Last visit was: 19 Nov 2025, 16:15 It is currently 19 Nov 2025, 16:15
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
805+ Level|   Algebra|   Arithmetic|   Word Problems|      
User avatar
souvik101990
User avatar
Joined: 19 Mar 2012
Last visit: 11 Nov 2025
Posts: 4,321
Own Kudos:
53,094
 [87]
Given Kudos: 2,326
Location: United States (WA)
Concentration: Leadership, General Management
Schools: Ross '20 (M)
GMAT 1: 760 Q50 V42
GMAT 2: 740 Q49 V42 (Online)
GMAT 3: 760 Q50 V42 (Online)
GPA: 3.8
WE:Marketing (Non-Profit and Government)
Products:
My Reviews
Expert
Expert reply
Schools: Ross '20 (M)
GMAT 3: 760 Q50 V42 (Online)
Posts: 4,321
Kudos: 53,094
 [87]
List M consists of 50 decimals, each of which has a value between 10 May 2018, 11:15
5
Kudos
Add Kudos
82
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

33% (02:46) correct 67% (02:52) wrong based on 654 sessions

History

Date
Time
Result
Not Attempted Yet
List M consists of 50 decimals, each of which has a value between 1 and 10 and has two non-zero digits after the decimal place (e.g. 5.68 could be a number in List M). The sum of the 50 decimals is S. The truncated sum of the 50 decimals, T, is defined as follows. Each decimal in List M is rounded down to the nearest integer (e.g. 5.68 would be rounded down to 5); T is the sum of the resulting integers. If S - T is x percent of T, which of the following is a possible value of x?

I. 2%
II. 34%
III. 99%

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III­

Show Spoiler

GST Week 5 Day 3 Manhattan Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and 6 Practice Tests + 9 Question Banks + Challenge Problem Archive + GMAT Navigator from Manhattan Prep. See the GMAT Spring Training Thread for all details
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,739
Own Kudos:
35,355
 [18]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,739
Kudos: 35,355
 [18]
List M consists of 50 decimals, each of which has a value between 29 Sep 2018, 07:46
11
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
souvik101990

GST Week 5 Day 3 Manhattan Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and 6 Practice Tests + 9 Question Banks + Challenge Problem Archive + GMAT Navigator from Manhattan Prep. See the GMAT Spring Training Thread for all details

List M consists of 50 decimals, each of which has a value between 1 and 10 and has two non-zero digits after the decimal place (e.g. 5.68 could be a number in List M). The sum of the 50 decimals is S. The truncated sum of the 50 decimals, T, is defined as follows. Each decimal in List M is rounded down to the nearest integer (e.g. 5.68 would be rounded down to 5); T is the sum of the resulting integers. If S - T is x percent of T, which of the following is a possible value of x?

I. 2%
II. 34%
III. 99%

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Show more

Let's examine the EXTREME CASES

S - T = x percent of T
So, S - T = (x/100)T
Divide both sides by to get: (S - T)/T = x/100
Multiply both sides by 100 to get: x = 100(S - T)/T

First, we we'll MINIMIZE the value of x by minimizing the value of S - T and maximizing the value of T.
This occurs when list M = {9.11, 9.11, 9.11, 9.11, 9.11, 9.11, . . . . .9.11, 9.11}
So, S = (50)(9.11)
And T = (50)(9)

So, S - T = (50)(9.11) - (50)(9)
= (50)(9.11 - 9)
= (50)(0.11)

Plug these values into the above equation to get x =100(50)(0.11)/(50)(9)
= 100(0.11)/9
= 11/9
≈1.2222...
So, the MINIMUM value of x is approximately 1.22%

First, we we'll MAXIMIZE the value of x by maximizing the value of S - T and minimizing the value of T.
This occurs when list M = {1.99, 1.99, 1.99, 1.99, 1.99, . . . 1.99, 1.99}
So, S = (50)(1.99)
And T = (50)(1)

So, S - T = (50)(1.99) - (50)(1)
= (50)(1.99 - 1)
= (50)(0.99)

Plug these values into the above equation to get x =100(50)(0.99)/(50)(1)
= 100(0.99)/1
= 99
So, the MAXIMUM value of x is 99%

Combine the results to get: 1.22% < x ≤ 99%
All three values (2%, 34% and 99%) fall within this range of x-values.

Answer: E

Cheers,
Brent
avatar
gump2020
avatar
Joined: 02 May 2018
Last visit: 14 Jun 2019
Posts: 3
Own Kudos:
11
 [11]
Posts: 3
Kudos: 11
 [11]
List M consists of 50 decimals, each of which has a value between 10 May 2018, 14:14
8
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
IMO Answer is E.

