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GMAT Club Olympics 2025 (Day 9): What was the average speed of a deliv

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average 4 hours = sum all boxes 4 hours / 80?

(1)
average first 2 hours = sum all boxes first 2 hours / number of boxes first 2 hours
20 = sum all boxes first 2 hours / number of boxes first 2 hours

INSUFFICIENT

(2)
average last 2 hours = sum all boxes last 2 hours / number of boxes last 2 hours
30 = sum all boxes last 2 hours / number of boxes last 2 hours

INSUFFICIENT

(1)+(2)
20 = sum all boxes first 2 hours / number of boxes first 2 hours
30 = sum all boxes last 2 hours / number of boxes last 2 hours
sum all boxes first 2 hours + sum all boxes last 2 hours = sum all boxes 4 hours
number of boxes first 2 hours + number of boxes last 2 hours = 80

5 unknowns and 4 equations

INSUFFICIENT

IMO E

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t = 4 hours
n = 80 boxes
What was the avg. weight of the boxes ?

Statement 1:
We know avg. weight of boxed loaded in first 2 hours = 20 Kg. This is NOT SUFFICIENT.

Statement 2:
We know avg. weight of boxed loaded in last 2 hours = 30 Kg. This is NOT SUFFICIENT.

Combining:
We cannot find the number of boxes in st.1 and st.2 which essential to get the answer required. NOT SUFFICIENT.

Answer is 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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Mark loaded a total of 80 boxes into a truck
4-hour shift
We want average weight of boxes loaded during the shift?

Given statements,

(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 he loaded in the first 2 hours.
Without that we cant compute the total weight from this period, nor can we compute the full total weight or overall average.

Statement (1) alone is 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 how many boxes he loaded in the last 2 hours.
Without that we cant compute the total weight from this period, nor can we compute the full total weight or overall average.

Statement (2) alone is insufficient

Combining statements (1) and (2),

Even combined we still dont know how many boxes were loaded in each half of the shift.
Since,
Average = total weight / number of boxes

We are only given partial average weights but not the breakdown of the total number of boxes
=> We still cannot find the total weight

Lets take 2 cases,

Case 1:
First 2 hours 40 boxes with average 20 kg each
=> Total weight = 800 kg

Last 2 hours 40 boxes with average 30 kg each
=> Total weight = 1200 kg

Total = 800+1200 = 2000 kg

=> Average = 2000 / 80 = 25 kg

Case 2:
First 2 hours 30 boxes with average 20 kg each
=> Total weight = 600 kg

Last 2 hours 50 boxeswith average 30 kg each
=> Total weight = 1500 kg

Total = 2100 kg

=> Average = 2100 / 80 = 26.25 kg

Since multiple weights possible,
Statements (1) and (2) together are still insufficient.

(E) – Statements (1) and (2) together are not sufficient.

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Option E is the correct answer.

Lets understand the information mentioned in the question before try to solve for it.

So the question starts by telling us that Mark has loaded a total of 80 boxes in his 4 hour shift. And then asks us was the average (arithmetic mean) weight of the boxes he loaded during the shift.

Now after understanding the information mentioned in the question lets check the given statements and see whether we can find out the answer with their help or not.

Statement 1: "During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms". Now this statement tells us that during the first 2 hours of his shift the average weight of the boxes which he loaded was 20 kg but does not gives us any information about second haft of the shift or the actual number of box which he loaded in this duration. So from here we can have multiple cases like: lets say he loaded 40 boxes in the first half and in the second half also he loaded 40 boxes of the same average i.e. 20 kg then this will give us the total average weight of 20 kg. Whereas we take that in the first half he loaded 30 boxes and in the second half he loaded 50 boxes of average weight 25 kg then the overall average will be: (20*30+50*25)/80 = 23.125 kg. So from these two cases only we can tell that we are getting multiple answers from this piece of information that's why this is Not Sufficient to answer the question.

Statement 2: "During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms". This statement also the same as the first statement it only gives us the average weight for second half of the shift but does not give any specific number of boxes or the average weight for first half. So as we checked for the first statement this statement will also give as multiple values that's why this is also Not Sufficient to answer the question.

As we have checked that both the statements alone cannot answer the question so now lets try to Combine both of then and see whether we can find our answer from their Combination or not.

So after combination we know the average weight of the boxes which were loaded in first half of the shift is 20 kg and average weight of the boxes which were loaded in second half of the shift is 30 kg.
Now lets assume the number of boxes loaded in first half to be 'x' then the number of boxes loaded in second half will be (80-x), it which will help us in easing the calculation part now.

