The closing price of Stock X changed on each trading

[BTGmoderatorRO]

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

OA is A
Can any Expert help me out here?
I am confused<i class="em em-angry"></i>. What formulas should I set here to get the correct answer?[/spoiler]

[mbawisdom]

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

OA is A
Can any Expert help me out here?
I am confused<i class="em em-angry"></i>. What formulas should I set here to get the correct answer?[/spoiler]

Hi Roland2rule, this question resonated with me given my trading background! The question is actually worded incorrectly. I believe that the question should say that the swings are always between -50% and +50% to starting price.

Okay so the key to this question is the following logic: Let's say that the starting price is P0 and the closing price each day is P1, P2 etc.... On each day during the month the price cannot be higher than 1.5P0 or less than 0.5P0! We know that on the second last day the closing price is $10.00. If the price had gone up 50% P0 would be ~$6.66 and if it had gone down 50% it would be $20.00. Our boundary for P0 then is: $6.66 < P0 < $20.00. If P0 is $6.66 the lowest price it can get to in the month is ~$3.33. If P0 is $20.00 the highest price it can get to is ~$30.00. Possible prices on last day range from $3.33 to $30.00.

(A) 3.00 is the only answer outside this boundary.

[GMATGuruNY]

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.

[Scott@TargetTestPrep]

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) ≈ 3.33.

Looking at the answer choices, the only price that is not between 3.33 and 30 is 3.

Answer: A