Last visit was: 20 May 2026, 21:53 It is currently 20 May 2026, 21:53
Home
Messages
Tests
Schools
Events
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   3   4   
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 May 2026
Posts: 110,751
Own Kudos:
816,021
 [17]
Given Kudos: 106,345
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,751
Kudos: 816,021
 [17]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:00
6
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
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:

64% (02:28) correct 36% (03:07) wrong based on 203 sessions

History

Date
Time
Result
Not Attempted Yet
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

M46-11

Gift
12 Days of Christmas Competition
This question is part of our holiday event
Win $40,000 in prizes: courses, tests, and more
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 May 2026
Posts: 110,751
Own Kudos:
816,021
 [5]
Given Kudos: 106,345
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,751
Kudos: 816,021
 [5]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 10:00
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only
Show more

GMAT Club Official Explanation:



The average rate over the two days is 240/14 ≈ 17.1. An average must lie between the individual rates. If the rate on the second day was r and the rate on the first day was r + 8, then the average of 17.1 must satisfy r < 17.1 < r + 8.

Now let's check the options:

I. 9

If r = 9, then r + 8 = 17. Both rates (9 and 17) are below the average of 17.1, which is not possible.

II: 14

If r = 14, then r + 8 = 22. The average of 17.1 lies between 14 and 22, so this is possible.

III: 19

If r = 19, then r + 8 = 27. Both rates (19 and 27) are above the average of 17.1, which is not possible.

Answer: B.
General Discussion
User avatar
adityamntr
User avatar
Joined: 15 Jul 2023
Last visit: 21 Feb 2026
Posts: 111
Own Kudos:
81
 [2]
Given Kudos: 13
Location: India
Concentration: General Management, Strategy
Schools: Booth '27 Fuqua '27 Kellog '27
Schools: Booth '27 Fuqua '27 Kellog '27
Posts: 111
Kudos: 81
 [2]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:09
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
taking avg of speed done on both day
a be speeed on day 1, b be speed on day 2
240/14 = 17.14
now seeing if the two days speed can make above average work
case 1 b = 9 , a= 17
not possible as avg cant be more than the max numebr

case 2 b = 14, a= 22
can be possible as avg lie betwenn both number

case 3 b =19, b = 27
not possible as avg cant be less than lower number

hence ans is B
User avatar
paragw
User avatar
Joined: 17 May 2024
Last visit: 20 May 2026
Posts: 189
Own Kudos:
198
 [1]
Given Kudos: 39
Posts: 189
Kudos: 198
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:16
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let the second day rate be r
Then the first day rate be r+8

Let the farmer work h hr on day 1 and 14-h hr on day 2.

Total work:
(r+8)h +r(14-h) = 240

h = (240-14r)/8

Check each options:

I. r=9
h = 14 + hr
Not possible

II. r =14
h = 5.5

III. h =19
h = -26/8
Negative not possible

Only II works.

Answer: B
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 20 May 2026
Posts: 6,005
Own Kudos:
5,880
 [1]
Given Kudos: 163
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: 6,005
Kudos: 5,880
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:29
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let the farmer's rate of clearing a field, in square meters per hour, on the second day be x square meters per hour.
The farmer's rate of clearing the field on the first day = (x + 8) square meters per day

Let us assume that the farmer spent y hours on second day.
The farmer spent 14-y hours on the first day.

(x+8)(14-y) + xy = 240 square meters

I. x = 9; 17(14-y) + 9y = 240; 238 - 17y + 9y = 240; -8y = 2; y = -1/4; Not feasible
II. x = 14; 22(14-y) + 14y = 240; 308 - 22y + 14y = 240; 8y = 68; y = 8.5 hours; Feasible
III. x = 19; 27(19-y) + 19y = 240; 513 - 27y + 19y = 240; 8y = 273; y = 273/8 = 34...; 14-y>=0; y<= 14

