If Bob produces 36 or fewer in a week, he is paid X dollars

[RonPurewal]

Isn't it sufficient to just see in the statement 1 + statement 2 scenarios that
n*x=480
(n+2)*x=510
where n is the number of items sold last week
then, n could be equal to 1 or 3 (as you showed in statement 2) and consequently, n + 2 could be 3 or 5.
Thus insuff.
?

no.

first of all, those equations are wrong because they don't account for the increase that occurs after the 36th item.
you're writing a constant "x", as if the cost per item were the same all the time no matter what.

second, those equations, if they were correct, would actually give answer (c), not (e).
you could divide them, in which case 'x' would cancel and you'd have (n + 2)/n = 510/480, or (n + 2)/n = 17/16. the only solution to that is n = 32, which you could then plug in to find x.
so, with your equations, you would actually (mistakenly) conclude that the two statements together are sufficient.

[sudaif]

okay. i'm going to re-attempt. to be clear and for practice, i am analyzing EVERY scenario.
If Bob produces 36 or fewer items in a week, he is paid x dollars per item. If Bob produces more than 36 items in a week, he is paid x dollars per item for the first 36 items and 1 1/2(1.5) times that amount for every additional item.
How many items did Bob produce last week?

(A) Last week Bob was paid a total of $480 for the items he produced that week.

(B) This week Bob produced 2 more items than last week and was paid a total of $510 for the items that he produced this week.

Let last week number of items produced = n= ?
Statement 1) For the n<=36 scenario - he could have produced 6 items for $480 or he could have produced 12 items for $480. For the n>36 scenario, he could have produced 48 total items for $480 or he could have produced 60 items for a total of $480. Clearly, many possibilities for n. Insuff.
Statement 2) This week Bob produced (n+2) items for $510.
For n<=36 scenario, Bob could have produced 30 items this week, and thus n could be 28 or Bob could have produced. Or Bob could have produced 15 items this week and thus 13 items last week. For the n>36 scenario, Bob could have produced 51 items this week for $510 and thus 49 items last week. Or Bob could have produced. Again, we have many possibilities for n, thus insuff.
Statement 1 + Statement 2) The incremental 2 items that Bob sold this week raked in $30. If number of items produced this week and last week were less than 36, then, 2x=30 and then, x=$15. If we know n<36 and we have x, can find a value for number of items sold last week, pretty quickly. It would be $480/$15= 32 = n. On the other hand, if the number of items produced this week and last week were greater than 36, then, 2(3/2x) = $30 or x = $10. If n>36, and x=$10, then we must have sold the first 36 items for $10, which amounts to total of $360. And, leaves behind $510 - $360 = $150. Since $150 could be sold for 3/2x or 3/2*10 = $15 if 10 items were sold, then we could have total items sold = 36 + 10 = 46. Then, n (last week items sold) = 44. Since we have two values for n, insuff.
This is one of the weirdest problems I've come across. strange strange.

[RonPurewal]

sudaif, yes, that's the correct analysis.

it is indeed a strange problem. one look at this problem, though, reveals the test writers' principal purpose in creating it -- namely, they were quite obviously going out of their way to construct a problem on which you can't get an easy solution with traditional algebra.
in particular, note the following:
1) there's no one, single equation you can write that will cover all the possibilities; AND
2) most people guessing the answer to this problem will take a look and go, "oh, hey, system of two equations" and will pick (c). (some of them might even -- mistakenly -- think that statement 2 is a system of two equations all by itself, since it mentions "last week", and might guess (b).)

therefore, the problem is cleverly written to foil these sorts of guesses.
at a glance it might seem like a trick. once you look at enough DS problems, though, you'll eventually realize that this is basically the entire purpose of that part of the test -- to prevent overly rules-based thinkers from scoring too high.

[aagar2003]

Can somebody please tell what time should I have spent on this one?

Here is my working, after looking at the answer and previous discussions :(

Premise (T is total payment to Mr. Bob):
if n<=36 then T = nx
if n>36 then T = 36x + (n-36)(1.5x)

1. We have 2 parameters to solve from one value of T. Hence NS
2. Same as (1) above: Since last week 'n' is not known, it is unknown this week too. Again solving for 2 parameters from one equation if this week 'n' > 36. Hence NS.

Using 1,2,T,E,N approach: 1,2 and E are already gone. Now Check for T (Option C in GMAT):

All bad things happen at 36.
Lets make cases arnd the bad point:

All three can be solvable for the difference between this week vs last week being 510-480 = 30
In Case 1: 2x = 30
In Case 2: 2.5 x = 30
In Case 3: 3x = 30
Hence this is NS.

Therefore, Answer is (E)

[RonPurewal]

Can somebody please tell what time should I have spent on this one?

Here is my working, after looking at the answer and previous discussions :(

your solution above is incorrect. it gives the correct separation between terms ($30) but not the correct values of the terms themselves, which are supposed to be $480 and $510.

i.e., in your "case 1" you would conclude that x = 15, but that doesn't work because 34x = 34(15) is not 480, and 36x = 36(15) is not 510.
in your "case 2" you would conclude that x = 12, but that doesn't work because 35x = 35(12) is not 480, and 36x + 1.5x = 36(12) + 1.5(12) is not 510.
finally, in your "case 3" you would conclude that x = 10, but that doesn't work either, because 36x = 36(10) is not 480, and 36x + 2(1.5x) = 36(10) + 3(10) is not 510.

have you read the rest of this thread? there are 19 posts, which contain several correctly worked solutions to the problem. please check them out.

[aagar2003]

Can somebody please tell what time should I have spent on this one?

your solution above is incorrect

You are correct Ron. I don't think I put too much caution while answering this one. I am looking for strategy to save time. This one consumes a lot of quality time. How much time do you suggest a test-taker to spend on this one?

