Last visit was: 19 Nov 2025, 16:01 It is currently 19 Nov 2025, 16:01
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   3 
User avatar
jkkamau
User avatar
Joined: 25 May 2020
Last visit: 19 Nov 2025
Posts: 132
Own Kudos:
107
Given Kudos: 122
Location: Kenya
Schools: Haas '25
GMAT 1: 730 Q50 V46
GPA: 3.5
Products:
GMAT Club Tests
Schools: Haas '25
GMAT 1: 730 Q50 V46
Posts: 132
Kudos: 107
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 04:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Assume the containers are a,b,c,d. Question is (b+c)/2
Statement 1
d-a=2(d-100)
d+a=200 (Insufficient)
Statement 2
d= (b+c)/2+50
Median = d-50 (Insufficient)
Combine the two statements
Median =200-a-50= 150-a but we do not how much is in container a thus insufficient
Choice E

Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

In the first step of a scientific experiment, 400 milliliters of a certain solution were divided among four empty containers. What was the median volume of solution among the containers?

(1) The range of the volumes in the four containers was twice the difference between the greatest volume and the average volume.
(2) The container with the greatest volume of solution had 50 milliliters more than the median volume.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

Show more
User avatar
LastHero
User avatar
Joined: 15 Dec 2024
Last visit: 11 Nov 2025
Posts: 134
Own Kudos:
147
 [1]
Given Kudos: 1
Posts: 134
Kudos: 147
 [1]
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 04:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
V4>=V3>=V2>=V1

We know that V1+V2+V3+V4=400

(1)
Average volume=400/4=100

V4-V1=2*(V4-100)
V1+V4=200

Median=(V2+V3)/2=(400-(V1+V4))/2=100

Condition (1) is sufficient

(2)
V4=50+(V2+V3)/2
2V4=100+V2+V3

If V2=V3=100, V4=150, V1=50 and Median is 100
If V2=V3=110, V4=160, V1=20 and Median is 110

Condition (2) is insufficient

Answer A
User avatar
pintukr
User avatar
Joined: 03 Jul 2022
Last visit: 19 Nov 2025
Posts: 1,591
Own Kudos:
1,089
 [1]
Given Kudos: 22
GMAT 1: 680 Q49 V34
Products:
My Reviews
GMAT 1: 680 Q49 V34
Posts: 1,591
Kudos: 1,089
 [1]
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 04:57
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
In the first step of a scientific experiment, 400 milliliters of a certain solution were divided among four empty containers. What was the median volume of solution among the containers?


(1) The range of the volumes in the four containers was twice the difference between the greatest volume and the average volume.

Average volume = 400 /4 = 100 ml

Let, maximum volume be = g
minimum volume be = l

then, g - l = 2 (g - 100)
g + l = 200

that means, the sum of two middle-volume containers = 400 - (g+l)
= 400 - 200
= 200

So, Median volume = 200/ 2 = 100 ml (since there are 'even' number of containers)


SUFFICIENT


(2) The container with the greatest volume of solution had 50 milliliters more than the median volume.

Case - 1 : 150, 100, 100, 50 (Median = 100 ml)
Case - 2 : 160, 130, 90, 20 (Median = 110 ml)

Different values of median satisfy the given stimulus


INSUFFICIENT


(A) is the CORRECT answer
User avatar
Nsp10
User avatar
Joined: 22 May 2023
Last visit: 19 Nov 2025
Posts: 122
Own Kudos:
88
 [1]
Given Kudos: 112
Location: India
Schools: IE Schulich
GPA: 3.0
Products:
My Reviews
Schools: IE Schulich
Posts: 122
Kudos: 88
 [1]
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 05:37
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A Fine Q indeed,
let the containers are A,B,C,D,
where A being lowest and D being Highest, so we know A+B+C+D=400,
Avg volume will be 400/4=100

Statement 1.
Range=D-A=2 * {D-Avg} and we know the avg which is 100,
so,
D-A=2*{D-100}
on solving it is
D+A=200,
and we also know that A+B+C+D=400 so on putting A+D=200 will give us B+C=200,
since we have 4 containers which is an even quantity so median will be avg of middle 2 elements so
Median =B+C/2=200/2=100,
Hence
Statement A is Sufficient.

