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Integers

by parulmahajan89 » Sun Nov 24, 2013 7:42 pm
A set of 15 different integers has a medium of 25 and range of 25. What is the greatest possible integer that could be in this set?

a) 32
b) 37
c) 40
d) 43
e) 50

Why is answer not 50?
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by [email protected] » Sun Nov 24, 2013 8:00 pm
Hi parulmahajan89,

In these types of "stats" questions, it's important to pay attention to all of the limitations that the information provides:

We're told that there are 15 different integers with a median of 25 and a range of 25. We're asked for the maximum possible value of any integer in the set.

Since there are 15 different integers and the median is 25, then 7 numbers are BELOW 25 and 7 numbers are ABOVE 25.

- - - - - - - 25 - - - - - - -

Since the range is 25, to make the largest number as large as possible, we need to make the smallest number as large as possible also. Here's how THAT would happen:

18 19 20 21 22 23 24 25 - - - - - - -

If the biggest "smallest" number is 18, and the range is 25, then the biggest number is 18 + 25 = 43

Final Answer: D

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by Uva@90 » Sun Nov 24, 2013 8:05 pm
parulmahajan89 wrote:A set of 15 different integers has a medium of 25 and range of 25. What is the greatest possible integer that could be in this set?

a) 32
b) 37
c) 40
d) 43
e) 50

Why is answer not 50?
Hi Parulmahajan89,
In this question you have to note many words,
1) 15 different integers
2) greatest possible integer

Coming to Answer,
Median is 25 and Range is 25 and there are 15 different integers,

_ _ _ _ _ _ _ 25 _ _ _ _ _ _ _


To the left of 25 there should be 7 and to the right of 25 there should be 7 numbers.

But what question say is greatest possible integer. So we need to minimize to the left so that we can get the max number on the right side,
18,19,20,21,22,23,24,25_ _ _ _ _ _ _
And the range given is 25.
Hence max number should be 18+25 = 43.

Hence Answer is D

Regards,
Uva.
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by theCodeToGMAT » Sun Nov 24, 2013 9:52 pm
Range = Largest - Smallest

15 Terms & 25 is median.. So that means we have 7 terms on left of Median.

TO maximize the RHS of Median we must minimize the LHS of Median... we can do this by subtracting "1" as we got left from Median.

So, Smallest = 25-7 = 18

==> 25 = Largest - 18

Largest = 43
[spoiler]
{D}[/spoiler]
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by parulmahajan89 » Mon Nov 25, 2013 9:04 pm
Thank you everyone
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by parulmahajan89 » Mon Nov 25, 2013 9:06 pm
Thank you everyone
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by parulmahajan89 » Mon Nov 25, 2013 9:07 pm
Thank you everyone
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by Mathsbuddy » Tue Nov 26, 2013 12:09 am
x = maximum
m = minimum
Range = x - m = 25

Median is at position (15 +1)/2 = 8
Therefore there are 15 - 8 = 7 numbers both above and below it
To maximise x, we need to maximise m
Maximimum value of m = 25 - 7 = 18
x = 25 + 18 = 43 (D)
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