Data Sufficiency

Can someone explain to me the best/easiest way to solve this problem? The Answer is E.


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 1.5 times that amount for each additional item. How many items did Bob produce last week?

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

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

In the q itself it says :

If I < OR = 36 then he's paid x dollar/item. (I is item here)

and if I > 36, then 36x+1.5xy (y being the additional item/s after first 36 items)

From 1 : 480 = 36x+1.5xy and 36x=480 (possibilities) or it could be any no. less than 36 * x =480 , so items are not definable.
Insufficient

From 2 : (y+2) =$510 y being the last week's items
again from q data we don't know how many items are produced !! Insufficient

Combining both also we have no idea that, how many items Bob produced.
The fact is that there an inequality data in q and there is no closing limit for it.So, basically not sufficient to fetch the no. of items, irrespective of any other data given in statement 1 and 2.

This is my understanding here.
Any better suggestion/s ; would be much appreciated !

This is how I would approach this problem:

I look at (I) and I immediately see I have two unknowns: x, the pay per item, and y, the number of items produced. So, we can't solve for y.

I look at (II) and see the exact same issue.

Now we are down to C or E.

Even combining the information, I don't know whether y < 36. So, I don't know whether I should set up (I) like this:

36x + 1.5(y - 36) = 480

or like this:

xy = 480

I have the same issue with setting up (II). Since we have two possible equations for one side, and two possible equations for the other, we cannot determine a single value for y. Thus, the answer is E.

Hope that made it easier; ask if you have any questions.

Best wishes,

Tatiana

Hi VP,

Thanks.

why are we not considering the case#3...i.e. last week she made say 35 items...and this week she made 37...i.e. one over time and one normal case ?

Thanks
Mohit