Statement 2.
D=Median + 50,
D={B+C}/2+50,
and for median we need to know the values of B and C ,
we do not have much further information about A, so we can not calculate any further,
hencce Insufficient .

The ans is A.
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

In the first step of a scientific experiment, 400 milliliters of a certain solution were divided among four empty containers. What was the median volume of solution among the containers?

(1) The range of the volumes in the four containers was twice the difference between the greatest volume and the average volume.
(2) The container with the greatest volume of solution had 50 milliliters more than the median volume.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

Show more
User avatar
Karanjotsingh
User avatar
Joined: 18 Feb 2024
Last visit: 03 Oct 2025
Posts: 139
Own Kudos:
94
 [1]
Given Kudos: 362
Location: India
Concentration: Finance, Entrepreneurship
Posts: 139
Kudos: 94
 [1]
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 06:39
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Problem Summary:
  • Total Volume: 400 milliliters divided into four containers.
  • Goal: Find the median volume of the containers.
Understanding the Median:
  • For four numbers arranged in order (a ≤ b ≤ c ≤ d):
    Median = )b + c)/2
Analyzing the Statements:
Statement (1):
"The range of the volumes in the four containers was twice the difference between the greatest volume and the average volume."
  1. Define Terms:
    • Range: d − a
    • Average Volume: 400/4 = 100 milliliters
    • Difference Between Greatest Volume and Average: d − 100
  2. Given Relationship:
    d − a = 2(d − 100)
    Simplifying:
    d − a = 2d − 200 ⟹ a=200−d
  3. Total Volume Equation:
    a + b + c + d = 400
    Substitute a = 200 - d:
    (200 − d) + b + c + d = 400 ⟹ b + c = 200
  4. Calculate Median:
    Median = (b + c)/2 = 200/2 = 100 milliliters
Conclusion:
Statement (1) alone allows us to determine that the median volume is 100 milliliters.

Statement (2):
"The container with the greatest volume of solution had 50 milliliters more than the median volume."
  1. Define Terms:
    • Median Volume: M = (b + c)/2
    • Greatest Volume: d = M + 50
  2. Total Volume Equation:
    a + b + c + d = 400
    Substitute d = M + 50 and b + c = 2M:
    a + 2M + (M + 50) = 400 ⟹ a + 3M = 350
  3. Lack of Specificity:
    • Unknowns: Both a and M are unknown.
    • Possible Values: Multiple combinations satisfy a + 3M = 350.
      • Example 1: If M = 100, then a = 50.
      • Example 2: If M = 90, then a = 80.
      • Example 3: M = 110, then a = 20.
Conclusion:
Statement (2) alone does not provide enough information to determine the exact median volume.

Final Conclusion:
  • Statement (1): Sufficient to find the median.
  • Statement (2): Not sufficient on its own.

Therefore, the correct answer is:
A) Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
User avatar
Lizaza
User avatar
Joined: 16 Jan 2021
Last visit: 17 Nov 2025
Posts: 165
Own Kudos:
219
Given Kudos: 5
GMAT 1: 710 Q47 V40
GMAT 1: 710 Q47 V40
Posts: 165
Kudos: 219
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 06:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let's say that containers are distributed as follows: \(a<=b<=c<=d\) and \(a+b+c+d=400\)
Also, median is \(m=\frac{b+c}{2}\)

(1) As the average volume is 400/4=100, then we're given \(d-a=2(d-100)\), so \(d=a+200\)
This is quite a lot of info, but we only know that \(b+c=400-a-d=400-200-2a=200-2a\), and this can be interpreted in many ways. Insufficient.

(2) \(d=m+50\) and \(b+c=2m\), so \(400=m+50+2m+a=a+3m+50\), and this is impossible to assess without knowing a. Insufficient.

(1+2) From this, \(400=a+3m+50\) and \(2a=200-(b+c)=200-2m\), so \(a=100-m\) and then \(400=150+2m\) and this is sufficient.
Therefore, the answer is C.
User avatar
HansikaSachdeva
User avatar
Joined: 17 May 2024
Last visit: 17 Nov 2025
Posts: 60
Own Kudos:
64
Given Kudos: 143
Location: India
Concentration: Social Entrepreneurship, Sustainability
Products:
GMAT Club Tests Forum Quiz
Posts: 60
Kudos: 64
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 07:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
There are 4 containers a, b, c, d

