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.
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