The closing price of Stock X changed on each trading day last month.

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) ≈ 3.3.

Looking at the answer choices, the only price that is not greater than 3.3 and less than 30 is 3.

Answer: A
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Price of stock X on 2nd day was $10
Since %ge change of first day w.r.t any other day of the month cannot be more than 50%
So, y<Price of stock X on 1st day <x
Now ((10-y)/y )*100 = 50
-> (10-y)/y = .5
-> 10 - y = .5y
y = 10 /1.5 = 6.666

x-10 /x = .5
x -10 = .5x
.5x = 10
x = 20

So, 6.6666< Price of stock X on 1st day < 20
Since price on other days can vary by only 50% from the 1st day.
So, 6.6666*0.5 < Price of stock X on other days < 20*1.5
3.3333< Price of stock X on other days < 30

Only option A i.e. $3 doesn't lies in this range.

Hence Answer A

Appreciate if you liked my solution ...

Hi..

Although the solution is already provided, just a point for knowledge..

whenever we are looking at a Q like this, where there is an open ended range , for example less than 50% here..
ONE of the extremes should be the answer..
here it is either 3 or 29..
so your probability of answering is now 50%..

otherwise..
10 could be after increase from 1st day..
so \(x+0.5x>10.... 1.5x>10 .... x>\frac{10}{1.5}....x>6.67\)
now the lowest value possible is \(6.67*0.5 = 3.33\)
straight 3 is out..

otherwise if 10 has come after decrease from 1st day..
x-0.5x<10....0.5x<10...x<20
upper end is 20*1.5=30..

ans A
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One doubt. So is the question suggesting that the percent change is with respect to the price on the first day?? I thought the price of the stock on the last day if we assume that there were 30 days depends on the price of the stock on the 29th day. Where am I going wrong. Kindly help. Thanks

I believe the information you are referring t is in this sentence "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."

I think you are saying that the percent change is less than 50% from each day to the next day, but the section above is saying that the price cannot change more or less that 50% from the first day.

For example day 2 is $10, so to find the range of x for the first day we need 2 equations:
x(1.5) = 10 .... x=6.67
x(.5) = 10 .... x=20

This is the range of values for the first day, 6.67 < x < 20, so every other day in the month can not vary more than 50% from these extremes.

6.67*(.5)<x<20*(1.5) .... 3.33 < x < 30

So this 3.33 to 30 is not only the range for the last day of the month, it is also the range for all the days of the month (besides day 2 which is known) because all days can not vary by more than 50% from the first day.

The most important part of the question is " 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" Which defines what our answer will be because the price on last trading day would also deviate at most 50 % from prices on day 1. i.e It could be at most 50% more than price in day 1 or it could be at most 50% less than price on day 1.

So essentially we need to know the range of prices on day 1.
Now ,We are told that the price on second day is 10 $. This 10 $ is at most 50 % more than price on day 1 or it is at most 50% less than price on day 1.
So lets say price on day 1 was x if it increased at most 50 % to be 10$ on day 2. which means x(1.5) =10 Then x= 10/1.5=> x= 6.66
So lets say price on day 1 was y if it decreased at most 50 % to be 10$ on day 2. Which means y(.5) =10 ,Then y= 10/.5=> y= 20

Now the price on last day would be at most more than 50% of the price on day 1
Price on day 1 was either 6.66 or 20
20(1.5)= 30
6.66(1.5) =10

or it could be a most less than 50% of the price on day 1
20(.5)=10
6.66(.5)= 3.333

we have max and min prices as 30 and 3.33

So the price would never go below 3.33, hence $ 3 can never be the price any day.
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The variation between intraday prices is less than 50%- essentially has to be <= 49.999999%
Let the Price on the first day be x
So if the price on second day is 10 then the price on the first day can be between either of the 2 extreme limits
1.5 *x = 10 to 0.5 *x =10
x= 20/3(if 10 is a 50% increment) or
x=20 (if 10 is a 50% decrement)

If x=20/3 then the range of x will be +/- 50% i.e. 3.33 to 10

If x=20 then the range of x will be +/- 50% i.e. 10 to 30

Either condition option A-> 3 is not possible

First important thing to notice is the language of the question
comparison of anyday is done with first day

0.5 first < second or any other day <1.5 first (cause change is less than 50%) (Hence second cannot be 1.5 or more and 0.5 or less )

so first < (2* second = 20)
first > (2/3*second = 20/3)

now let's use the inequality again

0.5 first < any day < 1.5 first

20/6 < anyday < 30

$3 is out of the range, hence cannot be the closing price.

This is sort of a ballparking question (maybe more logic than ballparking, but stop picking nits!).

The answer can't be B, C, or D. If the stock couldn't reach $19, it wouldn't be able to reach $29, either, and both answers can't be right. So, we need one of the extreme answers: either A or E. Just test one. If it works, you've got your answer; if it doesn't work, go with the other one.

I'd rather work up from $10 rather than down, so I'll go with E.

The highest the price could have been on day 1 was $20. If it lost 50% of that from day 1 to day 2, it would have been at $10, which is what we're given.

Okay, is $29 within the bounds? Yes, $29 is less than a 50% increase over the $20 from day 1. Answer choice E is wrong.

Answer choice A.

ThatDudeKnowsBallparking

the stem tells us that the closing price of the stock is comprize between +50 and -50 of the closing price of the first day.
we have the price of the second day though, and this price can be reached, from day one, with an increase or with a decrease.
Lets take into account both possibility, and then from the prices of day one with +-50 we can find the band that must contain all the prices.



look at the figure and the only price that does not fit is 3$.

MartyTargetTestPrep
Happy Holidays! I am so sorry to bother you but am really struggling with this problem still. I interpreted the percentage change as a consecutive increase or decrease. So, 10*.5*.5*.5+.5... or 10*1.5*1.5*1.5....

Why isn't this the case?

Thank you in advance.

I agree that the question is somewhat challenging to understand. At the same time, notice that it says the following:

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.

We see only "from the first trading day last month" TO "each of the other trading days."

The question doesn't mention "the percent change each day" or "the daily change" or something along those lines.

So, we go with the idea that the change in question is the change in price from the first day's closing price to the closing price on any other day.
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Hi Jeff,

Why do you say that the closing price on the last trading day can be at most 50% more/less than the closing price of the first day of last month?
Doesn't it change daily?
If it is daily, shouldn't be the reference is the day before the last trading day, instead of the first day of last month?

­Hello MartyMurray Sir,

I am asking this just to enhance my understanding and not to fall for traps in exam. 

Suppos if the question mentions this line :

If the closing price on the FIFTH trading day last month was $ 10.00 .

Then how should we proceed to solve it?­ (Assumption : X = clsoing price on 1st trading day )

Will this be (4*0.5 x) < x < (4* 1.5 x) ?­

So, (4 * 0.5 x ) = 10 & (4*1.5 x) = 10 ; to determine the value of x ?­

­

No, the price of the stock on the first day would still be in the range from $20/3 to $15. What "The percent change in the price of the stock the first day to each of the other trading days was less than 50 percent" essentially means is that the price of the stock did not change by more than 50% from the first day compared to any of the other days.­
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­
Bunuel

I am trying to understand what you just said .

So , suppose closing price of the stock on first trading day is 100$ then, on second trading day it will be in the range of 50$ to 150$ . Am I correct ?
Then, what about 3rd day closing price? What range will it be in ? 

­If the price of the stock on the first day was $100, then on ANY other day it's in the range from $50 to $150.­
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