How many items did Bob produce last week?

St1: Last week Bob was paid $480
If per item price = 24, he produced 20 items
If per item price = 20, he produces 24 items
Not sufficient

St2: This week, bob paid $510 and produced 2 more items than last week.
THIS WEEK: Let per item price be $17, then items produced = 30 items THEREFORE last week items produced must be 32 items
THIS WEEK: Let per item price be $30, then items produced = 17 items THEREFORE last week items produced must be 19 items
Again Insufficient

Together, there are 2 cases to consider:
If we assume the REGULAR price, we know 2 items cost $510 - $480 = $30 therefore 1 item cost $15.
THIS WEEK Bob produced: 510/15 = 34 items
Last WEEK Bob produced 32 items.

But if we dont assume REGULAR price,
LAST WEEK Bob produced Y items and Bob's revenue = 36X + (Y-36)*1.5x
THIS WEEK Bob produced Y+2 items and Bob's revenue = 36X + (Y+2-36)*1.5x => 36X + (Y-34)*1.5x
This week's Revenue - LAst Week's Revenue = 30
therefore solving the above 2 equations we get 3x = 30 or x = 10
For x = 10, last week bob produced 480 = 360 + (y-36)*15 or y = 44 items
THIS WEEK Bob produced 44 items
Hence Insufficient

Ans E

ela07mjt wrote: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 3/2 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 two items more than last week, and was paid a total of $510 for the items that he produced this week.

When the two statements are combined, the 2 additional items produced this week result in an earnings increase of $30 (from $480 to $510).
Thus, the amount earned by each of the 2 additional items produced this week = 30/2 = 15.
It is possible that these 2 additional items were paid at the regular rate (x) or at the higher rate (1.5x).

Case 1: x=15
Since x=15, every item produced up to the 36th item earns $15.
Since 15*36 = 540, and the total amount earned last week was $480, the total number of items produced last week was LESS than 36.
Thus, every item produced last week was paid at the regular rate:
Total items produced last week = 480/15 = 32.

Case 2: 1.5x = 15, implying that x=10
Since x=10, every item produced up to the 36th item earns $10.
Since 1.5x = 15, every item produced beyond the 36th item earns $15.
Since 10*36 = 360, and the total amount earned last week was $480, the total number of items produced last week was GREATER than 36.
Total amount earned by the first 36 items produced last week = 36*10 = 360.
Total amount earned by the additional items produced last week = 480-360 = 120.
Since each of these additional items earns the higher rate ($15), the number of additional items produced last week = 120/15 = 8.
Total items produced last week = 36+8 = 44.

Since the total number of items produced last week could be 32 or 44, the two statements combined are INSUFFICIENT.

The correct answer is E.