Last visit was: 19 Nov 2025, 20:38 It is currently 19 Nov 2025, 20:38
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
   1   2 
avatar
agar123
avatar
Joined: 03 Sep 2019
Last visit: 19 Oct 2021
Posts: 105
Own Kudos:
46
Given Kudos: 40
Posts: 105
Kudos: 46
On January 1, 2076, Lake Loser contains x liters of water. B 03 Dec 2019, 12:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
TheRob
The answer is D

here is the long explanation

This fraction problem contains an "unspecified" total (the x liters of water in the lake). Pick an easy "smart" number to make this problem easier. Usually, the smart number is the lowest common denominator of all the fractions in the problem. However, if you pick 28, you will quickly see that this yields some unwieldy computation.
The easiest number to work with in this problem is the number 4. Let's say there are 4 liters of water originally in the lake. The question then becomes: During which year is the lake reduced to less than 1 liter of water?
At the end of 2076, there are 4 × (5/7) or 20/7 liters of water in the lake. This is not less than 1.
At the end of 2077, there are (20/7) × (5/7) or 100/49 liters of water in the lake. This is not less than 1.
At the end of 2078, there are (100/49) × (5/7) or 500/343 liters of water in the lake. This is not less than 1.
At the end of 2079, there are (500/343) × (5/7) or 2500/2401 liters of water in the lake. This is not less than 1.
At the end of 2080, there are (2500/2401) × (5/7) or 12500/16807 liters of water in the lake. This is less than 1.
Notice that picking the number 4 is essential to minimizing the computation involved, since it is very easy to see when a fraction falls below 1 (when the numerator becomes less than the denominator.) The only moderately difficult computation involved is multiplying the denominator by 7 for each new year.
The correct answer is D.
Show more

Can you please tell me how you have selected smart number as 4 and how you came up with 28?
User avatar
hero_with_1000_faces
User avatar
Joined: 02 Jan 2016
Last visit: 17 Mar 2025
Posts: 358
Own Kudos:
146
Given Kudos: 314
Status:Studying 4Gmat
Location: India
Concentration: Strategy, Entrepreneurship
Schools: Darden '22 Marshall '22 AGSM '23
GMAT 1: 590 Q37 V33
GPA: 4
WE:Law (Manufacturing)
Products:
My Reviews
Schools: Darden '22 Marshall '22 AGSM '23
GMAT 1: 590 Q37 V33
Posts: 358
Kudos: 146
On January 1, 2076, Lake Loser contains x liters of water. B 23 Feb 2020, 11:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I did this on the basis of estimation
Lets say X =100%

2/7 = 8/98 almost 30%.

year 76 = 100 -30 = 70
year 77 = 70 * 2/7 = 70-20 = 50
year 78 = 50*30/100 = 50 - 15 = 35
year 79 = 35*2/7 = 35 - 10 = 25
year 80 = 25 at begining. 100/4 = 25

hence year 80
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 19 Nov 2025
Posts: 8,422
Own Kudos:
4,982
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,422
Kudos: 4,982
On January 1, 2076, Lake Loser contains x liters of water. B 01 Mar 2020, 02:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
TheRob
On January 1, 2076, Lake Loser contains x liters of water. By Dec 31 of that same year, 2/7 of the x liters have evaporated. This pattern continues such that by the end of each subsequent year the lake has lost 2/7 of the water that it contained at the beginning of that year. During which year will the water in the lake be reduced to less than 1/4 of the original x liters?

A. 2077
B. 2078
C. 2079
D. 2080
E. 2081
Show more

at beginning of 2076 its x liters
and later each year reduced by 2x/7 liters
so at beginning we have 5x/7 liters
need to find time when reduction is less than 1/4 *x
i.e
(5x/7)^n<x/4
n has to be 5 ; 2080
IMO D
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 19 Nov 2025
Posts: 5,794
Own Kudos:
5,514
Given Kudos: 161
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,794
Kudos: 5,514
On January 1, 2076, Lake Loser contains x liters of water. B 25 Sep 2022, 06:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given: On January 1, 2076, Lake Loser contains x liters of water. By Dec 31 of that same year, 2/7 of the x liters have evaporated. This pattern continues such that by the end of each subsequent year the lake has lost 2/7 of the water that it contained at the beginning of that year.

Asked: During which year will the water in the lake be reduced to less than 1/4 of the original x liters?

If water at the start of a year is x, water left after end of that year = x - 2x/7 = 5x/7

At the end of year 2076, water left = 5x/7
At the end of year (2076 + y), water left = x(5/7)^(y+1) < x/4

(5/7)^(y+1) < 1/4
y = 4

2076 + 4 = 2080
In the year 2080, the water in the lake will be reduced to less than 1/4 of the original x liters.

IMO D
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
On January 1, 2076, Lake Loser contains x liters of water. B 24 Mar 2025, 01:55
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.
   1   2 
Moderators:
Bunuel
Math Expert
105390 posts
Krunaal
Tuck School Moderator
805 posts