Last visit was: 31 Oct 2024, 16:34 It is currently 31 Oct 2024, 16:34
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
655-705 Level|   Percent and Interest Problems|                     
User avatar
carcass
User avatar
Board of Directors
Joined: 01 Sep 2010
Last visit: 31 Oct 2024
Posts: 4,592
Own Kudos:
Given Kudos: 4,654
Posts: 4,592
Kudos: 34,472
 [558]
23
Kudos
Add Kudos
534
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 3,026
Own Kudos:
7,037
 [191]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert reply
Posts: 3,026
Kudos: 7,037
 [191]
111
Kudos
Add Kudos
79
Bookmarks
Bookmark this Post
User avatar
shashankism
Joined: 13 Mar 2017
Last visit: 20 Jun 2024
Posts: 623
Own Kudos:
617
 [44]
Given Kudos: 88
Affiliations: IIT Dhanbad
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy)
Posts: 623
Kudos: 617
 [44]
34
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
General Discussion
User avatar
chetan2u
User avatar
RC & DI Moderator
Joined: 02 Aug 2009
Last visit: 31 Oct 2024
Posts: 11,495
Own Kudos:
37,129
 [32]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert reply
Posts: 11,495
Kudos: 37,129
 [32]
18
Kudos
Add Kudos
14
Bookmarks
Bookmark this Post
priyesh92
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


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
User avatar
longhaul123
Joined: 03 Jul 2017
Last visit: 11 Nov 2018
Posts: 142
Own Kudos:
33
 [8]
Given Kudos: 27
Status:IF YOU CAN DREAM IT, YOU CAN DO IT
Location: India
Concentration: Finance, International Business
Posts: 142
Kudos: 33
 [8]
8
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
Dorsano505
Joined: 10 Feb 2018
Last visit: 30 Jan 2022
Posts: 6
Own Kudos:
94
 [14]
Given Kudos: 67
GMAT 1: 670 Q44 V38
GMAT 2: 710 Q48 V40
WE:Project Management (Healthcare/Pharmaceuticals)
GMAT 1: 670 Q44 V38
GMAT 2: 710 Q48 V40
Posts: 6
Kudos: 94
 [14]
13
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
longhaul123
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.
User avatar
Probus
Joined: 10 Apr 2018
Last visit: 22 May 2020
Posts: 183
Own Kudos:
475
 [6]
Given Kudos: 115
Location: United States (NC)
Posts: 183
Kudos: 475
 [6]
4
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
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.
User avatar
MidhilaMohan
Joined: 03 Mar 2017
Last visit: 22 Oct 2024
Posts: 115
Own Kudos:
66
 [1]
Given Kudos: 76
Location: India
GMAT 1: 680 Q49 V34
Products:
GMAT 1: 680 Q49 V34
Posts: 115
Kudos: 66
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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
User avatar
gauravjain0211
Joined: 19 Jan 2017
Last visit: 29 Oct 2024
Posts: 15
Own Kudos:
7
 [1]
Given Kudos: 13
Posts: 15
Kudos: 7
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
carcass
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

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.
User avatar
ThatDudeKnows
Joined: 11 May 2022
Last visit: 27 Jun 2024
Posts: 1,080
Own Kudos:
784
 [4]
Given Kudos: 79
Expert reply
Posts: 1,080
Kudos: 784
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
carcass
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

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
User avatar
genericUser
Joined: 31 Jan 2022
Last visit: 22 Dec 2023
Posts: 113
Own Kudos:
Given Kudos: 35
Location: Italy
GMAT 1: 670 Q49 V33
GMAT 2: 690 Q47 V37
GPA: 3.9
GMAT 1: 670 Q49 V33
GMAT 2: 690 Q47 V37
Posts: 113
Kudos: 77
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.

Attachment:
File comment: figure
fig.png
fig.png [ 17.94 KiB | Viewed 25265 times ]

look at the figure and the only price that does not fit is 3$.
User avatar
woohoo921
Joined: 04 Jun 2020
Last visit: 17 Mar 2023
Posts: 532
Own Kudos:
Given Kudos: 623
Posts: 532
Kudos: 101
Kudos
Add Kudos
Bookmarks
Bookmark this Post
JeffTargetTestPrep
carcass
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

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.
User avatar
MartyTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 24 Nov 2014
Last visit: 11 Aug 2023
Posts: 3,479
Own Kudos:
Given Kudos: 1,431
Status:Chief Curriculum and Content Architect
Affiliations: Target Test Prep
GMAT 1: 800 Q51 V51
Expert reply
GMAT 1: 800 Q51 V51
Posts: 3,479
Kudos: 5,302
Kudos
Add Kudos
Bookmarks
Bookmark this Post
woohoo921
JeffTargetTestPrep
carcass
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

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.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
JeffTargetTestPrep
carcass
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

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?
avatar
MT1302
Joined: 10 Jan 2023
Last visit: 30 Oct 2024
Posts: 104
Own Kudos:
Given Kudos: 36
Location: India
Posts: 104
Kudos: 349
Kudos
Add Kudos
Bookmarks
Bookmark this Post
carcass
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
­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 ?­
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 31 Oct 2024
Posts: 96,533
Own Kudos:
Given Kudos: 87,883
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,533
Kudos: 673,099
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Gangadhar111990
carcass
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
­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.­
avatar
MT1302
Joined: 10 Jan 2023
Last visit: 30 Oct 2024
Posts: 104
Own Kudos:
Given Kudos: 36
Location: India
Posts: 104
Kudos: 349
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Gangadhar111990
carcass
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
­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.­
­
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 ? 
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 31 Oct 2024
Posts: 96,533
Own Kudos:
Given Kudos: 87,883
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,533
Kudos: 673,099
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Gangadhar111990
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.­
User avatar
Catman
Joined: 03 Aug 2017
Last visit: 05 Oct 2024
Posts: 365
Own Kudos:
305
 [1]
Given Kudos: 219
Products:
Posts: 365
Kudos: 305
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
 
Quote:
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.
The stock market regulators have implemented new rules to manage the volatility of a specific stock, let's call it "P". According to these rules, the price of stock P throughout the entire month will be confined within a range determined by its first day's trading price. Here's how it works: 
  1. The upper limit or highest range of the stock price cannot exceed 50% of its price on the first trading day.
  2. The lower limit or lowest range of the stock price cannot be less than 50% of its price on the first trading day.
Given the price of stock "P" on the second day = $10.

Now, depending on whether the stock ended the first day in an upper circuit or a lower circuit, the range for the first day's price can be determined : 
  • If the stock ended in the upper circuit on the second day, the lowest price on the first day would be \(\frac{$10 }{ 1.5}\)=  $6.67.
  • If the stock ended in the lower circuit on the first day, the highest price on the first day would be \(\frac{$10 }{ 0.5} \)= $20
  Now, let's apply these rules to determine the price range for the entire month:
  • The lowest price for the entire month would be \(\frac{$6.67 }{ 0.5}\) = $3.33.
  • The highest price for the entire month would be \($20 * 1.5\) = $30
On any trading day throughout the month, the price of stock P can fluctuate between $3.33 and $30.

Option A $3 cannot be the price of the stock on any day.
 ­
Moderator:
Math Expert
96533 posts