Now to find the total average weight of the boxes we have to calculate: (20*x + 30*(80-x)/80
Lets assume x to be 40 then (80-x) will also be 40. Now lets put these values in the above equation.
=>(20*40+30*40)/80 = 25 kg.

Now lets assume the value of x to be 60 then the value of (80-x) will be 20, lets see whether we get the same average in this case as well or not.
=>(20*60+30*20)/80 = 22.5 kg

As we can clearly see that here also we are not getting any unique value to the question that's why we can conclude that neither Statement-1 nor Statement-2 are sufficient to answer the question and the Combination is also Not Sufficient to answer the question. That's why Option E is our answer.

Bunuel

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Even after all the information, we don’t know the number of boxes loaded in the periods. Neither in the first two hours, not in the last two hours.
So, even with the information provided in the both statements, we cannot determine the average weight of the total boxes.
Answer: E

Bunuel

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We have to find the total weight of the 80 boxes loaded during the 4-hour shift and divide the result by 80.

(1)
We have no information about the last 2 hours of the shift.

Statement is insufficient

(2)
We have no information about the first 2 hours of the shift.

Statement is insufficient

(1)+(2)
We need to calculate the total weight of the 80 boxes, that will be equal to the sum of the total weight of the boxes during the first 2 hours plus the total weight of the boxes during the last 2 hours, but:
- we cannot calculate the total weight of the boxes during the first 2 hours of the shift because we do not know the number of boxes that were loaded in those 2 hours.
- we cannot calculate the total weight of the boxes during the last 2 hours of the shift because we do not know the number of boxes that were loaded in those 2 hours.

Both statements are insufficient

The right answer is E

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Bunuel

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For arithmetic mean we use the formula of weighted averages:

x(mean) = n1*x1+n2*x2/n1+n2
Here we know,
n1+n2=80

Statement 1:
We just get the value of x1 from this.
Still need the value of n1, n2 and x2 to find the mean
Not Sufficient.

Statement 2:
We just get the value of x2 from this.
Still need the value of n1, n2 and x1 to find the mean
Not Sufficient

Statement 1 and 2:
We still don't have the value of n1 and n2
We just know n1+n2=80
Not Sufficient.

ANSWER: E

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80 Boxes were loaded in 4hour shift.

Statement 1- Avg weight of boxes loaded during first two hours is 20kg. From this we don't know how many boxes were loaded.
(2)Statement 2- Similar to the first statement we still dont know the number of boxes.

Both Statements combined-
let us assume n1 and n2 be the number of boxes loaded in first and second halfs.
n1+n2=80
20n1+30n2/n1+n2= average
20n1+30(80-n1)/n1+80-n1
2400-10n1/80
we still dont have any detail about n1. So both statements together are not sufficient.

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To find mean weight = total weight divide by 80
S1 is insufficient because we have no info about no of boxes
S2 too is insufficient because we have no info about no of boxes
S1+S2
Assume first 2 hours he did x boxes meaning he did 80-x in the last two hours
Total weight would be 20x+30(80-x)= 2400-10x
so mean would be (2400-10x)/80 which is impossible to compute coz x is unknown hence both are insufficient
ANS E

Bunuel

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Correct Answer: We can't find average (arithmetic mean) weight of the boxes he loaded during the shift.
Both the statements together and alone are not sufficient.

Let’s check each statement alone and together:

(1) During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
Here we don't know exactly what number of boxes are of 20 kg weight. Even, we don't know about the number of boxes and their weights in last two hour. So without having either if these two information we can't use this statement alone.

(2) During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.
Similarly if we use this statement alone, we don't know about first two hours number of boxes and their weights. Also we don't know exactly what number of boxes are of 30 kg weight. So without having either if these two information we can't use this statement alone.

3) Using both the statements:

If we use both statements also, we can't answer this question.
Let’s check this using an example:
Suppose we have 50 boxes of 20kg weight and 30 boxes of 30Kg weight
Average= (1000 + 900)/ 4 hours= 475kg
Let's take another example,
Suppose we have 40 boxes of 20kg weight and 40 boxes of 30Kg weight
Average= (800 + 1200) / 4 hours= 500 kg

Hence we cannot solve this question using both the statement together.

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Q: Avg. weight of the boxes?
Avg. weight of boxes = Total weight/Total boxes (80)
We need the total weight of these boxes.

St1: This statement does not tell us how many boxes were loaded during this period. Without the number of boxes, we cannot get the total weight of boxes loaded in the first 2 hours. Insufficient.

St2: Similarly, this statement gives us the average weight of boxes loaded in the last 2 hours but not the number of boxes loaded during this period. Thus, we cannot calculate the total weight for the last 2 hours. Insufficient.

