GMAT Percentages Explained — Closing price of Stock X...

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?

percentagesinequalitiesword problemstranslationsrelative changes

Explanation	Calculations	Help
$We first create variables for the closing price on the first trading day and on the last trading day.$	$P_{1} = closing price on first trading day P_{n} = closing price on last trading day$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the statement that the percent change from the first trading day to any other trading day is less than 50 percent.$	$(∣ \frac{P _{j} - P _{1}}{P _{1}}) ∣ < 0.5$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We apply this inequality to the second trading day, where the closing price was ten dollars, and solve for P_{1} .$	$(∣ \frac{10 - P _{1}}{P _{1}}) ∣ < 0.5 - 0.5 < \frac{10 - P _{1}}{P _{1}} < 0.5 - 0.5 P_{1} < 10 - P_{1} < 0.5 P_{1} 10 > 0.5 P_{1} P_{1} < 20 10 < 1.5 P_{1} P_{1} > \frac{10}{1.5} \approx 6.667 6.667 < P_{1} < 20$
$We translate the same percent change constraint for the last trading day price and express its bounds in terms of P_{1} .$	$(∣ \frac{P _{n} - P _{1}}{P _{1}}) ∣ < 0.5 0.5 P_{1} < P_{n} < 1.5 P_{1}$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We test option A by checking if any P_{1} in the valid range can satisfy the bound for P_{n} = 3.00, and find none, so 3.00 cannot be the closing price on the last trading day.$	$P_{n} = 3.00 0.5 P_{1} < 3 < 1.5 P_{1} 2 < P_{1} < 6 But from before 6.667 < P_{1} < 20, so there is no overlap.$

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A. 3.00 cannot satisfy the percent change constraint.