Here is why:

Given is the expression (S-T)/T = ((S/T) - 1)

Where S - Sum of 50 decimals
T - Sum of the 50 truncated decimals

Let’s test each answer choice:

i) 2%

((S/T)-1) = 2/100

S/T = (2/100)+1 = 102/100

Simplified to S/T = 51/50

Certainly a possibility if each decimal in S is 1.02, added 50 times & hence each decimal in T is 1, added 50 times.

So i) is possible.

ii) 34%

((S/T)-1) = 34/100

S/T = (34/100) + 1 = 134/100

Simplified to S/T = 67/50

Certainly possible if each decimal in S is 1.34, added 50 times & hence each decimal in T is 1, added 50 times.

So ii) is possible


iii) 99%


((S/T)-1) = 99/100

S/T = (99/100) + 1 = 199/100

Simplified to S/T = 99.5/50

Certainly possible if each decimal in S is 1.99, added 50 times & hence each decimal in T is 1, added 50 times.

So iii) is possible.

Answer is choice E.

I may have gone horribly stupid wrong here, since it’s past 2 am & I am half sleepy, with slightly drunk from my birthday party. Thanks if you wished me.

Gump.



Sent from my iPhone using GMAT Club Forum
General Discussion
avatar
Ritz1605
avatar
Joined: 20 Jan 2018
Last visit: 02 Jan 2021
Posts: 11
Own Kudos:
6
 [1]
Given Kudos: 58
Location: India
Schools: ISB '20 (A)
GMAT 1: 620 Q50 V24
GMAT 2: 710 Q51 V34
GPA: 3.9
Products:
My Reviews
Schools: ISB '20 (A)
GMAT 2: 710 Q51 V34
Posts: 11
Kudos: 6
 [1]
List M consists of 50 decimals, each of which has a value between 10 May 2018, 11:42
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
souvik101990

GST Week 5 Day 3 Manhattan Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and 6 Practice Tests + 9 Question Banks + Challenge Problem Archive + GMAT Navigator from Manhattan Prep. See the GMAT Spring Training Thread for all details

List M consists of 50 decimals, each of which has a value between 1 and 10 and has two non-zero digits after the decimal place (e.g. 5.68 could be a number in List M). The sum of the 50 decimals is S. The truncated sum of the 50 decimals, T, is defined as follows. Each decimal in List M is rounded down to the nearest integer (e.g. 5.68 would be rounded down to 5); T is the sum of the resulting integers. If S - T is x percent of T, which of the following is a possible value of x?

I. 2%
II. 34%
III. 99%

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Show more

C according to me,
can be checked by taking values for eg (reducing the cardinal no of set M):
case 1: M={1.96,1.97,1.98,1.99}
s-t/t =3.9/4 = 97.5 approx(taking only 4 maximum values)
so the % cannot be 99 in any case since 50 elements are there)

case2: M={5.12,6.02,7.03,8.04}
s-t/t is definetly <2%, so, 2 can be a possible value.

so these are the two extremes and any value b/w these % can be a ratio.
User avatar
kunalcvrce
User avatar
Joined: 05 Feb 2016
Last visit: 09 Apr 2025
Posts: 132
Own Kudos:
131
 [4]
Given Kudos: 72
Location: India
Concentration: General Management, Marketing
WE:Information Technology (Computer Software)
Posts: 132
Kudos: 131
 [4]
List M consists of 50 decimals, each of which has a value between 10 May 2018, 11:47
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
souvik101990

GST Week 5 Day 3 Manhattan Prep Question 3


Give your best shot at writing a top notch explanation and you will have the chance to win GMAT Club tests daily and 6 Practice Tests + 9 Question Banks + Challenge Problem Archive + GMAT Navigator from Manhattan Prep. See the GMAT Spring Training Thread for all details

List M consists of 50 decimals, each of which has a value between 1 and 10 and has two non-zero digits after the decimal place (e.g. 5.68 could be a number in List M). The sum of the 50 decimals is S. The truncated sum of the 50 decimals, T, is defined as follows. Each decimal in List M is rounded down to the nearest integer (e.g. 5.68 would be rounded down to 5); T is the sum of the resulting integers. If S - T is x percent of T, which of the following is a possible value of x?

