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.
Quantitative Revision from Richa Q #1
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- richachampion
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Tricky Question.
OA: E
OA: E
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Statements combined: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.
(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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As per the information, if the number of items (n) ≤ 36, the payment = $nx.richachampion 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 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.
However, if n > 36, the payment = 36x + 1.5(n - 36)x
S1: Since we are not given the pay rate of an item, we cannot get the number of units. Insufficient.
S2: This statement is a comparison between the two weeks. We need help from statement 1 to make any meaning out of this statement. Insufficient.
S1 & S2:
Scenario 1: Assume that Bob produced (n) ≤ 36 items this week.
The payment of 2 items = 510-480 = $30.
=> x = $15
=> Number of items produced last week = 480/15 = 32.
Scenario 2: Assume that Bob produced (n) > 36 items this week and the two units are paid at $1.5x per item.
We know the payment of 2 items = 510-480 = $30.
Thus, per unit payment of the items = $30/2 = $15.
=> x = 15/(1.5) = $10.
We know that if n > 36, the payment = 36x + 1.5(n - 36)x
=> 480 = 36*10 + 15*(n-36)
=> n=44 units. No unique answer. Insufficient.
Answer: E
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Suppose Bob produces b items this week. We know that he'll make
bx
if b ≤ 36, and
bx + (b - 36)*1.5x
if b > 36.
S1::
We could have bx = 480, which has many solutions (b = 36, x = 15; b = 480, x = 1, etc.), so this is INSUFFICIENT
S2::
We could have bx = 510, which has many solutions, as above, again INSUFFICIENT
S1 + S2::
Together, the crucial question is whether the additional $30 for the two apples represents:
1) $x for each apple
2) $x for the first, and $1.5x for the second
3) $1.5x for each apple
Even together, we can't resolve this. If it's Case 1, we've got x = 15, from which b = 32. If it's case 2, we've got x = 12, from which b = 40 (though this contradicts Case 2, since the second extra apple wouldn't push us over 36). If it's Case 3, we've got x = 10, in which case b = 44.
Since we have two values of b that work, we can't answer the question definitively, and the answer is E.
bx
if b ≤ 36, and
bx + (b - 36)*1.5x
if b > 36.
S1::
We could have bx = 480, which has many solutions (b = 36, x = 15; b = 480, x = 1, etc.), so this is INSUFFICIENT
S2::
We could have bx = 510, which has many solutions, as above, again INSUFFICIENT
S1 + S2::
Together, the crucial question is whether the additional $30 for the two apples represents:
1) $x for each apple
2) $x for the first, and $1.5x for the second
3) $1.5x for each apple
Even together, we can't resolve this. If it's Case 1, we've got x = 15, from which b = 32. If it's case 2, we've got x = 12, from which b = 40 (though this contradicts Case 2, since the second extra apple wouldn't push us over 36). If it's Case 3, we've got x = 10, in which case b = 44.
Since we have two values of b that work, we can't answer the question definitively, and the answer is E.