12 Days of Christmas GMAT Competition 2025 - Day 2: At a certain

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Bunuel

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16 Dec 2025, 10:00

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GMAT Club Official Explanation:

At a certain shipping depot, each package has a weight recorded in grams. How many packages in the depot weigh more than 420 grams?

(1) The average (arithmetic mean) weight per package is equal to the weight of the lightest package.

If the average weight equals the lightest weight, then all packages must have the same weight. But we do not know what that weight is, and we do not know how many packages there are. Not sufficient.

(2) The median weight of all the packages in the depot is 410 grams.

A median of 410 grams does not tell us how many packages are above 420 grams. Depending on the distribution and the number of packages, the count above 420 could vary. Not sufficient.

(1)+(2) From (1), all packages have the same weight. If the median is 410 grams, that common weight must be 410 grams. So all packages, however many there are, weigh 410 grams. Therefore, no packages weigh more than 420 grams. Sufficient.

Answer: C.

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paragw

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16 Dec 2025, 09:32

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I. Average = lightest =>all packages have same weight W
W could be > 420 or less than equal to 20
Cannot decide.
Insufficient

II. Median = 410
=> Tells nothing exact about weights >420.
Insufficient

I & II
All packages same weight and median = 410
=> every package weight 410
Packages >420 => 0

Answer. C

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16 Dec 2025, 09:33

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At a certain shipping depot, each package has a weight recorded in grams. How many packages in the depot weigh more than 420 grams?

(1) The average (arithmetic mean) weight per package is equal to the weight of the lightest package.
(2) The median weight of all the packages in the depot is 410 grams.

how many packages weigh > 420 gms
#1
avg mean per package is = lightest package
means all weigh same , but no value given
insufficient
#2
median of all packages is 410 gms
not sufficient as other packages not given
from 1 &2
we can determine that all packages weigh same 410
sufficient
OPTION C is correct

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16 Dec 2025, 09:34

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Bunuel

Deconstructing the Question
Target: Find the number of packages weighing > 420 grams.
Let the weights of the $n$ packages be $w_1, w_2, \dots, w_n$.

Analyze Statement (1)
"The average (mean) weight is equal to the weight of the lightest package."
Let $w_{min}$ be the lightest weight.

Equation:
$\mu = w_{min}$.

Theory: Mean vs Min
The mean of a set is always $\ge$ the minimum value.
The mean equals the minimum value if and only if all elements in the set are equal.

(Proof: If even one element were greater than $w_{min}$, the sum would increase, pulling the average above $w_{min}$).

So, Statement (1) implies: All packages have the exact same weight.
However, we do not know what that weight is (could be 10g, could be 1000g), nor do we know how many packages there are. INSUFFICIENT

Analyze Statement (2)
"The median weight is 410 grams."
This tells us the central value is 410.
It does not restrict the values above the median.

Example A: $\{410, 410, 410\}$. Count > 420 is 0.
Example B: $\{400, 410, 500\}$. Count > 420 is 1. INSUFFICIENT

Combine Statements (1) and (2)
From (1): All packages have the same weight, let's call it $W$.
From (2): The median is 410.
If all numbers in a set are $W$, the median must also be $W$.

Therefore, $W = 410$.

This means every single package in the depot weighs exactly 410 grams.

Question: How many packages weigh more than 420 grams?
Answer: Zero (since $410 < 420$).

Since we can answer with a unique number (0), the statements are sufficient. SUFFICIENT

Answer: C

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Statement 1: Mean is equal to lightest, means all weights are equal. But does not give a number hence NS
Statement 2: Median is 410, the number of packages above 410 could be any. NS
Two together: All packages weigh 410. Hence answer is 0.
C

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16 Dec 2025, 09:42

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At a certain shipping depot, each package has a weight recorded in grams.
How many packages in the depot weigh more than 420 grams ?

(1) The average (arithmetic mean) weight per package is equal to the weight of the lightest package.
Means weight of all packages is equal
But the weight of the packages is unknown
Not sufficient

(2) The median weight of all the packages in the depot is 410 grams.
Case 1: Weight of the packages = {390, 400, 410, 420, 430}: Answer = 2
Case 2: Weight of the packages = {400,405,410,415,420} : Answer = 0
Number of packages in the depot weighing more than 420 grams can not be derived.
Not sufficient

(1) + (2)
(1) Weight of all packages is same
(2) Median weight of all the packages in the depot = 410 grams
Weight of each package = 410 grams < 420 grams
No package in the depot weighs more than 420 grams
Sufficient

IMO C

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16 Dec 2025, 09:43

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# of packages with weight > 420?

