Question: 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?
- $3.00
- $9.00
- $19.00
- $24.00
- $29.00
The Closing Price of Stock X Changed on Each Trading Day Last Month GMAT Problem Solving – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical understanding.
Solution and Explanation:
Approach Solution:
Given to us that 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. The closing price on the second trading day last month was $ 10.00, it is asked which of the following cannot be the closing price on the last trading day last month.
Firstly it is important to determine the range for the closing price on the first trading day of the previous month.
Let the closing price of the first day be denoted by x.
We are given that the closing price of stock X on the second day of last trading month was $10.
It should be noted that x cannot increase by more than 50% to become $10. Also x could not decrease by more than 50% to become 10.
Let us assume that x increased by 50 % to become $10 then,
1.5(x) = $10
=> x = 6.67
And if we assume that x is decreased by 50% to become $10 then,
0.5(x) = $10
=> x = 20
Therefore by taking boundary conditions we found the upper limit and lower limit of x in the last trading day of the previous month.
Since the closing price on the last trading day can be at most 50% more than the closing price on the first trading day of the previous month. The closing price on the last day of the previous month has to 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 on the first trading day of the previous month. The closing price on the last day of previous month has to be more than (0.5)*6.67 = 3.33
Therefore the only value that is not in the limit of [3.33, 30] is 3.
Therefore $3.0 is the correct answer which is option A.
Correct Answer: A
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