Bunuel wrote:

The price of each share of stock K, when traded at a certain stock exchange, first goes up by p percent and then falls down by p percent every alternate day. After one such up-down cycle, the price of the stock fell by $2. If, after another such up-down cycle, the price per share of stock K comes to $196.02, what was the original price per share of stock K?

(A) $300

(B) $270

(C) $250

(D) $200

(E) $150

We are given that after the first up-down cycle, the price only fell $2 and the price is $196.02 after two up-down cycles. So, the original price would be higher than $196.02 but not that much higher. We see that of all the given answer choices, $200 is the one that fits the criteria. So, we can make an educated guess that $200 is the right answer. Of course, we should also check that it is the right answer:

If the original price is $200 and after the first up-down cycle the price fell $2, the price fell to $198, which is a 1% decrease. After the second up-down cycle, the price should fall another 1% (but from $198). So, the price would be 198(0.99) = $196.02, which is exactly what the price was after two up-down cycles. So, the original price was indeed $200.

Answer: D

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