Running at their respective constant rates, Machine X takes

[jean.spellman]

Thanks, RonPurewal! It was the later...and that's what I thought was going on, but regardless, your explanation helped :)

[RonPurewal]

Thanks, RonPurewal! It was the later...and that's what I thought was going on, but regardless, your explanation helped :)

cool. you're welcome

[andy.wy.tam]

There's no way I can finish this question in 2 minutes

Had to bust out the quadratic equation too

Is there an easier method w/ picking numbers?

Instructors, can you please enlighten me as to how I can finish this question in 2 minutes time.

Thanks.

[RonPurewal]

There's no way I can finish this question in 2 minutes

Had to bust out the quadratic equation too

Is there an easier method w/ picking numbers?

Instructors, can you please enlighten me as to how I can finish this question in 2 minutes time.

Thanks.

you don't really have to.

this is one of the biggest problems that people have in the quant section -- this whole persistent idea that, no matter what, you must be able to solve every problem in exactly two minutes or less.

well, no.

remember, folks -- 2 minutes is the average time for a quant problem.
that's average as in average. not an upper limit!
because it's an average, you will have lots of problems that take over 2 minutes -- and these will be balanced out by problems that take less than 2 minutes.
the practice tests will help you calibrate this sort of thing. but, the most important idea is this: if a problem is clearly longer than most, it's ok to take more than 2 minutes on it.

this goes especially for word problems, which must be "decoded" before you can even start working on them.
if you give yourself a LIMIT of 2 minutes for word problems, what will happen is ... well, you just won't finish word problems, that's what.

--

as a rather extreme example, if you have OG12, check out multiple choice #163 and #164 (can't reproduce here).

* #163 is obviously very long (and challenging to boot). trying to finish #163 in two minutes is a fool's game; you should definitely allot substantially longer for that problem. (although, of course, you should still quit immediately if you are totally stuck.)

* #164, on the other hand, should not take anyone any longer than about twenty seconds.
there's no decoding/interpretation required; the equation is right there staring at you.
if you know how to do it, it's one step. (the least efficient solution is still only two steps, maybe three if you have to explicitly convert the negative exponents to/from fractions.
if you don't know how to do it, then, within fifteen or twenty seconds, you should admit to yourself "i don't know how to do this", guess, and move on.

if your strategy were to allot exactly two minutes to #163 and exactly two minutes to #164, that would be a very poor strategy indeed -- for both problems. you basically just wouldn't finish #163, and then, if you were stuck on #164, you would waste at least 1.5 minutes just staring blankly at it.

[marketmaker87]

I think insted of solving the equation, it is much better to substitute the values in the eqn and check.

D --> Number of days

1/D - rate of Y
1/(D+2) - rate of X

we get 3 (1/D + 1/(D+2)) = 5/4.

Now, just substitute D = 4 and see whether the eqn is satisfied.
So, 4 + 2 = 6 days - No. of days taken by X to produce W widgets.
Just multiply by 2 to get the number of days to produce 2 W widgets.
2* 6 = 12..so E is the answer :)

Thanks,
Shubh

I like the method Shubh used to solve this problem. My only question is- How did they know to substitute 4 in for D?

[RonPurewal]

I think insted of solving the equation, it is much better to substitute the values in the eqn and check.

D --> Number of days

1/D - rate of Y
1/(D+2) - rate of X

we get 3 (1/D + 1/(D+2)) = 5/4.

Now, just substitute D = 4 and see whether the eqn is satisfied.
So, 4 + 2 = 6 days - No. of days taken by X to produce W widgets.
Just multiply by 2 to get the number of days to produce 2 W widgets.
2* 6 = 12..so E is the answer :)

Thanks,
Shubh

I like the method Shubh used to solve this problem. My only question is- How did they know to substitute 4 in for D?

well, you could avoid a lot of issues here by being a bit more forward-thinking about choosing where to put "D".
in particular, the goal of this problem -- a.k.a. the only quantity that we even care about -- involves machine X, not machine Y. so, it's illogical to let D stand for the number of days that machine Y takes, since that just adds unnecessary steps (and also clouds the backsolving solution, as you noted here).

instead, let D stand for the number of days that machine X takes. then machine Y takes (D - 2) days.

--> 3(1/(D - 2) + 1/D) = 5/4

if you have this, then back-solving from the answer choices is easy. just
* take an answer choice
* divide it by 2 (since the answer choices are double time)
* plug it in.

when you plug in (e) 12, that means you're plugging D = 6 into the (better) equation above. that works.

[marketmaker87]

Thanks Ron...thats 10x easier than dealing with quadratics.

[tim]

:)

[alex_sokolovski]

Please correct me if I'm wrong, but I don't think that "w" is needed here to solve the problem. I just wrote "1" instead of "w" and "5/4" instead of "5w/4". Saved some time and avoided unnecessary variables.

Thanks!

[jnelson0612]

Please correct me if I'm wrong, but I don't think that "w" is needed here to solve the problem. I just wrote "1" instead of "w" and "5/4" instead of "5w/4". Saved some time and avoided unnecessary variables.

Thanks!

Yes, that works, as long as you plug in w=1 for all of the "w" terms in the problem. Good move!

[JordanK882]

Estimating also seems to be a good method here.

X & Y working together make 5/4w widgets in 3 days.

(5w/4)/3= 5w/12 widgets per day.

Since it would take X 2 days longer to finish the job than Y, you know if has a smaller rate. since 5w/12= X & Y's combined rates, estimate that X's rate is 2w/12 and Y's rate is 3w/12.

Take X's estimated rate and simplify: 2w/12 = 1w/6 --> it takes X 6 days to create w widgets. you want to know the time for 2w, so double to get 12 days.

[tim]

No. You got lucky with this analysis because you just happened to assign rates to X and Y that ended up agreeing with the overall answer. One thing you can do with estimation is this:

5/4w widgets in 3 days together means w widgets in 12/5 days together, meaning 2w widgets will take 24/5 days together. If x and y had equal rates, each one would take twice as long to do the job by itself, or 48/5 days. Since you know x takes four days longer than y to produce 2w widgets (remember it takes two days longer to produce w widgets), you know x takes more than 48/5 or 9.6 days, so you can eliminate any answer less than 9.6.

If you want to do even better, you can start by adding 2 days to 48/5 for x and subtracting 2 days from 48/5 for y, giving us 7.6 for y and 11.6 for x. However, subtracting the same amount from one time that you add to the other will actually speed up the process (consider how much time it takes if x and y both take 2 days to do a job versus 3 days for x and 1 day for y), so you have to slow the process down, forcing x to be larger than 11.6. Now you have backed into the correct answer since only one answer choice is larger than 11.6.

[RonPurewal]

If you want to do even better, you can start by adding 2 days to 48/5 for x and subtracting 2 days from 48/5 for y, giving us 7.6 for y and 11.6 for x. However, subtracting the same amount from one time that you add to the other will actually speed up the process (consider how much time it takes if x and y both take 2 days to do a job versus 3 days for x and 1 day for y), so you have to slow the process down, forcing x to be larger than 11.6. Now you have backed into the correct answer since only one answer choice is larger than 11.6.

^^
... impressive.

if you could actually come up with this on the spot, in less time than it would take to just solve the problem, then ... well, even more impressive.

[KwakuE764]

I dont understand how people are adding the rates without an explanation of how to do it. My quadratics dont match

[RonPurewal]

My quadratics dont match

what does your work look like thus far?