IMO B
User avatar
Ayeka
User avatar
Joined: 26 May 2024
Last visit: 20 May 2026
Posts: 529
Own Kudos:
402
 [1]
Given Kudos: 158
Location: India
Schools: ISB
GMAT Focus 1: 645 Q82 V83 DI80
GPA: 4.2
Schools: ISB
GMAT Focus 1: 645 Q82 V83 DI80
Posts: 529
Kudos: 402
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:34
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let, farmer second day rate = x squre meters per hour
First day rate = x+8
Let, the farmer works for day 1 = t hours
And for day 2 = 14-t
Total area cleared = 240
(x+8)t+x(14-t)=240
xt+8t+14x-xt=240
8t+14x=240
t=(240-14x)/8

1. x=9
t=(240-14*9)/8=14.25
Both day time combined is only14 hours but we get he worked for 14.25 hours on day 1, then on day 2 he worked (-0.25) hours which is not possible..........No

2. x=14
t=(240-14*14)/8=5.5
On day 1 he worked 5.5 hours and on day 2, (14-5.5=8.5) hours . ........Valid

3. x=19
t=(240-14*19)/8=-3.25
We get a negative value of time which is wrong.......No

2 only
B
User avatar
ghimires28
User avatar
Joined: 19 Jul 2025
Last visit: 20 May 2026
Posts: 27
Own Kudos:
18
 [1]
Given Kudos: 1
Location: Nepal
Concentration: Technology, Entrepreneurship
Posts: 27
Kudos: 18
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:36
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let day 1 rate be x and time be y
then day 2 rate is x-8 and time is 14-y

total=work in day 1 +day 2
xy+(x-8)(14-y)=240
solving we get
7x+4y=126
looking at the answer choice and see what works
1)x=19-8=1
try x=1
119 is not multiple of 4 so no
2)x=6;14-8=6
84 we get a value for y and multiple of 4
3)
x=19 (19-8=11)
does not work
so final answer is B
User avatar
sitrem
User avatar
Joined: 19 Nov 2025
Last visit: 24 Feb 2026
Posts: 91
Own Kudos:
84
 [1]
Given Kudos: 238
Posts: 91
Kudos: 84
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
First day's rate = r+8 hours worked the first day = t
Second day's rate = r hours worked the second day = 14 - t
Total work = 240

Total work = hours worked the first day * first day's rate + hours worked the second day * second day's rate
240 = t(r+8) + (14-t)r
240 = 14(r+8) - 8t
t = ( 14(r+8) - 240 ) / 8

Plugging in the values of r, the only one that gives an acceptable value (where the hours worked in the first day are >0 and <14) is II
User avatar
Abhiswarup
User avatar
Joined: 07 Apr 2024
Last visit: 04 May 2026
Posts: 198
Own Kudos:
172
 [1]
Given Kudos: 42
Location: India
Posts: 198
Kudos: 172
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
let X be farmer rate on 1st day , X-8 becomes the rate on 2nd day
a be the no of hours 1st day and b be the no of hours 2nd day
X*a+(X-8)*b=240
a+b=14
Option I X-8=9 so X=17
17a+9b=240 & a+b=14 solving a=14.25 & b=-0.25
b can't be negative

Option II X-8=14, X=22
22a+14b=240 & a+b=14 solving a=5.5 & b=8.5 Option satisfies

Option III X-8=19, X=27
27a+19b=240 & a+b=14 solving a=-3.25 & b=17.25
a can't be negative

So answer is B, II only
avatar
ManifestDreamMBA
avatar
Joined: 17 Sep 2024
Last visit: 21 Feb 2026
Posts: 1,387
Own Kudos:
901
 [1]
Given Kudos: 243
Posts: 1,387
Kudos: 901
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:41
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
RateTimeWork
D1R+8TTR+8T
D2R14-T14R-RT
Total14240

TR + 8T + 14R - RT = 240
4T + 7R = 120
T = 30-7R/4

Checking options

I R=9
T = 30 - 7*9/4 = 120-63/4 = 57/4 = 14.25
But total T = 14
Invalid

II R=14
T = 30 - 7*14/4 = 120-98/4 = 22/4 = 11/2 = 5.5
Valid

III R = 19
T = 30 - 7*19/4 = 120 -133/4 = -ve
Invalid

Answer B

Bunuel
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Gift
12 Days of Christmas Competition
This question is part of our holiday event
Win $40,000 in prizes: courses, tests, and more
Show more
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 20 May 2026
Posts: 8,652
Own Kudos:
5,199
 [1]
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)
Products:
GMAT Club Tests
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,652
Kudos: 5,199
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:44
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?
I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

total work is 240
let t1+t2=14
given answer options are of day 2 work
we know day 1 work is day2 +8
use options
#1
if day 2 work is 9 then that of day 1 is 17
17*t1 + 9*(14-t1)=240
solve for t1 we get t1 >14 which is not possible
#2
22*t1+14*(14-t1)= 240
t1 = 5.5 so t2 = 8.5
sufficient
#2
27*t1 +19(14-t1)=240
-ve number not possible

