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Statement 1: Average weight can only be equal to its lightest weight if all the weights are equal.
However we don't know the avg or the lightest weight or any other weight of the packages.
Insufficient

Statement 2: Median is 410 but does have any other info.
Insufficient.

Combining both: From 1 all the weights are same, and median weight is 410 hence all the weights must be 410 gms each.
Hence we can say 0 packages weigh more than 420 gms. And hence Ans is C.
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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statement1: we can't find the actual weight of lighest packet and number of packet is unknown. hence not sufficient
statement 2: we can't find the number of packets and hence it is not sufficient.

combining both doesn't make sense.

hence option E is correct
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Both statement together are not sufficiet
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S1:

If the average weight per package is equal to the weight of the lightest package, it means the weight of all the packages must be equal (then only this condition is possible).
We know the weight of all the packages is the same, but we do not have any idea about:
1) their weight
2) total number of packages

We may get multiple values in answer. Insufficient.

S2:

Even if the median weight of all the packages is 410g, we still don't know the total number of packages.
We just know half of the packages are less than or equal to 410 AND the other half is greater than or equal to 410.
We will get multiple answers. Insufficient.

S1&S2:

All values are the same, and the median is 410, which means the weight of all the packages is 410.
None of the packages weighs more than 420g (whatever the number of packages). Sufficient.

C (Both together are sufficient, not alone)
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Question is How many packages weight more than 420 grams. We need the exact qty of packages that weigh more than 420 grams.

S1. If avg weight is equal to lightest package that means that all packages are having the same weight. However, no weight is specified. Hence not sufficient.

S2. The median is 410 grams. But we don't know how many packages are more than 420 grams. Hence not sufficient.

combining S1 and S2. we know all packages are same weight i.e. 410 grams. Hence sufficient to answer that question that ZERO packages weight more than 420 grams.

ANSWER IS C

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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no. of pckg weighing > 420 gms.

S1 alone: avg = lowest pckg weight hence all pckg must have same weight which is the lowest weight but does not tell about how much.

S2 alone: median as 410 gms, what about left or right of median, hence not enough.

combined: S1 + S2 -> all have same weight that is 410 gms hence none is weighing > 420 gms.
Therefore C
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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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Statement 1:
Average weight = weight of the lightest packet.
If the average weight equals the minimum, then every packet has the same weight, but we don't know what it is.
If all < 420 = 0 Packets; all > 420 = all packets.
Hence, Option A & Option D eliminated.

Statement 2:
Median = 410
Half less than 410, half more than 410.
Still, we don't know the exact numbers. Hence, Option B eliminated.

Combining both: '
1) All packets have identical weight.
2) Median = 410
So that weight is 410
No packet above 420. Hence, OPTION C.
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Clue 1: mean = lightest => all the packets be of same weights
Clue 2: median = 410; so can't tell info about the population

Combined; all the packets are of 410 gms => 0 packets of weights more than 420gms
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Statement 1 implies that all packages are of the same weight since avg = lightest package
It doesnt mention count of packages or weight of lightest package so not sufficient

Statement 2 says that median wt (i.e. center most wt when packages are arranged from lightest to heaviest) is 410 gms - no clarity on total count of packages or lightest/heaviest details so not sufficient

Combining, since all packages are of same weight and median wt is 410gm, no package weighs more than 420 gms --> Sufficient

Option (C)
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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.

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From Statement I
Average weight is equal to lightest weight and this is only possible when all weights are equal because average always lies in between smallest & largest value including.
In this case we don't know the value of lightest weight. Can't answer the number of packages with weight >420g. (Not sufficient)

From Statement II
Median weight is given = 410g but we don't have any data regarding weights of packages. Not sufficient.

I & II together
Weight of all packages will be 410g. None is greater than 420g. Sufficient to answer. Correct Ans is C
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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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From the stem, we can identify that we need a concrete number of packages that weigh more than 420 grams.