S1
Avg weight = lightest weight
But weight is the central tendency
This means all packages weigh the same
But we don't know how much they weigh
Insufficient

S2
Median = 410
This means we have something like ... _ _ _ _ 410 _ _ _ _ ..., when weights are arranged in ascending order
We don't know though how weigh above 420
Insufficient

Combined we have all packages weighing 410. This means no package weighs more than 420
So number of packages weighing 420 = 0
Sufficient

Answer C

Bunuel

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16 Dec 2025, 09:43

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(1) alone
The only way the smallest value in a set can equal the mean is if all values are the same.
But we have no information on how much the smallest value is (and therefore each single package), so we don't know if all the packages are above or below 420g.

(2) alone
This tells us that half of the packages are below 410g and half are above 410g, but we don't know anything in relation to the value that we are asked about, which is 420g.

(1) and (2).
From (1) we know that all packages weigh the same, from (2) we know that one package is 410g -> all packages are 410g -> all packages are below 420g.

C both statements together are sufficient, but neither alone is sufficient

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16 Dec 2025, 09:45

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s1: implies all the packages are of equal weight
s2 : implies atlest half packages are less vthan 420 ( but the catch is we don't know the actual number)

s1 and s2 implies all the packages are of weight 410.
hence 0 packages are grater than 420

so ans is C

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16 Dec 2025, 09:50

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How many packages weigh more than 420 grams

(1) Average weight per package is equal to the weight of lightest package, thus all packages must have the exactly same weight. But we don’t know the weight of lightest package.
Insufficient

(2) Median weightis 410 grams.
No info about the packages that weight more or less than 410 grams.
Insufficient

(1)&(2)
All packages weigh the same and the median weight is 410 grams. Hence, every package weighs 410 grams.
Sufficient

C

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(1) tells us that all weights in the depot are same. But it tells nothing about whether they are more than or less than 420. Not sufficient.

(2) it tell us only about median, nothing about rest of the weights. Not sufficient.

using (1) and (2), we know that all items are same, and since median = 410, all weights are 410g. Hence no. of packages > 420 = 0 . Hence both (1) and (2) together are sufficient.

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16 Dec 2025, 09:58

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question is asking if n<410?
n represents the number of bags under 410;
we need to find n
1)
mean = ligtest means all the baggage way same
not suffient
2) median is 410
not sufficient
combining 1 and 2 we can say all baggage weight 410 which is less than 410,
we know all weight 410 which is less than 420 but we do not know the value of n
there not sufficient Therefore E

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16 Dec 2025, 10:00

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The answer should be C because:

S1 alone: This condition holds true only if all package have same weight equivalent to the light package.
S2 alone: Median alone is not sufficient to conclude anything.
Together: all package weigh 410 grams which is less than 420 grams and therefore the answer is C.

Bunuel

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16 Dec 2025, 10:06

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IMO C

Clearly 1 & 2 are not suff individually.
Combining both, if mean is equal to lightest package, so all weights must be same ----> all weights = 410 since median is given
So, no of packages weighing> 420 is 0
C- 1+2 together makes sufficient

Bunuel

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there are non of the packages, since all weights are the same (since the average of the package is the same as the lightest, so there is non, which is heavier), and median is then the same as average

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16 Dec 2025, 10:10

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(1) => all packages have same weight as mean = minimum. Not sufficient as nothing about actual weight is mentioned.
(2) => median is 420. Not sufficient as the higher weights are not being mentioned.
(1) and (2) => all packages have weight 410 as median is 410 and mean = minimum. Thus, no package has weight over 420.

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16 Dec 2025, 10:20

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We have to find if number of packages with Weight W>420

Statement 1:
Average weight per package is equal to weight of lightest package.
This can happen only when all packages are of equal weight.
But we do not have information on number of packages yet.
Hence insufficient

Statement 2:
Median weight is 410g
With just the median, we cannot know the number of packages.
Hence insufficient

Combining 1 and 2
Now we know that all packages are of same weight equal to 410g. We still do not know the number of packages. It can be any number.
Hence even after combining, we are unable to arrive at the number of packages weighing greater than 420

Hence answer is E

Bunuel

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16 Dec 2025, 10:21

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Bunuel

S1 : This statement tells us all packages weigh the same. But whats the weight of each package ? We don't know. Hence the statement alone is not sufficient, we can elimiate A and D.

S2: The statement doesn't help us tell anyting other than the median weight. Hence, we can elimiante B as S2 alone is not sufficient.

Combined

S1 + S2 = S1 Tells us all packages have same weight and S2 tells that the median is 410, which means each package is 410. So none weight more than 420 gms.

Option C

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16 Dec 2025, 10:35

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(1) This happens only when all the values are equal. But we still don't know that value.

(2) Clearly insufficient, as we still don't know how many weigh more than 420 grams.

(1)+(2) We now know that one value is 410 grams, and all weigh 410, which gives 0 packages that weigh more than 420 grams.
Option C

Bunuel