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

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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
[Reveal] Spoiler: OA

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Re: The closing price of Stock X changed on each trading day last month. T [#permalink]

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New post 29 Jul 2017, 19:30
Hi,

Can someone please explain how to solve this problem?

Thanks in advance

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Re: The closing price of Stock X changed on each trading day last month. T [#permalink]

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New post 29 Jul 2017, 20:22
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carcass wrote:
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


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 ... :)
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Re: The closing price of Stock X changed on each trading day last month. T [#permalink]

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New post 29 Jul 2017, 21:04
shashankism wrote:
carcass wrote:
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


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 ... :)



Thank you Shashank for solution

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The closing price of Stock X changed on each trading day last month. T [#permalink]

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New post 29 Jul 2017, 21:20
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Expert's post
priyesh92 wrote:
Hi,

Can someone please explain how to solve this problem?

Thanks in advance



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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Re: The closing price of Stock X changed on each trading day last month. T [#permalink]

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New post 09 Aug 2017, 13:36
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carcass wrote:
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) ≈ 3.3.

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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Re: The closing price of Stock X changed on each trading day last month. T   [#permalink] 09 Aug 2017, 13:36
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