Assuming that a <= b <= c <= d

Total volume of solution = a + b + c + d = 400 ml
Number of containers = 4
Average volume = 400/4 = 100 ml
Median = (b + c) / 2

Statement 1
Range = d - a

d - a = 2(d - 100)
Solving,
a = d - 200
There are no equations for b and c

Statement 1 is insufficient

Statement 2
d = Median + 50 ------ {1}
There are no equations for b and c

Statement 2 is insufficient

Combining Statements 1 and 2
a = (Median + 50) - 200
a = Median - 150 ------ {2}

There are 3 variables and 2 equations. The median cannot be determined

Answer: E
User avatar
rns2812
User avatar
Joined: 10 Nov 2024
Last visit: 28 Aug 2025
Posts: 50
Own Kudos:
51
Given Kudos: 14
Posts: 50
Kudos: 51
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 07:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total volume to be divided = 400 ml

Ask : What is median among 4 containers

Median would be the average of middle two containers

Assume containers have V1, V2, V3, V4 ml in each of them in ascending order

Median = \(\frac{(V2 + V3)}{2 }\)

Statement 1 :

Average of the 4 containers = Total volume/ Total number of containers = 60/4 = 15
V4 - V1 = 2 * (V4 - 15)

V4 = 30 - V1

Not sufficient

Statement 2 :

V4 = \(\frac{(V2 + V3)}{2 }\) + 50

Not sufficient to find median

Together :

\([fraction](V2 + V3) [/fraction]\) = ( V4 - 50 ) * 2

V1 = 30 -V4

Total = 60 = V1 + V2 + V3 + V4 = 30 - V4 + 2 * (V4 - 50) + V4

30 = 2* V4 - 100

V4 = 65ml

Median = 30ml

Sufficient together - OPTION C

Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

In the first step of a scientific experiment, 400 milliliters of a certain solution were divided among four empty containers. What was the median volume of solution among the containers?

(1) The range of the volumes in the four containers was twice the difference between the greatest volume and the average volume.
(2) The container with the greatest volume of solution had 50 milliliters more than the median volume.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

Show more
User avatar
nikiki
User avatar
Joined: 07 May 2023
Last visit: 19 Nov 2025
Posts: 56
Own Kudos:
57
Given Kudos: 89
Location: India
Posts: 56
Kudos: 57
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 08:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let the volumes of the four containers be v1,v2,v3,v4 in increasing order

(I)
v4 - v1 = 2(v4 - (v1+v2+v3+v4)/4)
This gives a relationship between the range and the average volume but does not directly provide enough information to find the median volume.
Not sufficient.

(II)
It gives a direct relationship v4=v2+5, but without knowing the other volumes, we cannot determine the median volume.
Not sufficient.

(I)+(II)
Combining both statements allows us to express the volumes in terms of each other and find the median volume.
Sufficient

Option C
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

In the first step of a scientific experiment, 400 milliliters of a certain solution were divided among four empty containers. What was the median volume of solution among the containers?

(1) The range of the volumes in the four containers was twice the difference between the greatest volume and the average volume.
(2) The container with the greatest volume of solution had 50 milliliters more than the median volume.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

Show more
User avatar
IssacChan
User avatar
Joined: 25 Sep 2024
Last visit: 21 Mar 2025
Posts: 55
Own Kudos:
50
 [1]
Given Kudos: 4
Posts: 55
Kudos: 50
 [1]
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 08:32
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

In the first step of a scientific experiment, 400 milliliters of a certain solution were divided among four empty containers. What was the median volume of solution among the containers?

(1) The range of the volumes in the four containers was twice the difference between the greatest volume and the average volume.
(2) The container with the greatest volume of solution had 50 milliliters more than the median volume.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

Show more
Let x be the greatest container
Let y be the lowest container

(1) x-y = 2(x-100)
x-y = 2x-200
200 = x+y

As the largest and the lowest container = 200
The sum of 2nd and 3rd container will be 400-200 = 200

Median
= (2nd + 3rd)/2
= 200/2
= 100 (Sufficient)

(2) Let m be the median
Let l be the lowest container

(50+m) + 2m + l = 400
50 + 3m + l = 400
3m + l = 350
3m + l can have any combination (insufficient)

Therefore the answer is A
User avatar
maddscientistt
User avatar
Joined: 09 Mar 2023
Last visit: 17 Jul 2025
Posts: 41
Own Kudos:
47
Given Kudos: 64
Posts: 41
Kudos: 47
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 08:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 1
The range is twice the difference between the greatest volume and the average volume. This equation alone doesn't provide enough information to determine the median volume. Insufficient.

