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Cybermusings wrote:Set of 15 different integers has a median of 25 and a range of 25. What could be the value of the greatest integer that could be in this set

1) 32
2) 37
3) 40
4) 43
5) 50

OA after few replies

I always fall for this kind of question. Ok, here goes...

Since the set is not sorted or not composed of consecutive integers,
the median can technically be the least integer in the set.

So, the highest integer is 25 + 25 (range) = 50.

e.g.

26, 27, 28, 29, 30, 31, 32, 25, 33, 34, 35, 36, 37, 38, 50

So, E?

OA please

jayhawk2001 wrote:

Cybermusings wrote:Set of 15 different integers has a median of 25 and a range of 25. What could be the value of the greatest integer that could be in this set

1) 32
2) 37
3) 40
4) 43
5) 50

OA after few replies

I always fall for this kind of question. Ok, here goes...

Since the set is not sorted or not composed of consecutive integers,
the median can technically be the least integer in the set.

So, the highest integer is 25 + 25 (range) = 50.

e.g.

26, 27, 28, 29, 30, 31, 32, 25, 33, 34, 35, 36, 37, 38, 50

So, E?

OA please

The definition of median goes like this: -
The middle value in a set of numbers arranged in increasing order. If there is an even number of values, then median is the average of the middle two values. For example: The median of the set {10, 12, 14, 19, 20} is 14. The median of the set {2, 3, 4, 6, 8, 9} is 5, which is the average of 4 and 6.

So 25 has to be middle value with 7 integers having less and 7 having more value.
Suppose we take the set like:-
18,19,20,21,22,23,24,25 Then the highest possible value can be 18+25 (lowest +range) = 43.
Now 50 can't be the answer because for 50 to be the answer, set has to take the following form: -
25,25,25,25,25,25,25,25,...50 - because lowest value has to be 25. (lowest +range) i.e. 25+25 = 50. But it is given that all the integers are different, so I think the answer is 43.

What is OA?

Hi jayhawk..the fact that median and range is specified, in itself means that the set is arranged in an increasing order

since the question asks about the greatest integer ,start with 50

G-S = 25
median = 25

the numbers are different

if G=50, then S = 25 but that contradicts the question since all the numbers are different

next, pick 43

G= 43, S = 18

hence the set can be written as

18,19,20,21,22,23,24,25,..........43

so the median in the above set is 25
and the range 43-18 is also 25

Hence D

anyway, this question should be in PS thread.
:!:

mendiratta wrote:
The definition of median goes like this: -
The middle value in a set of numbers arranged in increasing order. If there is an even number of values, then median is the average of the middle two values. For example: The median of the set {10, 12, 14, 19, 20} is 14. The median of the set {2, 3, 4, 6, 8, 9} is 5, which is the average of 4 and 6.

So 25 has to be middle value with 7 integers having less and 7 having more value.
Suppose we take the set like:-
18,19,20,21,22,23,24,25 Then the highest possible value can be 18+25 (lowest +range) = 43.
Now 50 can't be the answer because for 50 to be the answer, set has to take the following form: -
25,25,25,25,25,25,25,25,...50 - because lowest value has to be 25. (lowest +range) i.e. 25+25 = 50. But it is given that all the integers are different, so I think the answer is 43.

What is OA?

As expected I fell for this one .

I agree with Mendiratta. It has to be a sorted list. Back to basics !

Thanks for the clarification.

Official Answer - 43

Well....I don't have the official explanation...but the simple thing to remember here is that no two numbers are the same in the sequence....so the median could have easily been 50 had all the numbers preceding the 8th number (i.e. the median 25) was equal to the median....However, since this is not the case it rules out 50....and 43 is the next highest logical number available....

I didn't have time to go into greater depths...so I guess the explanations provided here might me more plausible than mine!!