Stimulus: If machine M is required to make 3000 items and machine N is required to make 4000 items, which of the machines will finish earlier than the other when both work at their respective constant rates?

Statement 1:
1. Machine N can make 1000 more items than M per hour

Scenerio 1: Let the rate of Machine M be 1000 units per hour therefore the rate of Machine N will be 2000 units per hour (1000 units more)
In this case Machine M will take three hours to finish the work and Machine N will take two hours to finish the work. In this case Machine N will finish its work earlier than Machine M.

Scenerio 2: Let the rate of Machine M be 3000 units per hour therefore the rate of Machine N will be 4000 units per hour (1000 units more)
In this case Machine M will take one hour to finish the work and Machine N will also take one hour to finish the work. Therefore both the machines will finish their respective work on the same time.

Since we have two different answers to statement 1, this is clearly insufficient.


Statement 2:
2. N's work rate is twice that of M

We should not use number testing to prove sufficiency. We should use algebra and logic.

Proof:-
Let x be the number of hours taken by Machine M to finish 3000 units.
- Machine M's rate of work is 3000/x (i.e. Number of units produced per hour) AND
- Machine N's rate is twice that of M or 6000/x (i.e. at twice the rate Machine N produces double the Number of units per hour)

By Definition Machine M will take x hours to complete 3000 units AND
Machine N will take (\(\frac{work to be done}{rate}\)) or (\(\frac{4000}{(6000/x)}\)) or \(\frac{2x}{3}\)

Hence \(\frac{2x}{3}\) < x Therefore sufficient. machine N will always take two third of the time when compared to the time taken by Machine M.

Correct Answer is B
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Hi Karthik200!
Please double check the OA.

Thanks,
V

Edit: Or give the OE
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If machine M is required to make 3000 items and machine N is required to make 4000 items, which of the machines will finish earlier than the other when both work at their respective constant rates?

1. Machine N can make 1000 more items than M per hour
Answer would depend on the speed ...
a) if the speed of M is 3000 items ph and that of N is 4000 items ph.... both will finish together
b) if the speed of M is <3000 say 1000 items per hr and that of N is 2000 items per hr...... N will do faster
c) speed of M is > 3000 say 9000 and that of N as 10000, M will finish faster
insuff

2. N's work rate is twice that of M
So N will take half the time for same work or N can make double the items in same time
Thus when N finishes 4000, N would finish 4000/2 = 2000 and N will finish first

B

I think you used number testing to prove sufficiency for Statement 1 and did not test for one hour. We could use algebra and logic for statement 1 as well.

Proof:-
Let x be the number of hours taken by Machine M to finish 3000 units.
- Machine M's rate of work is 3000/x (i.e. Number of units produced per hour) AND
- Machine N's rate is 1000 more units than that of Machine M or (\(\frac{3000}{x}\) + 1000) (i.e. at the rate Machine N produces 1000 more units than Machine M per hour)

By Definition Machine M will take x hours to complete 3000 units AND
Machine N will take (\(\frac{work to be done}{rate}\)) or (\(\frac{4000}{(3000/x + 1000)}\)) or \(\frac{4x}{(3+x)}\)

Hence we have 3 scenerios:-

1) \(\frac{4x}{(3+x)}\) = 1 when x = 1 which means Machine M will finish its work with machine N in one hours time.
2) \(\frac{4x}{(3+x)}\) = \(\frac{8}{5}\) hours when x = 2 which means Machine N will take less time to do its work than Machine M.
3) \(\frac{4x}{(3+x)}\) = \(\frac{4}{7}\) hours when x = 1/2 hours means Machine M will take less time to do its work than Machine N.

Since there are 3 scenarios, we have insufficiency.
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Question: Which machine finished work earlier than the other machine?

Statement 1: Machine N can make 1,000 more units than M per hour
Case 1: N makes 2000 per hour and M makes 1000 per hour i.e. M takes 3 hours and N take 2 hours to finish their work
Case 2: N makes 4000 per hour and M makes 3000 per hour i.e. M takes 1 hours and N take 1 hours to finish their work
NOT SUFFICIENT

Statement 2: N's work rate is twice that of M

i.e. When N makes 4000 Products then M makes 2000 i.e. N always makes 4000 product in a time less than the time taken by M to make 3000 parts.
SUFFICIENT

Answer: Option B
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I am just curious, why can we assume that the machines start to work at the same time?

The question is "which one will finish earlier?", but the posts (and the Math Revolution solution pdf, too) answer the question "which one works faster?" I mean, earlier and faster are not the same. Which one finishes earlier? What if the slower machine started the work 2 weeks ago and the faster will be ready to work in a few weeks time? I think that time data are missing to answer the question "earlier?" "When both work at their constant rate" could mean that one of them just immediately finished when the other one started and the overlapping period was just 1 second. It is not implied at all that they started at the same time or the overlapping period is constant, hence starting time does not matter.

The question is just simply misleading; it is not an SC question to figure out the intended meaning

The same thought crossed my mind.

Given that this is a DS question, I did not want to assume that they have started the same time.

chetan2u - please help

Hi
Don’t worry, the official questions will never leave any ambiguity.

I think an adjustment should be made to the question. It is not stated that both machines start working at the same time. Either this statement should be added or the question should be adjusted to the following.
Which machine will finish its task in less time than the other?