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Range

by akash singhal » Sat Nov 07, 2015 9:56 pm
If a randomly selected non-negative single digit integer is added to set X {2, 3, 7, 8}, what is the probability that the median of the set will increase while its range will remain the same?

(A) 20% (B) 30% (C) 40% (D) 50% (E) 60%

OEB




Well My answer is 33.3%.
Is the question asking approximate increase or is the solution an exact answer?
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by MartyMurray » Sat Nov 07, 2015 10:06 pm
Total number of integers from which one could be selected (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), is 10.

Current median, (7 - 3)/2 = 5.

Current range, 8 - 2 = 6

So to increase the median while leaving the range the same we need an integer greater than 5 but not greater than 8. The ones that work are 6, 7 and 8.

So there are 3 out of 10 that work, and the probability of one of them being randomly selected is 30%.

I would bet dollars to donuts that you didn't notice that 0 is one of the integers that could be selected.
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by akash singhal » Sat Nov 07, 2015 10:25 pm
Marty Murray wrote:Total number of integers from which one could be selected (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), is 10.

Current median, (7 - 3)/2 = 5.

Current range, 8 - 2 = 6

So to increase the median while leaving the range the same we need an integer greater than 5 but not greater than 8. The ones that work are 6, 7 and 8.

So there are 3 out of 10 that work, and the probability of one of them being randomly selected is 30%.

I would bet dollars to donuts that you didn't notice that 0 is one of the integers that could be selected.

Thanks Murray,

But, I did notice that 0 is indeed an integer that could be selected.
I just applied a different wrong theory.
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by MartyMurray » Sun Nov 08, 2015 4:32 am
Guess that'll teach me not to bet on GMAT stuff at 1 AM, or something... :o
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by [email protected] » Sun Nov 08, 2015 3:48 pm
Hi akash singhal,

If you correctly noted that 0 was a possibility, then what error did you make? By walking through your steps, then reattempting the question with the proper steps, you'll be less likely to make a similar mistake later on.

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