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19 Mar 2026, 19:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
52% (02:17) correct
48%
(02:35)
wrong
based on 117
sessions
History
Date
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Not Attempted Yet
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
A. 17
B. 18
C. 19
D. 20
E. 21
20 Mar 2026, 01:42
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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
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
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20 Mar 2026, 05:18
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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
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
ExpertsGlobal5
