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

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AviNFC

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1. This shows range is zero. So, all the weights are equal. All these can be greater or less than 420gm. NOT SUFFICIENT
2. Median is 410 gm. other weights can be greater or less than 420 gm. NOT SUFFICIENT

Together,
as median = 410 gm, and all weights are equal. so, all weights are less than 420 gm. SUFFICIENT

Ans C

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1) Whenever the average is equal to the smallest value, all the values in the set are equal to the smallest value.
Hence here all values are equal to the smallest value. But we dont know the exact weight hence not sufficient

2) Median is 410, doesn't ans how many are more than 420, hence not sufficient

Combining all values are equal and median value is 410, hence all values in the set are 410, therefore no of packages weighing more than 420gms are 0, sufficient

Ans C

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16 Dec 2025, 12:49

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Bunuel

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.

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1) average weight = weight of light package.

we can have different possibilities like light package weight = 400g then, average weight = 400g
or light package weight = 450g then, average weight = 450g

Statement 1 alone is not sufficient

2) Median = 410g

So 1st half of the packages will be <= 410g and 2nd half of the packages will be >=410g
but we don't know how many are >=410g

Statement 2 alone is not sufficient.

3) Both Statements combined
we can say that Median is 410g also
Light package = 410g hence Average =410g

So None of the packages weigh more than 420g

Hence C is the answer Both statement together sufficient

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16 Dec 2025, 13:15

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Statement 1: No weights of the packages are mentioned neither Number of packages not mentioned
Statement 2: Median weight is given but number of packages is still missing
Statement 1 + Statement 2
Now if we consider 'n' as number of packages and given statement one all weights are same (average weight = lightest weight), Median from statement 2 we go one weight that is, 410
Now : n*410/ n = 410 so all weights are 410 and none are 420.
So answer choice: C

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16 Dec 2025, 15:29

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lets consider

total number of packages = N
set of all package weights = W

How many packages weight more than 420 grams?

lets check the statement 1 : average ( arithmetic mean) weight per package is equal to weight of lightest package

average weight = A
weight of lightest package = L [weight of any package >= L]
as per statement , A = L
sum of all weights / number of package = L
sum of all weights / N = L
sum of all weights = L*N
if we have set of weights which are not equal then sum of weights will be greater than N*L

example : Weights = { 10, 10, 20}
L = 10, sum = 40, N = 3
A = 40/3 = 13.33
A is not equal to L

A=L only if every single package weighs exactly the same as lightest one.
we can have L = 400 or 500..., we cant find the answer

Since answer could be anything, statement 1 is not sufficient

now lets check statement 2 - median weight of all packages in depot is 410 grams.
This tells us that exactly half of packages weigh 410 gms or less and exactly half more than 410 gms.

since number of packages weighing more than 420 grams can be different, statement 2 is not sufficient

now lets consider both statement 1 and statement 2

weight of all packages = median = 410 grams

since 410 is less than 420, answer is definitively 0 packages

therefor, statement 1 and statement 2 combined are sufficient

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I) From this we know that ALL the numbers from the set are EQUAL. Nothing else. Thus, we cannot determine.

II) From this we know that the median is 410. We cannot determine either.

From I and II:

We know that all numbers are equal to 410. Therefore, none number is more than 420.

CORRECT answer C. BOTH are sufficient.

Bunuel

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packages that weigh more than 420 grams?

(1)
The only way for the average weight per package is equal to the weight of the lightest package is that all the packages have the same weight.
But we don't know that weight. If the weight is 400 the answer is 0. If the weight is 430 the answer is all (but we also don't know the number of packages).

Insufficient

(2)
median weight = 410

If there are 3 packages: 400, 410, 430 the answer is 1
If there are 4 packages: 380, 390, 430, 450 the answer is 2

Insufficient

(1) + (2)
If all the packages have the same weight and median weight = 410 then all the packages weigh 410 grams and the answer is 0.

Sufficient

IMO C

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weight > 420 grams?