BTW my image link disappeared from the previous post. Was it removed because of violating the forum rules.

[RonPurewal]

I am looking for strategy to save time. This one consumes a lot of quality time. How much time do you suggest a test-taker to spend on this one?

i can't give one figure; this may take vastly different amounts of time for different test-takers.
two comments:
1 * if you get to about three minutes or so, it's probably time to move on.
2 * on this particular problem, it shouldn't be much of a job to get rid of the individual statements. if you can dispatch those statements intuitively (versus having to use actual algebra on them), then the problem might not take you that much time at all. on the other hand, if you actually have to use algebra for everything, including the individual statements, then, yes, this problem is going to be a bear.

BTW my image link disappeared from the previous post. Was it removed because of violating the forum rules.

i can still see it; maybe the problem is your browser.

[mcmebk]

Nobody seems to have quoted the third possibilities here, even though it does not affect the answer:

N<=36, while N+2>36, which means N could be 35, or 36.

when N is 35, 35X=480, 36X+1.5X=510 impossible;
when N is 36, 36X=480, 36X+3X=510 also impossible;

So N is either less than 34, or greater than 36, in either condition, you can get a legitimate result, 32 or 44, thus insufficient.

I spent 6mins on this question, hate it.

[RonPurewal]

Nobody seems to have quoted the third possibilities here
...
I spent 6mins on this question

^^ take a look at those two statements again; they're closely related to each other. think about it for a while.

the main reason that "no one seems to have quoted xxxxx" is that it's irrelevant to the problem (as you pointed out yourself). if you're even considering that case, that means you don't have a concrete goal in mind as you're solving the problem; instead, you're just putting your head down and grinding out a bunch of math.

if you have a concrete goal here, then you just have to do two things:
* Find a case where the extra $30 comes from two additional items at the regular rate.
* Find a case where the extra $30 comes from two additional items at the enhanced rate (the rate that kicks in after 36 items).

if you're grinding out every possible case of the algebra, then, in all likelihood, you've forgotten all about the goal of the problem.
remember, data sufficiency isn't really meant to be a math test; it's meant to be a test of organization and goal-oriented thinking.

[mcmebk]

Hi Ron

thank you for answering so promptly.

I do have the problem that I tend to list out all the possibilities, even when sometimes it is not necessary.

However, in this question, there could be a situation that we get no legitimate results for N≥36, we would be wrong to assume the two statements give us only one answer (32) without considering the scenario I just provided.

How to decide if such risk is worthwhile taking in the exam day?

[RonPurewal]

Hi Ron

thank you for answering so promptly.

I do have the problem that I tend to list out all the possibilities, even when sometimes it is not necessary.

However, in this question, there could be a situation that we get no legitimate results for N≥36, we would be wrong to assume the two statements give us only one answer (32) without considering the scenario I just provided.

How to decide if such risk is worthwhile taking in the exam day?

I don't know what "risk" you're talking about.

In any case, the issue is still focus.
You have this extra 30 dollars. There are only 3 places where you could have gotten that 30 dollars:
1/ Two extra items at the regular rate.
2/ One extra item at the regular rate, and one at the increased rate.
3/ Two extra items at the increased rate.

Just look at these possibilities one by one:
1/
This would mean that the regular rate is 15$ per item.
Does that work here?
Sure -- 32 items for $480, 34 items for $510.
That's one case.

2/
Since the rate changes between item #36 and item #37, in this case the extra 30$ has to come from those items.
if "x" is the regular rate, then x + 1.5x = 30 here. double this to 2x + 3x = 60, so x = 12.
therefore, in this scenario, the 36th item would be 12$ and the 37th item would be 18$.
would this work?
nope. under this scenario, we'd have 35 items originally (= before items #36 and #37). at these rates, that's only 35 x 12 = 420$, when it's supposed to be 480.
ignore this case.

3/
This means that the overtime rate is $15 per item. That's 1.5 times the regular rate, so the regular rate is $10 per item.
The first 36 items are 360$.
To make 480$, we need 120/15 = 8 more items.
does this work?
Sure... 44 items is $480, and 46 items will be $510.

it's (e).

this isn't six minutes of work.

[RonPurewal]

Hi Ron

thank you for answering so promptly.

I do have the problem that I tend to list out all the possibilities, even when sometimes it is not necessary.

here's what you should do.

you should have an annoying voice in the back of your head, asking you the same three questions over and over and over and over again:

1/
Do you know EXACTLY WHAT you are doing right now?

2/
Do you know EXACTLY WHY you are doing it? What do you hope to ACCOMPLISH?

3/
Are you making tangible progress toward a GOAL?

If the answers are not "yes", "yes", and "yes", then you should quit what you are doing.
that doesn't necessarily mean "guess right now and move on"; however, it does mean "try to find another method".

even with the approach that you described here, there's still no way this question should take six minutes.
if you took six minutes, then that means you must have spent a pretty decent amount of time just staring at the problem, without a concrete goal in mind.

just think of it like any real-world problem-solving scenario. like, say, sewing a piece of clothing.
would you ever, at any point, just start randomly stitching pieces of cloth together and seeing what you get?
... no, of course you wouldn't.
if you didn't have "yes" to the 3 questions above, you would stop sewing until you figured out what you were actually trying to DO ... and you wouldn't start sewing again until you'd figured that out.

this is the mentality that most people naturally have toward "problem-solving situations" in the real world -- and that's why people aren't incompetent problem-solvers in the real world. (just watch someone who's locked out of his house or car sometime, and you'll see that most people can be pretty darn good problem solvers.)
just try to adopt the same mentality here, and you'll be fine.