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One actually does not need to perform any calculations for this question. Note that we are given the additional variable of time as a non essential a information to this question.

Since our target question is to find the average weight of 80 boxes, we would need some relation about weight and quantity.

(1) During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.But how boxes were loaded in those 2 hours?.. 10.. 20 ..70, for each assumption the average mean of whole 80 boxes will change. Insufficient

(2) During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.Same issue as with statement 1. Insufficient

Further even if we consider both statements together, we still do not know the distribution of number of boxes between first 2 hours and next 2 hours.

There could be 20 boxes in first 2 hours and 60 boxes in next 2 hours or even just 1 box in first 2 hours and 79 in next 2 hours. For every combination the mean will change. Hence Insufficient.


Hence correct choice is E.
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total time is 4 hours
total boxes are 80

target
What was the average (arithmetic mean) weight of the boxes he loaded during the shift?
total weight of boxes / 80

#1

During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.

let boxes be x in 1st shift , so total weight moved is 20x

insufficient

#2

During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.

(80-x) boxes were moved avg weight 30 ; total weight moved 30*(80-x)

insufficient as x is not known
from 1 &2
since we do not know value of x so we cannot determine weight moved actual in both shifts

IMO OPTION E is correct
Bunuel
Over a 4-hour shift, Mark loaded a total of 80 boxes into a truck. What was the average (arithmetic mean) weight of the boxes he loaded during the shift?

(1) During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
(2) During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.


 


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Statement 1
Insufficient
Since we dont know the weights for the last 2 hours or even the average weight as the average weight can be different.

Statement 2
Insufficient
Since we dont know the weights for the first 2 hours or even the average weight as the average weight can be different.

Both together
Sufficient
As we can now calculate the total average weight as we have the complete picture now.

Ans : C
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Bunuel
Over a 4-hour shift, Mark loaded a total of 80 boxes into a truck. What was the average (arithmetic mean) weight of the boxes he loaded during the shift?

(1) During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
(2) During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.


 


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total number of boxes given = 80

asked: average weight of boxes lifted in 4 hours?

Statement 1: average weight of boxes lifted in first two hours = 20kg, But since the number of boxes lifted is not mentioned, so Not Sufficient

Statement 2: average weight of boxes lifted in last two hours = 30kg, But since the number of boxes lifted is not mentioned, so Not Sufficient

Combined 1 and 2: total weight lifted in first 2 hours = 40 kg
and total weight lifted in first 2 hours = 60 kg
So the total weight lifted in 4 hours = 100 kg and we are given 80 boxes in total were lifted. So we can find average weight of boxes lifted in 4 hours by 100kg/80
So sufficient. Hence the answer is Option C.
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Over a 4-hour shift, Mark loaded a total of 80 boxes into a truck. What was the average (arithmetic mean) weight of the boxes he loaded during the shift?

(1) During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
We don’t know about last 2 hours......
Insufficient

(2) During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.
We don’t know about first 2 hours......
Insufficient

(1)&(2)
First 2 hours: total weight = 20x
Last 2 hours: total weight = 30(80 - x)

So total weight of all 80 boxes =
20x + 30(80 - x) = 20x + 2400 - 30x = 2400 - 10x

So average weight = (2400 - 10x)/80

Still, we don’t know x
Insufficient

E
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Here we know the total number of boxes

In the first option the arithmetic weight is given in the first two hours,but we don't know number of boxes.So not suffient
In the second option,here also the number of boxes not given

Even if we take both of the options together we still don't know the number of boxes in the first half and also in the second half and I could not make equations for this

Hence E is the answer.
Bunuel
Over a 4-hour shift, Mark loaded a total of 80 boxes into a truck. What was the average (arithmetic mean) weight of the boxes he loaded during the shift?

(1) During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
(2) During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.


 


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Bunuel
Over a 4-hour shift, Mark loaded a total of 80 boxes into a truck. What was the average (arithmetic mean) weight of the boxes he loaded during the shift?

(1) During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
(2) During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.


 


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We need to average (arithmetic mean) weight of the boxes he loaded during the 4 hr shift.

Stmt 1 : During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
We need to know the overall avg weights to find the average weight for the entire shift. We can't find with this info.

Hence, stmt 1 is insufficient.

Stmt 2 : During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.

Similarly, we can't find the average weight of the load for the entire shift just by using 2 hr info. Hence, stmt 2 is insufficient.


When we combine, it's tempting to take the average of the averages. But this is a trap. As we need to find the weighted average, we don't have details about how many boxes are loaded in each shift. Hence, both combined is also insufficient.

IMO E
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We have Total boxes = 80, Average weight = Total weight/Total boxes


(1) During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
We don't know how many boxes were there with average weight of 20kgs, neither do we know the average weight of remaining boxes of last 2 hrs of the shift. Not sufficient.

(2) During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.
Same. We don't know how many boxes were there with average weight of 30kgs, neither do we know the average weight of remaining boxes of first 2 hrs of the shift. Not sufficient.

