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.

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.

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.

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)

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.

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.

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.



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