16 per day, so in 8 days he would complete 8/16 of the house.
Mike does 1/12 per day, so in 4 days he would complete 4/12 of the house.
Matt does 1/24 per day, so in 4 days he would complete 4/24 of the house.
8/16 + 4/12 + 4/24 =
1/2 + 1/3 + 1/6 =
3/6 + 2/6 + 1/6 = 1 complete house.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
1) Mark alone completes 1/16 of the total work in one day
2) Three of the together complete 1/12 + 1/16 + 1/24 = 9/48 of the work in one day.
so of the first day mark alone works, 1/16 of the work will be completed.
and one second day if all three work together, 9/48 of the work will be completed.
So in two days, 1/16 + 9/48 = 12/48 = 1/4 of the work will be completed.
So the total work will be completed in 8 days.
2) Three of the together complete 1/12 + 1/16 + 1/24 = 9/48 of the work in one day.
so of the first day mark alone works, 1/16 of the work will be completed.
and one second day if all three work together, 9/48 of the work will be completed.
So in two days, 1/16 + 9/48 = 12/48 = 1/4 of the work will be completed.
So the total work will be completed in 8 days.
1) Mark alone completes 1/16 of the total work in one day
2) Three of the together complete 1/12 + 1/16 + 1/24 = 9/48 of the work in one day.
so of the first day mark alone works, 1/16 of the work will be completed.
and one second day if all three work together, 9/48 of the work will be completed.
So in two days, 1/16 + 9/48 = 12/48 = 1/4 of the work will be completed.
So the total work will be completed in 8 days.
2) Three of the together complete 1/12 + 1/16 + 1/24 = 9/48 of the work in one day.
so of the first day mark alone works, 1/16 of the work will be completed.
and one second day if all three work together, 9/48 of the work will be completed.
So in two days, 1/16 + 9/48 = 12/48 = 1/4 of the work will be completed.
So the total work will be completed in 8 days.
