Problem Solving

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?

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.

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.

Guess that'll teach me not to bet on GMAT stuff at 1 AM, or something...