(1)
If arithmetic mean = weight of the lightest package then there are no packages with different weights. All packages weigh the same.

If the weight is 410 the answer is zero.
If the weight is 430 the answer is indeterminate.

Condition insufficient

(2)
median = 410

No info about the weight of the other packages.

Condition insufficient

(1)+(2)
same weight
median = 410

The same weight is 410 and the answer is zero.

Conditions sufficient

Answer C

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I initially thought E, but upon closer look I decided C.

(1) is clearly not sufficient on its own because there is no reference to the number of packages in the depot or what the weight is.
(2) also clearly not sufficient because any number of packages could weigh above 420 grams or none at all could.

(1) + (2)
If the average weight is equal to the lightest weight, that means all packages must be the same weight, because any weight that is heavier than the lightest weight will skew the average away from the lightest weight. This effectively says that each package weighs the same amount. And if that weight is 410 grams, then we can answer the question with 0.
Answer C.

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How many packages > 420 grams?

(1)
In a set of numbers, if the average of them is equal to the smaller one, the only possibility is that all of them are the same number.
If the weight is 200 -> answer 0
If the weight is 500 -> no answer (it would be 'all', but 'all' is not a number)

Condition (1) is insufficient

(2)
The median weight = 410
Impossible to answer the question

Condition (2) is insufficient

(1)+(2)
Combining the two conditions, all the packages weigh 410 and the answer to the question is 0.

Condition (1) and (2) are sufficient

The answer is C

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Packages in the depot weigh more than 420 grams?

(1)
All the packages weigh the same. If one had a different weight (greater than the weight of the lightest package), then the arithmetic mean would be greater than the weight of the lightest package, contradicting the condition.
weight = 400 the answer is 0
weight = 500 the answer is not known (number of packages)

Insufficient

(2)
packages: 100, 400, 410, 425, 430 the answer is 2
packages: 100, 200, 400, 405, 415, 425, 430, 450 the answer is 3

Insufficient

(1) and (2)
weight of all the packages must be 410 and the answer is 0

Sufficient

The correct answer is C

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Can I answer: How many packages weigh more than 420 grams?

1)
The average weight is the weight of the lightest package. | Interesting the average weight is the weight of the lightest package, indicating all packages are the same weight... | Regardless, I don't know the weight of the lightest package, or the number of packages. Not sufficient

AD
BCE

2)
The median weight of all packages is 410 grams.

I know that at least 1/2 the packages weight less than 410, but I don't know how many packages that is. It could be 10 it could be 1,000. No way for me to determine the number of packages weighing more than 420 grams.

1 & 2 )

Median weight is 410 grams & the average weight of each package is equal to the weight of the lightest package,

The only possible way for the average to be equal to the lightest package is for all the packages to be the same weight.

Consider the following.

410 + 410 + 410 + 410 + 415 = 2055 / 5 is 411

Becuase I understand that all the packages are equal to the lightest weight, and my known lightest weight is 410 grams. I can say the all packages are equal to 410 grams or ZERO packages are equal to 420 grams.

Option C

Bunuel

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HarishChaitanya

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From the statement 1: when it is mentioned average weight per package is= weight of the lightest package that makes us understand that all the packages weights are same

From the statement 2: we get to know that weight of all packages is 410

Therefore both these statements are required to tell if there are any packages that are weighing above 420 grams

So, the answer is c

Bunuel

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Bunuel

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To answer: How many packages > 420 g ?

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

Means all packages have same weight, we still don't know if they can be greater than or lesser than 420g

Insufficient AD/BCE

Statement 2:
Median weight is 410 grams,

without knowing total and distribution, we cannot say how many greater than 420.

Insufficient AD/BCE

Statement 1 & 2 Together
We know that all packages are equal in weight and we know median is 410, each is 410.
So 0 packages are > 420g in weight.

