akash singhal wrote: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.
Statements combined:
(this week's earnings) - (last week's earnings) = 510 - 480 = $30.
Implication:
The 2 additional items produced this week each account for an additional $15 in earnings, for a total earnings increase of $30.
Case 1: x=15
In this case:
Number of items produced last week = 480/15 = 32.
Number of items produced this week = 510/15 = 34.
Case 2: (3/2)x = 15, implying that x=10
Last week:
Total earnings for the first 36 items = 36*10 = 360.
Earnings paid at $15 per item = 480-360 = 120.
Number of items paid at $15 per item = 120/15 = 8.
Total items = 36+8 = 44.
This week:
Total earnings for the first 36 items = 36*10 = 360.
Earnings paid at $15 per item = 510-360 = 150.
Number of items paid at $15 per item = 150/15 = 10.
Total items = 36+10 = 46.
Since the total number of items produced last week is 32 in Case 1 but 44 in Case 2, INSUFFICIENT.
The correct answer is
E.
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