carcass wrote:
The closing price of Stock X changed on each trading day last month. The percent change in the closing price of Stock X from the first trading day last month to each of the other trading days last month was less than 50 percent. If the closing price on the second trading day last month was $ 10.00, which of the following CANNOT be the closing price on the last trading day last month?
A. $ 3.00
B. $ 9.00
C. $ 19.00
D. $ 24.00
E. $ 29.00
Let us begin by determining a range for the closing price on the first trading day of the last month.
Let us denote the closing price on the first day by x. We are given that the closing price on the second trading day was $10. We know x could increase by no more than 50% to become 10, or x could decrease by no more than 50% to become 10.
If x increases by 50% to become 10, then (1.5)x = 10 and hence x = 6.67.
If x decreases by 50% to become 10, then (0.5)x = 10 and hence x = 20.
We see that the closing price on the first day could be any value between 6.67 and 20.
Now, let’s determine upper and lower bounds for the closing price on the last trading day of last month.
Since the closing price on the last trading day can be at most 50% more than the closing price of the first day of last month, the closing price on the last day of last month must be less than (1.5)20 = 30.
Since the closing price on the last trading day can be at most 50% less than the closing price of the first day of last month, the closing price on the last day of last month must be greater than (0.5)(6.67) ≈ 3.3.
Looking at the answer choices, the only price that is not greater than 3.3 and less than 30 is 3.
Answer: A
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