Six baskets of tomatoes have been inspec

Question

4, 11, 12, 7, 1, n

Six baskets of tomatoes have been inspected for bruises, and the numbers of bruised tomatoes in the six baskets are listed above. The number of bruised tomatoes in one of the six baskets is equal to the average number of bruised tomatoes in the six baskets. What is the average of the possible values of n?

A. 20.5
B. 22
C. 25
D. 27.5
E. 34

paragw · Answer

Here's my solution

2448 · Answer

avg = 35+n/6 = 5+(n+5/6)
greater than 5 = 7, 11, 12, n
solving for all to get value of possible n as: 7, 31, 37, 7 for avg = 7, 11, 12, n respectively
so avg = 7+31+37/3 - 25. Ans.

suntprovident · Answer

How did you arrive at the assumption of average being 11, 12 and why only 11 and 12 ?

ankushsambare · Answer

It is mentioned in the question that:
The number of bruised tomatoes in one of the six baskets is equal to the average number of bruised tomatoes in the six baskets.

which means:
It means that if you add up the number of bruised tomatoes in all six baskets and divide by 6, the answer is exactly the same as the number of bruised tomatoes in one of the baskets.

egmat · Answer

Hi suntprovident,

11  and  12  aren't assumptions the solution pulled from nowhere. They're just  two of the numbers already sitting in the list  (4, 11, 12, 7, 1, n), and here's why every one of those numbers becomes a candidate.

Start from the condition

The question says one basket's count  equals the average  of all six. So the average has to be one of the six values in the list. That gives you six things to test - one for each basket:

- average =  4 
- average =  11 
- average =  12 
- average =  7 
- average =  1 
- average =  n

For each one, set (35 + n)/6 equal to that value and solve for n.

Why only some survive

Since n is a count of tomatoes, it can't be negative. Look at what the small values force:

- average =  4  -> 35 + n =  24  -> n =  -11  ❌
- average =  1  -> 35 + n =  6  -> n =  -29  ❌

Those get thrown out. That's exactly the point 2448 made: since the average is 5 + (n+5)/6, it's  always more than 5 , so it can never equal  4  or  1 . That's why the small numbers drop off and you're left checking  7 ,  11 ,  12 , and  n .

The survivors:

- average =  7  -> n =  7  ✅
- average =  11  -> n =  31  ✅
- average =  12  -> n =  37  ✅
- average =  n  -> n =  7  (same as above)

Distinct values:  7, 31, 37  -> average = 75/3 =  25 .

So  11  and  12  were picked simply because they're in the list - and they  stayed  because, unlike  4  and  1 , they give a valid (non-negative) n.

Answer: C

Six baskets of tomatoes have been inspec

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