Statement 1:

If the average is equal to the lightest package, that means all the packages weigh the same as the lightest package, thus all the packages weigh the same amount. But we have no information about whether that's more than 420 grams, or even how many packages are involved. Insufficient.

Statement 2:
If the median is 410, then half the packages weigh equal to or less than 410, and half the packages weigh equal to or greater than 410. We have no way of identifying how many weigh more or less. Insufficient.

Statement 1 & 2 combined:
We know all the packages weigh the same, and that the median is 410. Therefore, all the packages weigh 410 grams, and 0 weigh more than 420, which is a definitive value. Sufficient.

The answer is C.
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Solution:

Statement 1 Insufficient

When the mean is equal to the lightest package, this means the weights of the other packages are the same.

Statement 2 Insufficient

This only tells about the median of 410 grams.

By combining both statements, we get the answer that the weight of the packages in the set is less than 420 grams.

Hence, option C


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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Quote:
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. -> This means all packages are equal in their weight. However, we do not know what that specific weight is. This is insufficient.
(2) The median weight of all the packages in the depot is 410 grams. -> We do not know the number of packages in this case, meaning there's no way to determine how many of them weigh more than 420grams. This is insufficient as well.

(1)+(2). This means all packages weigh 410 grams, translating to none of them being heavier than 420grams. This is sufficient.
Answer: C
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Problem Statement: how many packages above 420 weigh?

Statement 1 concludes all the packages will be of same weight. But it can be less than 420 or more than 420 also. Not Sufficient
Statement 2 median is 410 which also not give us the exact number of packages above 420. Not Sufficient

From Statement 1 and 2,
All packages have same weight of median 410 which depicts there are 0 packages less than 420. Sufficient

So, correct answer is C
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S1. We do not know what the exact weight is even though we can tell all the packages weigh the same so insufficient
S1. We do not know about the rest of the packages and how much they weigh hence insufficient
1+2 Sufficient because we already know from 1 that all of them weigh the same so the answer to our question is NO
Ans C
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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Question: Number of packages that weigh > 420 g?

(1) The average weight per package = weight of lightest package.

If average = minimum value of the group. This implies that all the values of the group is same.

Hence (1) makes it is clear that the value is same, but it does not provide any value, comparing which we can find the answer to the asked question.

Therefore, (1) alone is not sufficient.

(2) The median weight = 410 g
This implies that for 50% of the group weight will be < 410 and for remaining weight will be > 410.

This information is not enough to identify the count of packages that weigh > 420 g

Therefore, (2) alone is not sufficient.

Considering (1) and (2) together:
From (1), we concluded that all values of the group are same. From (2), it is given that 410 is median.
Combining the two statements, it can be established that all packages weigh 410 g each. It further implies that none of them would weigh > 420 g.

Therefore, the answer to the question is 0 and both (1) and (2) together is sufficient to answer this.

(C) is the answer
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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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There are different packages in a shipping depot, and each package weight is recorded in grams.

We need to find: The number of packages weighing MORE THAN 420 grams.

Statement 1:

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

Average = ( heaviest weight + lightest weight ) /2

If that average value = lightest weight, then heaviest weight should be equal to lightest weight.

Which means, all the weights in the shipping depot are of equal weights (SAME).

As, we don’t know the exact weight of the depot. It can be either 420 grams, OR less than 420 grams OR more than 420 grams.

Hence, Insufficient

Statement 2:

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

The median weight is the middle value of the packages arranged in ascending order.

Since, there are many combinations for this case.

All values equal to 410 grams.

Some less than 410 grams and some greater than 410 grams.

Even in that, there are chances where the values are higher than 420 grams, and some less than 420 grams.

Hence, Insufficient

Combining both Statements 1 and 2, we get

There are packages where all values are equal, and the median is 410.

Thus, there is ONLY ONE CASE, where all the packages have equal values and the value is equal to 410.

So, the number of packages greater than 420 grams = 0

We have got a concrete unique solution.

Hence, Sufficient

Option C
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