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A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?
A. 15:46
B. 3:10
C. 12:23
D. 5:18
E. 10:3
OA D
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A husband and wife can complete a certain task in 1 and 2
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Ian Stewart
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Using whatever rates method one prefers, you can just find how long the husband and wife take, how long the children take, and take the ratio of those two times. I'd get the same time for the husband and wife:
h does 2 tasks in 2 hours
w does 1 task in 2 hours
h+w do 3 tasks in 2 hours so 1 task in 2/3 hours
rae does 3 tasks in 12 hours
herman does 2 tasks in 12 hours
children do 5 tasks in 12 hours, so 1 task in 12/5 hours
The ratio of those times is 2/3 to 12/5, and if we multiply everything by 15 and divide by 2, that becomes 5 to 18.
h does 2 tasks in 2 hours
w does 1 task in 2 hours
h+w do 3 tasks in 2 hours so 1 task in 2/3 hours
rae does 3 tasks in 12 hours
herman does 2 tasks in 12 hours
children do 5 tasks in 12 hours, so 1 task in 12/5 hours
The ratio of those times is 2/3 to 12/5, and if we multiply everything by 15 and divide by 2, that becomes 5 to 18.
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GMATGuruNY
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Global Stats
Let the job = 12 units.AAPL wrote:Veritas Prep
A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?
A. 15:46
B. 3:10
C. 12:23
D. 5:18
E. 10:3
Dividing the four given times into the 12-unit job, we get the following hourly rates:
Husband:Wife:Rae:Herman = (12 per hour): (6 per hour) : (3 per hour) : (2 per hour)
(Husband + Wife) : (Rae + Herman) = (12+6 per hour) : (3+2 per hour)
Couple : Children = 18:5
Rate and time have a reciprocal relationship.
Since the rate ratio for the couple and the children = 18:5, the time ratio for the couple and the children = 5:18.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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