To produce n bolts, Machine A takes 2 hours more than Machine B does.

Question

To produce n bolts, Machine A takes 2 hours more than Machine B does. If Machine A and Machine B work together, they can produce 5/4n bolts in 3 hours. How many hours does it take Machine A to produce 2n bolts.

a) 6
b) 9
c) 10
d) 12
e) 13

a) 6
b) 9
c) 10
d) 12
e) 13

TestPrepUnlimited · Answer

Since this is a rate question with every result related to n, we can divide all quantities of bolts by n and it won't change anything. Thus to produce 1 bolt, Machine A takes 2 hours more than Machine B does etc. Set the rate of A as  \frac{1}{x + 2}  and rate of B as  \frac{1}{x} .

Then we have:  \frac{3}{x + 2} + \frac{3}{x} = \frac{5}{4}

Here we can try plugging in numbers from the choices, the given choices in terms of x are  2(x + 2) , however, so we need to divide by 2 first then plugin for x + 2.

Start from C, we plug in x + 2 = 5 and get  \frac{3}{5} + \frac{3}{3} = \frac{8}{5} , that result is too big so we need a bigger x to reduce the result.

Next we try D, which gives  \frac{3}{6} + \frac{3}{4} = \frac{5}{4} .

Ans: D

vatsal323 · Answer

The question stem should say that it's (5/4)n or 5n/4. 5/4n makes it seem like the number is (5/4n)

Bunuel · Answer

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Edited. Thank you!

KarishmaB · Answer

Together they make 5n/4 bolts in 3 hrs. So they make n bolts in 3*(4/5) = 12/5 hrs. (Less work, less time taken) If each had the same rate, they would have taken 24/5 = 4.8 hrs alone. But one takes 2 hrs more than the other so possible combination is 6 and 4 hrs. Let's check 1/6 + 1/4 = 5/12 combined rate which gives 12/5 hrs taken when they work together. It checks out. So machine A takes 6 hrs to produce n bolts so it will take 12 hrs to produce 2n bolts. Answer (D) For details on work rate, check: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... -problems/

gogokevin13 · Answer

Hi VeritasKarishma, can you please clarify the below. 
If each had the same rate, they would have taken 24/5 = 4.8 hrs alone. But one takes 2 hrs more than the other so possible combination is 6 and 4 hrs.
Let's check.

Thank you vm for your response.

twobagels · Answer

Pick a number for n. I picked 100.

3*( \frac{100}{x} + \frac{100}{(x+2)} )=  \frac{5*n}{4} = 125

You solve the resultant polynomial and will get x=4, but that's B's rate. A's will be of course 2 more.

so to produce 2*n, or 200, it will take 12.

summerbummer · Answer

-----------------------------

Did not really understand 2(x+2) part. Below's how I've tried solving:

1/(x+2) + 1/x = 5/12

Post which, I get a quadratic equation, but it's taking a longer time. Any solutions to this?

bumpbot · Answer

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To produce n bolts, Machine A takes 2 hours more than Machine B does.

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To produce n bolts, Machine A takes 2 hours more than Machine B does.

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