OPTION B ;14 is correct
User avatar
Xdsa
User avatar
Joined: 07 Jul 2025
Last visit: 08 May 2026
Posts: 58
Own Kudos:
45
 [1]
Given Kudos: 1
Posts: 58
Kudos: 45
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:45
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
answer is b

(y+8).y + y.(14-x)=240

y= no of units in day 2 done in 1 hr
x is no of hours worked on day 1
substituting the value given in option for y
option 1 x becomes more than 14 hrs hence eliminated
option 2 x and y satisfies
option 3 x becomes negative
User avatar
batman10bigman
User avatar
Joined: 23 Apr 2025
Last visit: 20 May 2026
Posts: 44
Own Kudos:
38
 [1]
Given Kudos: 12
Products:
GMAT Club Tests
Posts: 44
Kudos: 38
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:52
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Gift
12 Days of Christmas Competition
This question is part of our holiday event
Win $40,000 in prizes: courses, tests, and more
Show more
Let rate of Day 1 = r and Day 2 = r - 8
Total work = 240 sq m in 14hrs

we can use the formula:
(hours on day 1) x r + (hours on day 2) x (r-8) = 240

Test 1: Day 2 = 9, r =9+8 = 17
h1 + h2 = 14, substitute in equation below
17h1 + 9h2 = 240 => h1 = 14.25, h2 = -0.75 NOPE

Test 2: Day 2 = 14, r = 14+8=22
h1 + h2 = 14, substitute in equation below
22h1 + 14h2 = 240 => h1 + h2 = 14 => h1 = 5.5, h2 = 8.5 WORKS

Test 3: Day 2 = 19, r = 19+8=27
h1 + h2 = 14, substitute in equation below
27h1 + 19h2 = 240 => h1 is negative NOPE

Only 2 works
Answer is B
User avatar
Sumimasen
User avatar
Joined: 21 Jan 2024
Last visit: 20 May 2026
Posts: 36
Own Kudos:
33
 [1]
Given Kudos: 11
Posts: 36
Kudos: 33
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 09:57
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Work = Rate x Time
Total work 240 sq. in 14 hours
Attachments

WhatsApp Image 2025-12-18 at 11.55.05 AM.jpeg
WhatsApp Image 2025-12-18 at 11.55.05 AM.jpeg [ 97.99 KiB | Viewed 1495 times ]

User avatar
yuvrajbhama
User avatar
Joined: 30 Jul 2025
Last visit: 20 May 2026
Posts: 37
Own Kudos:
20
 [1]
Given Kudos: 3
Location: India
Concentration: General Management, Nonprofit
Schools: Booth (Chicago) ESADE HEC MiM '26 Duke Fuqua ESSEC MiM '26
GPA: 6.6
WE:General Management (Energy)
Schools: Booth (Chicago) ESADE HEC MiM '26 Duke Fuqua ESSEC MiM '26
Posts: 37
Kudos: 20
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 10:01
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ASSUMING THAT FARMER WORKED 7 HRS ON BOTH THE DAYS

TRYING WITH THE FIRST VALUE

DAY1- 9+8= 17 * 7HRS=133
DAY2- 9*7= 63
I IS NOT THE ANSWER ELEMINATING OPTION A & D

II
DAY 1- 14+8=22*7= 154
DAY 2- 14*7= 94
154+94= 252
CLOSEST TILL NOW

III WILL BE BW TOO MUCH SO OPTION B IS THE ANSWER
Bunuel
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Gift
12 Days of Christmas Competition
This question is part of our holiday event
Win $40,000 in prizes: courses, tests, and more
Show more
User avatar
vikramadityaa
User avatar
Joined: 28 Jul 2025
Last visit: 23 Dec 2025
Posts: 55
Own Kudos:
41
 [1]
Given Kudos: 1
Posts: 55
Kudos: 41
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 10:03
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?