Statement 2
The greatest volume is 50 milliliters more than the median volume. This gives a relationship between the greatest volume and the median, but doesn't provide enough to determine the exact median. Insufficient.


Combining Statements 1 and 2
Together, the statements allow us to set up an equation to solve for the median. Sufficient.

Answer - Option C

Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

In the first step of a scientific experiment, 400 milliliters of a certain solution were divided among four empty containers. What was the median volume of solution among the containers?

(1) The range of the volumes in the four containers was twice the difference between the greatest volume and the average volume.
(2) The container with the greatest volume of solution had 50 milliliters more than the median volume.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

Show more
User avatar
Suyash1331
User avatar
Joined: 01 Jul 2023
Last visit: 20 Oct 2025
Posts: 118
Own Kudos:
61
Given Kudos: 22
Location: India
Schools: IIMA '26 IIM IIM Calcutta '26 Judge '26 ISB '27 Said '27
GMAT Focus 1: 575 Q65 V70 DI70
GMAT 1: 250 Q20 V34
GPA: 7
Products:
My Reviews
Schools: IIMA '26 IIM IIM Calcutta '26 Judge '26 ISB '27 Said '27
GMAT Focus 1: 575 Q65 V70 DI70
GMAT 1: 250 Q20 V34
Posts: 118
Kudos: 61
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 08:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
total 400, number of containers = 4.
hence average = 100mm

statement 1:
H - L = 2(H-100)
H - L = 2H- 200
H + L = 200
Insufficient to find the median

Statement 2:
H = m + 50
Insufficient

Combing both the statements:
m + 50 + L = 200
m + L = 150

insuficient

hence E is correct

Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

In the first step of a scientific experiment, 400 milliliters of a certain solution were divided among four empty containers. What was the median volume of solution among the containers?

(1) The range of the volumes in the four containers was twice the difference between the greatest volume and the average volume.
(2) The container with the greatest volume of solution had 50 milliliters more than the median volume.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

Show more
User avatar
BatrickPatemann
User avatar
Joined: 29 May 2024
Last visit: 19 Nov 2025
Posts: 64
Own Kudos:
55
Given Kudos: 153
Products:
GMAT Club Tests
Posts: 64
Kudos: 55
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 08:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We know from the question that: S: {x1, x2, x3, x4}; Sum of S = 400 and median = (x2+x3)/2.

(1) |x4-x1| = 2*|max(S)-avg(S)|

As formulated we can't get anything from here with the information provided. Eliminate A & D

(2) max(S) = 50 + ((x2 + x3)/2)

Eliminate B. Clearly insufficient.

Both combined still do not provide enough information to know x2 + x3 divided by 2 or the median in any other way, like through knowing the property of consecutive integers and its average value.
User avatar
Nikhil17bhatt
User avatar
Joined: 25 Aug 2018
Last visit: 31 May 2025
Posts: 70
Own Kudos:
75
Given Kudos: 14
Posts: 70
Kudos: 75
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 08:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO E

Using 1 and 2 we have 2 secaniros when each container has a volume of 100 and when highest is 200 the result is multiple solution hence we can' t determine
User avatar
mpp01
User avatar
Joined: 13 Dec 2024
Last visit: 08 Jun 2025
Posts: 49
Own Kudos:
48
Given Kudos: 9
Location: Spain
Posts: 49
Kudos: 48
12 Days of Christmas GMAT Competition - Day 9: In the first step of a 27 Dec 2024, 09:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(1) The range of the volumes in the four containers was twice the difference between the greatest volume and the average volume.
(2) The container with the greatest volume of solution had 50 milliliters more than the median volume.

In this question we are asked for the median, we can compute median as the middle value or the average of the two middle values in a set of even numbers. Now also, under series of consecutive numbers or evenly spaced numbers, the average = median.

1) insuffcient, nothing from the above is remotely near what we need.
2) Not sufficient again

Combined still not enough information to compute the median value of the series. We can get multiple solutions, hence answer E
   1   2   3 
Moderators:
Bunuel
Math Expert
105390 posts
kingbucky
496 posts