The price of each share of stock K, when traded at a certain stock exc

Question

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

(A) $300
(B) $270
(C) $250
(D) $200
(E) $150

ScottTargetTestPrep · Accepted Answer

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

elegantm · Answer

Logical Approach   
After 1st up-down cycle, Price decreased by = 2
After 2nd up-down cycle, final Price of the stock is = 196.02
 After 2nd up-down cycle, Price should also decrease by the same tune. But this time, decrease would be little bit less than $2 because after first cycle price of the stock has decreased by 2

So we could safely assume that after two cycles price decrease by 4. 
So the initial price of the stock should be = 196.02 + 4 = 200

Closest option is D

Hence Answer D

TimeTraveller · Answer

Let the original price per share of stock K be $100, and p = 10%.

First cycle: $100 --> $110 --> $99.

Fall in price for a $100 share = $1, so for a $2 fall in price, the share price might be $200.

First cycle: $200 --> $220 --> $198
Second cycle: $198 --> $217.8 --> $196.02.

Ans - D.

The price of each share of stock K, when traded at a certain stock exc

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The price of each share of stock K, when traded at a certain stock exc

Prep Toolkit

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