12 Days of Christmas GMAT Competition 2025 - Day 4: A farmer worked on

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Bunuel

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18 Dec 2025, 10:00

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Bunuel

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.

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18 Dec 2025, 09:09

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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

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18 Dec 2025, 09:16

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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

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18 Dec 2025, 09:29

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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

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18 Dec 2025, 09:34

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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

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18 Dec 2025, 09:36

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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

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18 Dec 2025, 09:40

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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

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18 Dec 2025, 09:40

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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

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18 Dec 2025, 09:41

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	Rate	Time	Work
D1	R+8	T	TR+8T
D2	R	14-T	14R-RT
Total		14	240

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

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18 Dec 2025, 09:44

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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

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18 Dec 2025, 09:45

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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

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18 Dec 2025, 09:52

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Bunuel

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

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18 Dec 2025, 09:57

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Work = Rate x Time
Total work 240 sq. in 14 hours

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18 Dec 2025, 10:01

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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

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18 Dec 2025, 10:03

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Bunuel