Combining Average weight = 20*(no of boxes of first 2hrs of shift) + 30*(no of boxes of last 2hrs of shift) /80

We still dont know how many boxes were there in the individual 2hr shifts, neither do we have weights/ratios of boxes in both the shifts, Hence Not Sufficient

Ans E
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1. if 20box 20kg=400 or 30box 20kg=600.. avg. weight of rest 60 or 50 box not given.. NOT SUFFICIENT
2. if 60box@30kg=1800 or 50box@30kg=1500...avg. weight of rest 20 or 30 box not given..NOT SUFFICIENT

Together,
20 box 20 & 60 box @ 30..total wt.=2200
30 box 20 & 50 box @30..total wt=2100.....NOT SUFFICIENT

Ans E
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Here's the brief analysis for the Data Sufficiency problem:

Goal: Find the average weight of 80 boxes loaded over 4 hours.

Statement 1: Average weight for the first 2 hours was 20 kg.

Problem: We don't know how many boxes were loaded in those first 2 hours.

Sufficiency: Not sufficient.

Statement 2: Average weight for the last 2 hours was 30 kg.

Problem: We don't know how many boxes were loaded in those last 2 hours.

Sufficiency: Not sufficient.

Combining Statements 1 & 2:

Let N1 be boxes in the first 2 hours and N2 in the last 2 hours.
N1 +N2 =80 (total boxes)

Total weight from first 2 hours = 20×N1
Total weight from last 2 hours = 30×N2

Overall total weight = 20N1 +30N2
Overall average = (20N1 +30N2 )/80

Problem: We still don't know the individual values for N1 and N2
​ Since the boxes could be distributed in various ways (e.g., 40 in each period, or 30 in the first and 50 in the second), the overall average changes.

Sufficiency: Not sufficient.

Conclusion: Neither statement alone nor both statements together are sufficient.

Answer: E
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Mark loaded a total of 80 boxes over a 4-hour shift, and we are asked to find the average weight of all the boxes. Statement (1) tells us that the average weight of the boxes loaded during the first 2 hours was 20 kilograms, but it does not tell us how many boxes were loaded in that time, so we cannot determine the total weight contributed by that part of the shift. Statement (2) gives the average weight during the last 2 hours as 30 kilograms but, again, without knowing how many boxes were loaded, we cannot determine the total weight for that period. Even when combining both statements, we still lack information on how many boxes were loaded during each half of the shift, which is necessary to compute the weighted average. Since different distributions of box counts would lead to different overall averages, the two statements together are still not sufficient. Therefore, the correct answer is E.
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Alright, so today's problem is about figuring out the average weight of 80 boxes in 4 hours, which is (total weight) ÷ 80. We need to know the total weight.

Condition 1:
First 2 hours, average is 20.
From this, we can only assume the amount moved in the first 2 hours is 'a', so the weight is 20a.
But we don't know the total weight of the remaining boxes or how many 'a's there are. Not enough info.

Condition 2:
Next 2 hours, average is 30.
From this, we can only assume the amount moved in the next 2 hours is 'b', so the weight is 30b.
But again, we don't know the total weight of the remaining boxes or how many 'b's there are. Still not enough info.

Combining Conditions 1 & 2:
(20a + 30b) / (a + b) = (20a + 30b) / 80
We still don't know what 'a' and 'b' are. Not enough info.

Answer: E
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Time taken to load 80 boxes is 4 hours, avg weight will be 80/4= 20kgs. First option provides that evidence of this solution , so do the second option. Hence, both statements are sufficient, but neither statement alone is sufficient.
Answer is Point C.
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The right answer is E. We cannot tell the overall average weight because we never know how many boxes Mark loaded in each two‐hour segment. Knowing that his first‐half average was lighter and his second‐half average heavier still leaves open whether he loaded most of the 80 boxes early or late. Without the split in quantities, neither the first‐period data nor the second‐point data by itself (and not even both together) let us calculate the true overall mean. This is because the total of 80 could be split in a lot of ways that each way will change the average.
Bunuel
Over a 4-hour shift, Mark loaded a total of 80 boxes into a truck. What was the average (arithmetic mean) weight of the boxes he loaded during the shift?

(1) During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
(2) During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.


 


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Time = 4
Boxes = 80

What was the average (arithmetic mean) weight of the boxes he loaded during the shift?

S1
During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
Let number of boxes loaded in the first 2 hrs be x
Weight loaded in the first 2hrs = 20x
We do not know the avg weight of 80-x remaining boxes to calculate the avg weight
Insufficient

S2
During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.
Let number of boxes loaded in the first 2 hrs be x
Boxes loaded in the last 2hrs = 80-x
Weight loaded in the last 2hrs = 30(80-x) = 2400-30x
We do not know the avg weight of x remaining boxes to calculate the avg weight
Insufficient

Combined, we have total weight of boxes loaded in first 2hrs as 20x and boxes loaded in last 2hrs as 2400-30x
Total weight = 20x+2400-30x=2400-10x
We still don't have value of x to calculate the weight
Insufficient

Answer E


Bunuel
Over a 4-hour shift, Mark loaded a total of 80 boxes into a truck. What was the average (arithmetic mean) weight of the boxes he loaded during the shift?

(1) During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
(2) During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.


 


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Statement (1):
But we don't know how many boxes he loaded in the first 2 hours vs. the last 2 hours.
So this info alone is not sufficient.

Statement (2):
Same issue — we don’t know how many boxes were loaded during this time.
So this info alone is not sufficient.

Combining 1 and 2 :
Still, we don’t know how many boxes were loaded in each 2-hour period, so we can’t compute a total average weight unless we know that split.
So even together, the statements are not sufficient.

Final Answer E.
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