A set of 7 different integers has a median of 11, range of 10

Question

A set of 7 different integers has a median of 11, range of 10, and average of 12. What is the highest possible value of the greatest integer in the set?

A. 17
B. 18
C. 19
D. 20
E. 21

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Adit_ · Answer

This problem is really simply when you realise that from the options C,D,E are ruled out.
Why? Because any of those numbers -10 = 9/10/11 as the 1st number, 4th number is 11 and you cant have all distinct integers in between.
So answer is either 17 or 18 only.

If you take 17. Then deviation to the right would be 1+5 = 6
And when we have 7 as our first number we easily see that deviation more than covers it like 5+4+3.. >> 6

So now try 18.
Deviation = 1+6 = 7
Smallest number = 8
Deviation to the left = 4+3+2 Also covers it completely.

No need to check remaining as well already cancelled them out!

Answer:  Option B

poojaarora1818 · Answer

Solution:

Already mentioned in the question stem.

Range = 10

Median = 11

If the average is 12, then the sum = 7*12 = 84.

Let's set up the set of distinct integers = 8, 9, 10, 11, 12, 16, 18.

By looking at the options, only option B fits into this series. As we already know, 11 is the median, and if the last number is 18 and the range is 10, then the smallest number will be 8, so the next has to be greater than 8 and should be distinct, that is, 9, and so on.

As we know, the sum of the distinct integers is 84, so the sum of 8 + 9 + 10 + 11 + 18 =56 => 84-56= 28. So, the numbers fall between the median and the greatest no should be 12 & 16.

Answer: B

MartyMurray · Answer

A set of 7 different integers has a median of 11, range of 10, and average of 12. What is the highest possible value of the greatest integer in the set?

Since the median is 11, three of the integers must be lower than 11. Since they are different integers, the greatest possible values of those three are 10, 9, and 8.

Thus, since the range is 10, max value of the highest is constrained to 18 or lower.

Now, to choose between the two choices that fit that constraint, A. 17 and B. 18, we can determine whether 18 is possible.

Since the average of the seven integers is 12, their sum is 7 × 12 = 84.

8 + 9 + 10 + 11 + ? + 18 = 84

? = 28

Since 12 + 16 or 13 + 15 = 28, 18 is possible.

A. 17
B. 18
C. 19
D. 20
E. 21

Correct answer:   B

dp1234 · Answer

Can you please explain how deviation to right or left was calculated ?

ExpertsGlobal5 · Answer

B is the correct answer choice.  
 
  Video explanation:

https://www.youtube.com/watch?v=YbZnVsDqpfI

salphonso · Answer

Can you please explain this concept / point to someplace I can understand this?

If you take 17. Then deviation to the right would be 1+5 = 6 
 And when we have 7 as our first number we easily see that deviation more than covers it like 5+4+3.. >> 6

So now try 18. 
 Deviation = 1+6 = 7 
 Smallest number = 8 
 Deviation to the left = 4+3+2 Also covers it completely.

Adit_ · Answer

Hello.

Look at the arrangement:

a,b,c,11,d,e,f

Now last value is 10 + Smallest value.

When u take 17 as largest value, 7 is the smallest value.
Now to make the highest value as high as possible you need to maximize the deviation.

What I mean by deviation? Its just the difference in value from the mean.

Now when u indeed take 17:

7,b,c,11,d,e,17
How can u maximize the deviation to the left? By taking the next integers from 7. Why? So the deviation is the maximum from 12 which is our average!
At the end of the day we need the sum to be 12*7 or any value above 12 should be matched by an equal value less than 12.

So in this case to maximize deviation left side of median we take:
7,8,9,11,d,e,f.

What is the deviation? 12-7 + 12-8 + 12-9 = 5+4+3 = 12.  
For f to be maximum we also need to max the values of d,e close to the mean itself.
Keep d,e, as 12,13

Thus
7,8,9,11,12,13,17 is our sequence

Deviation from mean on left including 11 = 13 and right side of our mean = 1+5 = 6
Clearly 17 is not "max" enough like you can see.

Take 18 with same rules:

8,9,10,11,12,13,18

What you now see is left side deviation with mean of:
4+3+2+1 = 10
Right side:
1+6=7

Can u increase to 19 now?
It is funny because unique values wont even fit in.

Hope it helps.

A set of 7 different integers has a median of 11, range of 10

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A set of 7 different integers has a median of 11, range of 10

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615 to 715 in 15 Days (Ria's Strategies)

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