Xavier Aptitude Test 2015 Paper

Question : 67 of 113

Marks: +1, -0

The median of 11 different positive integers is 15 and seven of those 11 integers are 8, 12, 20, 6, 14, 22, and 13.
Statement I : The difference between the averages of four largest integers and four smallest integers is 13.25.
Statement II: The average of all the 11 integers is 16.
Which of the following statements would be sufficient to find the largest possible integer of these numbers ?

Statement I only.
Statement II only.
Both Statement I and Statement II are required.
Neither Statement I nor Statement II is sufficient.
Either Statement I or Statement II is sufficient.

Validate

Solution:

(e) If these 7 numbers are arranged in ascending order,they will be 6, 8, 12, 13, 14, 20 and 22. If the median of11 numbers is 15, then 15 is the 6th number. Hence, all3 remaining numbers are above 15.
From Statement I : Average of 4 smallest integers
=

{6 + 8 + 12 + 13}/{4}

= 9.75
Now, (Average of 4 largest integer) –
(Average of 4 smallest integer) = 13.25
Therefore, average of 4 largest integers
= 9.75 + 13.25 = 23
Hence, sum of 4 largest integers = 92
To find largest possible integer, the 7

^{th}

and 8

^{th}

integer should be minimum i.e. 16 and 17.
If largest integer be x, then sum of the four largest integer, i.e. 17 + 20 + 22 + x = 92 ⇒ x = 33
Hence, statement I alone is sufficient to find thesolution.
From Statement II :
Average of 11 integers = 16
Hence, sum of 11 numbers = 16 × 11 = 176
Now, sum of 8 available integers = 110
Therefore, sum of 3 unknown integers = 66
To find largest possible integer, the 7th and 8th integers should be minimum i.e. 16 and 17
∴ 16 + 17 + x = 66 ⇒ x = 33
Hence, statement II alone is sufficient to find thesolution.
Therefore, correct option is E.

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