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A husband and wife can complete a certain task in 1 and 2

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A husband and wife can complete a certain task in 1 and 2

by AAPL » Wed May 22, 2019 10:01 am

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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

OA D
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Source: — Data Sufficiency |

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by Ian Stewart » Fri May 24, 2019 5:54 am

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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.
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by GMATGuruNY » Fri May 24, 2019 8:02 am

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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
Let the job = 12 units.
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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