I. 2%
II. 34%
III. 99%

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Show more

Question mention possible values:
So let find the range of \(\frac{(S - T )}{T}*100\)

Maximum percent will be when S-T will be max and T will be min
since S is in the form abc.yz and T will be x(rounded down)
List M , term will be in form a+.bc
when rounded down it will be a
subtracting both=.bc
Therefore ,S-T=.YZ
max value S-T=.99*50 when first term= 1.99 and rounded down value=1
T=1*50
\(((S-T)/T)*100=99\)

Min value when first term =9.11 and rounded value =9
S-T=.11*50
T=9*50

\(((S-T)/T)*100=1.22\)

So all three value will satisfy

option E
avatar
issacsolomon
avatar
Joined: 13 Nov 2017
Last visit: 14 Jun 2021
Posts: 3
Given Kudos: 21
Posts: 3
Kudos: 0
List M consists of 50 decimals, each of which has a value between 12 May 2018, 11:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gump2020
IMO Answer is E.

Here is why:

Given is the expression (S-T)/T = ((S/T) - 1)

Where S - Sum of 50 decimals
T - Sum of the 50 truncated decimals

Let’s test each answer choice:

i) 2%

((S/T)-1) = 2/100

S/T = (2/100)+1 = 102/100

Simplified to S/T = 51/50

Certainly a possibility if each decimal in S is 1.02, added 50 times & hence each decimal in T is 1, added 50 times.

So i) is possible.

ii) 34%

((S/T)-1) = 34/100

S/T = (34/100) + 1 = 134/100

Simplified to S/T = 67/50

Certainly possible if each decimal in S is 1.34, added 50 times & hence each decimal in T is 1, added 50 times.

So ii) is possible


iii) 99%


((S/T)-1) = 99/100

S/T = (99/100) + 1 = 199/100

Simplified to S/T = 99.5/50

Certainly possible if each decimal in S is 1.99, added 50 times & hence each decimal in T is 1, added 50 times.

So iii) is possible.

Answer is choice E.

I may have gone horribly stupid wrong here, since it’s past 2 am & I am half sleepy, with slightly drunk from my birthday party. Thanks if you wished me.

Gump.



Sent from my iPhone using GMAT Club Forum
Show more

Just one thing in the first part of your explanation

1.02 can be possible right? given that the two decimal digits need to be non zero?
User avatar
push12345
User avatar
Joined: 02 Oct 2017
Last visit: 10 Feb 2019
Posts: 536
Own Kudos:
535
Given Kudos: 14
Posts: 536
Kudos: 535
List M consists of 50 decimals, each of which has a value between 26 May 2018, 22:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gump2020
IMO Answer is E.

Here is why:

Given is the expression (S-T)/T = ((S/T) - 1)

Where S - Sum of 50 decimals
T - Sum of the 50 truncated decimals

Let’s test each answer choice:

i) 2%

((S/T)-1) = 2/100

S/T = (2/100)+1 = 102/100

Simplified to S/T = 51/50

Certainly a possibility if each decimal in S is 1.02, added 50 times & hence each decimal in T is 1, added 50 times.

So i) is possible.

ii) 34%

((S/T)-1) = 34/100

S/T = (34/100) + 1 = 134/100

Simplified to S/T = 67/50

Certainly possible if each decimal in S is 1.34, added 50 times & hence each decimal in T is 1, added 50 times.

So ii) is possible


iii) 99%


((S/T)-1) = 99/100

S/T = (99/100) + 1 = 199/100

Simplified to S/T = 99.5/50

Certainly possible if each decimal in S is 1.99, added 50 times & hence each decimal in T is 1, added 50 times.

So iii) is possible.

Answer is choice E.

I may have gone horribly stupid wrong here, since it’s past 2 am & I am half sleepy, with slightly drunk from my birthday party. Thanks if you wished me.

Gump.



Sent from my iPhone using GMAT Club Forum
Show more

Explanation of I) 2% is not correct as we can't have 1.02 as it is mentioned in question that we have two non zero decimal digits.

