Data Sufficiency

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 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.

OA E

Units, U<= 36
Price Per Unit upto 36 units = X
Price Per Unit after 36 Units = 1.5X

To find: Units produced

Statement 1:
Payment = 480
UX + (U-36)1.5X = 480
UX + UX(1.5) - 54X = 480
.5UX - 54X = 480
We don't have any info about the price per item.
INSUFFICIENT

Statement 2:
U' = U + 2
We don't have any information about the price per units and number of units
INSUFFICIENT

Combining..
510 - 480 = Price of 2 items
If units are less than 36
30 = 2 * X = 15

If units are greater than 36
30 = 2 * 1.5x => X = 10
Since, we cannot conclude the value of "x" we cannot conclude the value of "U"
INSUFFICIENT

Answer [spoiler]{E}[/spoiler]

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.