I. 9
II. 14
III. 19

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Gift
12 Days of Christmas Competition
This question is part of our holiday event
Win $40,000 in prizes: courses, tests, and more
Show more
Let the first day rate be r; the second day rate be (r-8)
Let hours worked on the first day be hi; and the second day be h2

Total time=h1+h2=14
Total area cleared = rh1+(r-8)h2=840
h1=14-h2

r(14-h2)+(r-8)h2=240
14r-8h2=240
8h2=14r-240
h2=(14r-240)/8
For value to be possible, h2 must be positive and ≤14

1) r2=9; r=17
h2=(14(17)-240)/8=-(1/4) - not possible.

2) r2=14; r=22
h2=(14(22)-240)/8=8.5 - possible

3)r2=19;r=27
h2=(14(27)-240)/8=17.25 - not possible.


Hence, OPTION B (II ONLY)
User avatar
hershehy
User avatar
Joined: 28 Jul 2025
Last visit: 20 May 2026
Posts: 24
Own Kudos:
18
 [1]
Given Kudos: 5
Posts: 24
Kudos: 18
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 10:32
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO B

we can do it using tables

RATETIMEWORK
DAY 1 x+8t1(x+8)t1
DAY 2xt2xt2
TOTAL14240

now we have two eqns

t1+t2= 14
(x+8)t1 +xt2= 240

substitute 1 in eqn 2, it will be
(x+8)t1+ x(14-t1)= 240

so t1= (240-14x)/8

Now we test all value given in eqn that is x= 9, 14 and 19.
From 9, we get t11= 14.25, can not be because t1+t2= 14, so t1 has to be less than <14.
from 14 we get t1= 8.5, so could be.
from 19 we get t1= -3.25 it cant be negative.

so Only II one suffices.
User avatar
harishg
User avatar
Joined: 18 Dec 2018
Last visit: 09 Apr 2026
Posts: 176
Own Kudos:
174
Given Kudos: 31
GMAT Focus 1: 695 Q88 V84 DI81
Products:
My Reviews
GMAT Focus 1: 695 Q88 V84 DI81
Posts: 176
Kudos: 174
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 10:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Assuming y amount of work is done on day 1 and 240-y on day 2, we have

y/x + 240-y/(x-8) = 14

Rearranging the above equation, 352x = 14x^2+8y

We are given three options for x-8. Substituting the value of x accordingly in the above equation, we can see that y is positive for 9 and 14 but turns negative for 19.

Therefore, Option D
User avatar
gemministorm
User avatar
Joined: 26 May 2025
Last visit: 19 May 2026
Posts: 143
Own Kudos:
114
 [1]
Given Kudos: 57
GMAT Focus 1: 565 Q82 V79 DI73
GMAT Focus 2: 605 Q84 V83 DI73
GMAT Focus 2: 605 Q84 V83 DI73
Posts: 143
Kudos: 114
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 11:06
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
assuming D1 -> r+8, h D2 -> r, 14-h
acc to question: h(r+8) + (14-h)r = 240 => h = 120-7r/4
substituting values:
I -> r = 9 -> h = 57/4 = 14.25 -> which is greater than 14 hence not possible.
II -> r = 14 -> h = 22/4 = 5.5 - ok
III -> r = 19 -> h = -13/4 -> -ve time hence not possible.

hence, II only.
User avatar
AviNFC
User avatar
Joined: 31 May 2023
Last visit: 10 Apr 2026
Posts: 306
Own Kudos:
366
 [1]
Given Kudos: 5
Posts: 306
Kudos: 366
 [1]
12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on 18 Dec 2025, 11:10
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rate on day1 (work time t1) be r, so rate on day2 r-8 (time t2)
given:
t1+t2=14
rt1+(r-8)t2=240
solving, 8t2=14r-240
now, as per options, r=17,22,27
for r=17, t2=-ve
for r=27, t2>14
so only r=22 possible.
thus r-8 is 14

Ans B
 1   2   3   4   
Moderators:
Bunuel
Math Expert
110750 posts
Krunaal
Tuck School Moderator
852 posts