Was I wrong about this QR question?

[DATlongshui]

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Q: If Sarah can do a work in 8 days and Julie can do the same work in 12 days, which of the combinations given below can complete the work in the least amount of time?

A. 50% work done by Sarah and rest with Julie
B. 60% work done by Sarah and rest with Julie
C. 40% work done by Sarah and rest with Julie
D. only Sarah
E. only Julie

The correct answer is B. The explanation given is that: When they work together, it will take 4.8 days. During 4.8 days, Sarah can do 60% of the work and Jule can do 40% of the work....

I chose D, and I still think I am correct, as nowhere from the question stem was it mentioned that it is asking for "they work together". Should we assume that no matter what? What about the real DAT? Will the QR questions be written in such an ambiguous way?

 

[Streetwolf]

Q: If Sarah can do a work in 8 days and Julie can do the same work in 12 days, which of the combinations given below can complete the work in the least amount of time?

A. 50% work done by Sarah and rest with Julie
B. 60% work done by Sarah and rest with Julie
C. 40% work done by Sarah and rest with Julie
D. only Sarah
E. only Julie

The correct answer is B. The explanation given is that: When they work together, it will take 4.8 days. During 4.8 days, Sarah can do 60% of the work and Jule can do 40% of the work....

I chose D, and I still think I am correct, as nowhere from the question stem was it mentioned that it is asking for "they work together". Should we assume that no matter what? What about the real DAT? Will the QR questions be written in such an ambiguous way?

If Sarah does the work herself it will be finished in 8 days. If they work together it gets done faster. But since Sarah works faster than Julie, she should do more work. B is the only one that makes any sense.

Math:

Every day Sarah does 1/8 (3/24) work and Julie does 1/12 (2/24) work. As it stands like that, any given day Sarah is doing 60% of the work and Julie is doing 40% of the work. If you adjust the percentage of work that they're doing, you would have to make one of them work more days than the other.

For example:

If they split it evenly then Julie has to work 3 days for every 2 that Sarah works. This would mean that every 3 days Julie would do 6/24 of the total work. Sarah would only work 2 of those 3 days and do 6/24 work. They split it evenly but Sarah would be wasting a day she could work! In 6 days they'll finish the job.

If they did Julie 60% and Sarah 40% then Sarah would have to work 2 days (do 6/24 work) and Julie would have to work 4.5 days (do 9/24 work). So Sarah would waste 2.5 days not working. It would take almost 6 days to finish the job.

If Sarah does 100% of the job then every day she is doing 3/24 of the work and Julie does 0. It will take 8 days for Sarah to finish the job. Julie is wasting 8 days of potential work.

The way the problem is worded is the best possible case. If you let them do the amount of work they can max out on each day then you won't be wasting any days of them not working. So here Julie does 2/24 work a day and Sarah does 3/24 work a day. It will take them 4.8 days to finish the job.

 

[edcampbe]

I can see why you might have been confused by this question. However, when I read through the options, I picked B. I Just assumed the questions inferred the two would be working together.

 

[kpanesar]

yeah you add up how much work each does in one day (which is basically the rate at which they work) and that ends up being 5/24...so in one day 5/24 of the job is done therefore dividing 5 into 24 you get 4.8, which is how long it takes for both of them to complete the job.

4.8 is 24/5 in fractions and then multiplying that by the rate of julie (1/12) you can easily simply and get 2/5 = .4 = 40%

100-40 = 60% which is amount of work sarah does.