Combing St1 and St2: Even after combining, we still don’t know the number of boxes loaded in the first 2 hours and the number of boxes loaded in the last 2 hours and the total weight of the 80 boxes.

Option E

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The correct answer is choice (E) both statements are not sufficient

Statement 1 - this provides information about the first 2 hours of the shift and and the 20 kg average of the boxes but we don't know how many boxes of the 80 were loaded in order to calculate the final average.

Statement 2 - similarly, this provides information about the second half of the shift and the 30 kg average but we don't know how many boxes of the 80 were loaded in this half.

Since the number of boxes within each shift half is important to calculate the average overall, we cannot solve the question without more information and both of those statements are not enough to solve it.

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Given -> 4 hour shift. Mark loaded 80 boxes
To determine -> Average weight of the 80 boxes.

Statement 1 -> During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
Say the number of boxes loaded during these two hours is $N$ and $S_1$ is the sum of the weight of the boxes
$\frac{S_1}{N} = 20$
We don't know how many boxes were loaded in the next 2 hours nor do we know their weights. Insufficient.

Statement 2 -> During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.
Say the number of boxes loaded during these two hours is $80-N$ and $S_2$ is the sum of the weight of the boxes
$\frac{S_2}{80-N} = 30$
We don't know how many boxes were loaded in the first 2 hours nor do we know their weights. Insufficient.

1+2 -> The average weight of all the boxes $= \frac{S_1+S_2}{80}$
$S_1=20N$

$S_2=30(80-N)$

$\frac{S_1+S_2}{80} = \frac{20N+30(80-N)}{80}$

We don't know what $N$ is. Not sufficient.

Answer - E

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Given:
Mark loaded 80 boxes in 4 hour shift

Question
Avg mean of weight during shift?

Statement 1: During the first 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 20 kilograms.
In first 2 hours of 4 hours shift he loaded boxes of avg weight 20 kg. But we dont know if his rate of work was similar throughout or different.
So this is not sufficient.

Statement 2: During the last 2 hours of the shift, the average (arithmetic mean) weight of the boxes Mark loaded was 30 kilograms.
Same reason, we know last 2 hours but no idea on what was his rate of of work in first 2 hours.
So this is not sufficient.

Combine:
We know in first 2 hours he loaded boxes weighing 20kg avg, In last 2 hours he loaded boxes weighing 30kg avg.

But we dont know the quantity of how many boxes were loaded in each hour or we dont know the total weight of 80 goods.

What if he loaded 50 boxes in first 2 hours then 30 in next 2 hours
his rater will be 100+90/4=190/4=47.5 kg

If he loads 40 boxes in first 2 hours and 40 in next two hours
His rate will be 80+120/4=200/4=50 kg/box

So we cannot determine the exact weight.

So no statement is sufficient.
Answer E

Bunuel

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To calculate average is necessary to know total weight of the 80 boxes.

(1)
It's impossible to calculate total weight of the 80 boxes.

Insufficient

(2)
It's impossible to calculate total weight of the 80 boxes.

Insufficient

(1) and (2)
Knowing parcial averages without knowing the number of boxes in each part, it is still impossible to calculate the total weight of the 80 boxes.

Insufficient

Correct answer is E

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Statement (1):
Average in first 2 hours = 20 kg
But we don’t know how many boxes were loaded in those 2 hours.
Not sufficient

Statement (2):
Average in last 2 hours = 30 kg
Again, no info on how many boxes in those 2 hours.
Not sufficient

Combine (1) and (2):
Still no info. on how many boxes in each half of the shift.
So we cannot compute total weight or average.
Still not sufficient.

So, the correct answer is option E

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average = sum all boxes / 80

(1)
No information about sum all boxes.

Statement (1) alone is insufficient.

(2)
No information about sum all boxes.

Statement (2) alone is insufficient.

(1)+(2)
To calculate the sum of the 80 boxes, we would need to know how many boxes were loaded in the first 2 hours or in the second 2 hours. Since we don't know this, we can't calculate the total sum of the 80 boxes and, therefore, can't calculate the average for the 4 hours.

Statement (1) and (2) together are insufficient

Answer E

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Statement I:
If mark loads k1 boxes during first 2 hours:
20k1 = Sum of weights of k1 boxes.
We have no information about the avg. weight during last 2 hrs. Insufficient.

Statement II:
If mark loads k2 boxes during lasr 2 hours:
30k2 = Sum of weights of k2 boxes.
We have no information about the avg. weight during first 2 hrs. Insufficient.

Statement I and II:
Avg. weight = 20k1 + 30k2/80
We do not know k1 and k2. Therefore insufficient.

Therefore , option E is correct.
Bunuel

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