Sufficient.
Correct Answer C

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16 Dec 2025, 20:44

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Given that each package has a weight recorded in grams , we need to find the number of packages weighing more that 420 grams. Let's have a look at first statement:

1. We need to understand the meaning of statement. When it says the average weight per package is equal to weight of the lightest package, it means that all the packages are having same weight. No other case is possible. Now , average weight is not provided , so we cannot answer the question regarding number of packages weighing more than 420 grams. So 1st statement is insufficient.
2. Here it is said that median is 410 grams. Many combinations are possible and data is clearly insufficient.

Now combine both statements , here it implies that all the packages weigh same and is equal to 410 grams. So there is no package weighing more than 420 grams. So we can answer the question and C will be the answer.

Bunuel

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16 Dec 2025, 21:18

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How many packages in the depot weight more than 420 grams ?

Statement 1 :
For the average of a set of numbers to be equal to smallest number in that set, all numbers in the set must be identical.

While this tells us every package weighs the exact same amount , we do not know what the weight is.
If every package weights 500 grams it is more than 420 grams.
If every package weighs 400 grams it is less tha 420 grams.
Hence Statement 1 alone is not sufficient.

Statement 2 :

The Median is middle vale of a data set.
A median of 410 tells us that at least 50% packages weigh 410 or less and at least 50% weigh 410 or more.

This does not tells us exactly how many packages are above specific 420 grams.
Hence statement 2 alone is not sufficient.

Combining statement 1 and 2
If every package is identical and median is 410, then every single package must weigh exactly 410 grams.
Since every package is 410 grams ,
No package is more than 420 grams hence the answer is zero.

Conclusion: Combined , the statements are sufficient.

Correct answer: C

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Statement 1:
average = least
=> it means all the values are same

insufficient to guess the weight though

Statement 2:

Median = 410. So there can be packages with 420 like 1 or 2 or even 0

insufficient

Combined:

All are same and median = 410, means all are 410. So 0 packages of weight >= 420 grams

Together sufficient

Ans: Option C

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IMO answer is C.

Question doesn't provide n so it is a yes or no answer instead of value answer.

Statement 1 defines that mean is equal to lightest. If mean is lightest then it cannot be in the center or in middle as avg. So we can infer that all weights are same. But this doesn't share any information about the specific weight. It can be more than 420gm and still be lightest.

Statement 2 defines the median as 410 but doesn't tell how many packages are in total so it cannot be defined. If it was in percentage then I think this would been sufficient to answer like <50%.

Combining the above statements you get that all the package are same and the middle one is 410 so conclusion is that no package is more than 420gm which makes this sufficient.

Hope this helps

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What question is asking :

How many packages weigh more than 420 gram ?

Statement 1: it's just a information, exclusively we can't determine anything from this except that all the packages will be of same weight

Statement 1 alone is not sufficient

Statement 2 : ok, so median is 410. however, exclusively with this statement also we can't say how many packages, which are weighing above 420, is there.

statement 2 alone is not sufficient

Statement 1 + 2 :

so we know average package is the lightest one, which means all the packages are of same weight and as statement 2 says that weight of median package is 410, that means all the packages are of 410 grams.

So packages weighing above 420 = 0

So statement 1+ 2 is sufficient - Answer - C

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IN THIS QUESTION WE NEED A EXACT ANSWER
WE HAVE TO FIND HOW MAY PACK ARE WEIGHT>420 GRAM

1) AVERAGE IS = TO LIGHTEST WEIGHT WHIS ONLY POSSIBLE IN CASE WHEN ALL THE WEIGHTS ARE EQUALAND WEIGHTS CAN'T BE -VE ALSO
EG. 2+2+2+2+2/5=2 AS MEAN EVEN A SLIGHT CHANGE IN VAIABLE WILL CHANGE THE MEAN
SO A IS NOT THE ANSWER

2) MEDIAN IS 410
MEADIAN IS MIDDLE VALUE AND IN CASE WHEN ALL THE OTHER VALUES ARE SAME SO 410 DOEST MAKE ANY BIG DIFFERNCE B IS ALSO OUT

COMBINING ALSO GIVES NO RESULT COZ WE WANT EXACT NUMBER HENCE E IS CORRECT

Bunuel

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