If Bob produces 36 or fewer in a week, he is paid X dollars per item. If Bob produces more than 36 items, he is paid X dollars per item for the first 36 items, and 3/2 times that amount for each additional item. How many items did Bob produce last week?

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

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

This is GMAT prep question. What is best approach to this question.

When reproducing questions, please make sure that you do so exactly. I think I got everything here, but there are some words missing, which makes me wonder if something important was left out...

36 or fewer: X per item
> 36: X per item for first 36 + 1.5X for each item over 36.

How many items last week?

Some upfront thought: For exactly 36 items, Bob would be paid $36*X. For, say, 40 items, Bob would be paid 36*X + 4*1.5*X. I don't know what X is.

(1) Last week, Bob was paid $480. Maybe he made one item and is paid 480 per item. Maybe he made two items and is paid 240 per item. ??? Not sufficient. Elim A and D.

(2) Bob made Y items last week and Y+2 items this week. Bob make $510 this week. Maybe Bob made 1 item last week and 3 this week, and was paid 170 per item. Maybe Bob made 3 items last week and 5 this week and was paid 102 per item. ??? Not suff. Elim B.

(1) + (2) Bob was paid 480 for Y items last week. Bob was paid 510 for Y+2 items this week. Y = 480. Y + 2 = 510. So two items added an additional $30, of $15 per item. But wait - is this the regular X rate, or the "overtime" 1.5X rate?

If it's the regular rate, then he produced 480/15 items last week, or 32 items. That's one possibility. If it's the 1.5X rate, then this week he produced some number of items at $15 per and $10 per. He had to have made at least 36 items at the $10 per rate (in order to get to the point of making $15 per item). So that's 36*10 = 360. He made 510 this week, so he still has another 150 to make, at 15 per. That's 10 items. So Bob made 36 + 10 = 46 this week. Then according to statement 2, he made 44 last week (46-2).

Two answers. Not sufficient. Elim C. E is the answer.

Notice that I checked the work for (1) + (2) even once it became apparent that there are two possibilities. You can go with it or keep checking - I checked b/c I figured there was a possibility that one of the options wouldn't be acceptable given the parameters of the question, so I wanted to make sure. But if I was behind on time on the test, I might not have checked.

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

Actually C is the correct answer. Please help! :-(

Taking the information present in the question, x is the cost of each of the first 36 items and 1.5x is the cost of each of the items produced after 36.

According to 1) if n is the number of additional items produced after 36, then

36x + n(1.5x) = 480.
In this equation we have two unknowns, hence cannot be solved.

According to 2, if the number of items produced last week was (36 + n), then this week the number of items produced are (36+n+2). The new equation would be
36x + (n+2)(1.5x) = 510. ==> 36x+1.5nx+3x=510 or 39x+1.5nx=510.
This also has two unknowns, hence cannot be solved.

Combining both of these we have two unknown variables and two linear equations, which when solved gives n as 8 and x as 10, hence C is the answer.

I also got e as my answer given that we have no way to determine what rate of payment should be used.

Your explaination assumes that he produced a min of 36 items. Do confirm your thought on this...

sumit, i am having a similar problem. i am still confused :-(

what if bob produced less than 36 items?
in this case, statement 1 will be still insufficient.
state 2 still does not tell you much.
okay for 1+2: since we are told there is a difference in bob's pay, bob must have made more than 34 products last week (if less than or equal to 34, producing 2 more items will still result in same pay for bob). knowing this fact that bob must have produced more than 34 products. i got to this far and i didn't know how to solve the problem further... so chose E.

can someone explain why we are not considering the senario explained above to arrive at the correct answer??

thanks so much

the oa, as reported in this post, is (e).
perhaps somebody here just read the oa wrong. or someone thinks they're a wise guy.

ron,

i am getting a tad confused about (1) + (2). could you please help me understand and give some TAKEAWAYS for similar problems?

C is the answer.

Given Data,
let Y be the number of items bob produced last week,
X - bob pay/item for the first 36 items

36X + 1.5X(Y-36)

Stmt1:
36X + 1.5X(Y-36) = 480 -- INSUFF

Stmt2:
36X + 1.5X((Y+2)-36) = 510 -- INSUFF

from 1) and 2)
3X = 30 ; X = 10

Sub X=10 in (1)
360 + 15Y - 540 = 480

Y = 44 -- This is what we require.

So C
But OA says E
can somebody correct me!!

Stmt 1:
xy = 480 when y <= 36
36x + 1.5x(y-36) = 480 when y > 36..
Insufficient.

Stmt 2:
x(y+2) = 510 when y <= 36
36x + 1.5x(y+2-36) = 510 when y > 36
Insufficient

Combining both,
x = 15 when y <= 36
=> y = 32
or x = 10 when y > 36
=> y = 44
Insufficient

Ans E.

sure.

first, go ahead and tell what you do and don't already understand about (1) and (2) together.

between this thread and this other one, there are already 5-6 posts discussing the combination of the two statements. therefore, it's likely that most of the source of your confusion is already addressed in those posts.

anything you don't understand - and still don't understand, after viewing the above posts - come back and ask.
but if your question is just "how do we handle (1) and (2) together?" then it is almost certainly addressed already.

thanks ron.

If I were tutoring someone for the GMAT (which, I'm NOT hehe), i'd leave my student with this take home message "Be careful when you are dealing with inequalities because you are dealing with different rates, so you can't just solve/substitute like you can in non -nequality linear systems". If someone were pressed for time, this nuggett alone MIGHT lead to a "good" guess of "E" after some thought.

perfect and insightful, thank you

Stacey -

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.
?