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30 Apr 2025, 05:49
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (02:09) correct
36%
(01:54)
wrong
based on 103
sessions
History
Date
Time
Result
Not Attempted Yet
At the beginning of the month, a clothing store had 5 shirts for every 11 pairs of pants in its inventory. During the month, no new items had been added, and some items may have been sold. What was the ratio of shirts to pants in the inventory at the end of the month?
(1) The store sold 150 shirts during the month.
(2) For every 3 shirts the store sold during the month, it sold 12 pairs of pants.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
(1) The store sold 150 shirts during the month.
(2) For every 3 shirts the store sold during the month, it sold 12 pairs of pants.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
10 May 2025, 14:45
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Official Solution:
At the beginning of the month, a clothing store had 5 shirts for every 11 pairs of pants in its inventory. During the month, no new items had been added, and some items may have been sold. What was the ratio of shirts to pants in the inventory at the end of the month?
(1) The store sold 150 shirts during the month.
This tells us how many shirts were sold, but it is not sufficient to determine the final ratio. Not sufficient.
(2) For every 3 shirts the store sold during the month, it sold 12 pairs of pants.
This simply implies that four times as many pairs of pants as shirts were sold, which is also not sufficient. For example, if the initial inventory was 50 shirts and 110 pants, and the store sold 3 shirts and 12 pants, the final ratio would be different from a case where it sold 6 shirts and 24 pants. Not sufficient.
(1)+(2) From (1), we know the store sold 150 shirts. From (2), that means it sold 600 pairs of pants. But we still do not know the initial quantities of shirts and pants, only their ratio. For example, if the initial inventory was 500 shirts and 1100 pants, the final ratio would differ from a case where the store started with 1000 shirts and 2200 pants. Different starting values lead to different outcomes, so we cannot determine a unique final ratio. Not sufficient.
Answer: E
At the beginning of the month, a clothing store had 5 shirts for every 11 pairs of pants in its inventory. During the month, no new items had been added, and some items may have been sold. What was the ratio of shirts to pants in the inventory at the end of the month?
(1) The store sold 150 shirts during the month.
This tells us how many shirts were sold, but it is not sufficient to determine the final ratio. Not sufficient.
(2) For every 3 shirts the store sold during the month, it sold 12 pairs of pants.
This simply implies that four times as many pairs of pants as shirts were sold, which is also not sufficient. For example, if the initial inventory was 50 shirts and 110 pants, and the store sold 3 shirts and 12 pants, the final ratio would be different from a case where it sold 6 shirts and 24 pants. Not sufficient.
(1)+(2) From (1), we know the store sold 150 shirts. From (2), that means it sold 600 pairs of pants. But we still do not know the initial quantities of shirts and pants, only their ratio. For example, if the initial inventory was 500 shirts and 1100 pants, the final ratio would differ from a case where the store started with 1000 shirts and 2200 pants. Different starting values lead to different outcomes, so we cannot determine a unique final ratio. Not sufficient.
Answer: E
General Discussion
08 May 2025, 13:58
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Bunuel
Start of the month
\(\frac{\text{shirts}}{\text{pants}} = \frac{5*c}{11*c}\)
c → constant multiplier
Number of shirts sold = x
Number of pants sold = y
Ratio of inventory at the end of the month =
\(\frac{\text{shirts}}{\text{pants}} = \frac{5*c - x}{11*c - y}\)
Statement 1
(1) The store sold 150 shirts during the month.
x = 150
As we don't know the value of the constant multiplier c and y we won't be able to find the ratio.
The information alone is not sufficient to find the ration asked.
Eliminate A, and D.
Statement 2
(2) For every 3 shirts the store sold during the month, it sold 12 pairs of pants.
\(\frac{x}{y} = \frac{3}{12}\)
4x = y
\(\frac{\text{shirts}}{\text{pants}} = \frac{5*c - x}{11*c - 4x}\)
Depending on the value of x, and c the ratio can change.
Combined
x = 150
therefore y = 600
However we still don't have the value of c. Hence, for different values of 'c' we can have different ratios.
Option E
