Roland2rule 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 f = the price on the first day.
The percent change from the first trading day to each of the other trading days was less than 50 percent.
Thus, the percent change from f to the price on the second day -- $10 -- must be less than 50%.
We must determine the range of f.
To calculate the range, test a 50% percent change from the first day (f) to the second day ($10).
If f increases by 50% to yield the price on the second day -- $10 -- we get:
f + (50/100)f = 10
f + (1/2)f = 10
(3/2)f = 10
f = 20/3 = 6.67.
If f decreases by 50% to yield the price on the second day -- $10 -- we get:
f - (50/100)f = 10
f - (1/2)f = 10
(1/2)f = 10
f = 20.
Since the percent change from f to the second day must actually be LESS than 50%, f cannot be quite as small as 6.67 nor quite as big as 20.
Thus, f must be between the two extremes:
6.67 < f < 20.
Question stem:
Which of the following CANNOT be the closing price on the last trading day last month?
Since the percent change from the first trading day to each of the other trading days was less than 50 percent, we need to determine which answer choice must change by 50% OR MORE to yield a value for f such that
6.67 < f < 20.
A:
If $3 increases by 50%, the resulting price for f = 3 + (50/100)3 = 3 + 1.5 = 4.5.
Doesn't work:
The resulting price for f is TOO SMALL.
Implication:
For the resulting price for f to be within the green range above, option A must increase by MORE THAN 50%.
The correct answer is
A.
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