Rest all is fine.
I would love to go with approach kunalcvrce has .it covers all aspects in single way

Posted from my mobile device
User avatar
pushpakb
User avatar
Joined: 09 Sep 2019
Last visit: 21 Sep 2020
Posts: 3
Given Kudos: 12
Posts: 3
Kudos: 0
List M consists of 50 decimals, each of which has a value between 22 Oct 2019, 09:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATPrepNow

Hi Brent - could you kindly explain why you took 9.11 in the first case instead of 9.99, and 1.99 in the second case instead of 1.11?
Thanks,
Pushpak
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,739
Own Kudos:
35,355
 [2]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,739
Kudos: 35,355
 [2]
List M consists of 50 decimals, each of which has a value between 22 Oct 2019, 12:02
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
pushpakb
GMATPrepNow

Hi Brent - could you kindly explain why you took 9.11 in the first case instead of 9.99, and 1.99 in the second case instead of 1.11?
Thanks,
Pushpak
Show more

Given: x = 100(S - T)/T
To MINIMIZE the value of x we must minimize the value of S - T and maximizing the value of T.
9.99 rounds down to 9, and also 9.11 rounds down to 9. So, T is the same in both cases.
However, if we use 9.99, then S - T = 9.99 - 9 = 0.99, so (S-T)/T = 0.99/9
If we use 9.11, then S - T = 9.11 - 9 = 0.11, so (S-T)/T = 0.11/9

0.11/9 < 0.99/9
So, (S - T)/T is minimized when we use 9.11

Does that help?
User avatar
pushpakb
User avatar
Joined: 09 Sep 2019
Last visit: 21 Sep 2020
Posts: 3
Given Kudos: 12
Posts: 3
Kudos: 0
List M consists of 50 decimals, each of which has a value between 22 Oct 2019, 12:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATPrepNow
pushpakb


Hi Brent - could you kindly explain why you took 9.11 in the first case instead of 9.99, and 1.99 in the second case instead of 1.11?
Thanks,
Pushpak

Given: x = 100(S - T)/T
To MINIMIZE the value of x we must minimize the value of S - T and maximizing the value of T.
9.99 rounds down to 9, and also 9.11 rounds down to 9. So, T is the same in both cases.
However, if we use 9.99, then S - T = 9.99 - 9 = 0.99, so (S-T)/T = 0.99/9
If we use 9.11, then S - T = 9.11 - 9 = 0.11, so (S-T)/T = 0.11/9

0.11/9 < 0.99/9
So, (S - T)/T is minimized when we use 9.11

Does that help?
Show more

Ok! Now it makes sense! Thank you!
User avatar
Sarabjeets746
User avatar
Joined: 26 Sep 2020
Last visit: 29 Apr 2023
Posts: 34
Own Kudos:
19
Given Kudos: 191
Status:I'm done with GMAT.
Location: India
Concentration: Marketing, Entrepreneurship
Schools: DeGroote (A) Schulich Sep'23 intake (A) Desautels '25 (D) MBS (D) Said '24 (D)
GMAT 1: 630 Q44 V32
GMAT 2: 690 Q48 V38
GMAT 3: 700 Q48 V37
GPA: 1
WE:General Management (Retail: E-commerce)
Schools: DeGroote (A) Schulich Sep'23 intake (A) Desautels '25 (D) MBS (D) Said '24 (D)
GMAT 3: 700 Q48 V37
Posts: 34
Kudos: 19
List M consists of 50 decimals, each of which has a value between 18 Mar 2021, 02:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gump2020
IMO Answer is E.

Here is why:

Given is the expression (S-T)/T = ((S/T) - 1)

Where S - Sum of 50 decimals
T - Sum of the 50 truncated decimals

Let’s test each answer choice:

i) 2%

((S/T)-1) = 2/100

S/T = (2/100)+1 = 102/100

Simplified to S/T = 51/50

Certainly a possibility if each decimal in S is 1.02, added 50 times & hence each decimal in T is 1, added 50 times.

So i) is possible.

ii) 34%

((S/T)-1) = 34/100

S/T = (34/100) + 1 = 134/100

Simplified to S/T = 67/50

Certainly possible if each decimal in S is 1.34, added 50 times & hence each decimal in T is 1, added 50 times.

So ii) is possible


iii) 99%


((S/T)-1) = 99/100

S/T = (99/100) + 1 = 199/100

Simplified to S/T = 99.5/50

Certainly possible if each decimal in S is 1.99, added 50 times & hence each decimal in T is 1, added 50 times.

So iii) is possible.

Answer is choice E.

I may have gone horribly stupid wrong here, since it’s past 2 am & I am half sleepy, with slightly drunk from my birthday party. Thanks if you wished me.

Gump.



Sent from my iPhone using GMAT Club Forum
Show more

There is a slight error indeed. The question clearly says here that there are two 'non-zero' digits after the decimal. In your solution you have mentioned '1.02' as a possibility for statement I.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,589
Own Kudos:
1,079
Posts: 38,589
Kudos: 1,079
List M consists of 50 decimals, each of which has a value between 01 Nov 2024, 04:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105390 posts
Krunaal
Tuck School Moderator
805 posts