Problem Solving

Please time yourself...

If a randomly selected non negative single-digit integer is added to the 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%

49 sec
median at present=5
thus to increase median, value should be greater than 5. thus 6,7,8,9
But range should remain same thus 9 is rejected (increases range)
3/10 = 30%
IMO B

If range is not be changed, then 1 & 9 can't be added.
The numbers that can be added to the set are 2,4,5,6,7,8. Then the median should be greater than 5.
This gives the numbers 6,7,8.

That is 3 out of 10 numbers.
The probability is 3/10 = 30 %
Answer is B

OA B

Nice work on this one, everyone! It looks like you all did this pretty quickly, and in that case one of my favorite activities with GMAT questions is to follow up by proposing a tweak to the problem or creating your own "trap" answer choice. This way you start to anticipate what the authors of the test will do to add difficulty to problems, and you'll be aware of those devices as you're testing.

Here, that word non-negative stands out to me - that means that we're dealing with all single-digit integers 0 through 9. But since it's one of multiple adjectives in the introductory clause, I think it's one of the more-likely-to-be-missed (or misunderstood) parts of this problem. My bet is that, simply by adding the answer choice 33% (3 out of 9), the GMAT could make this question a healthy 10-15 percentile points more difficulty by tricking people into thinking that there were only 9 eligible values.

Brian@VeritasPrep wrote:Nice work on this one, everyone! It looks like you all did this pretty quickly, and in that case one of my favorite activities with GMAT questions is to follow up by proposing a tweak to the problem or creating your own "trap" answer choice. This way you start to anticipate what the authors of the test will do to add difficulty to problems, and you'll be aware of those devices as you're testing.

Here, that word non-negative stands out to me - that means that we're dealing with all single-digit integers 0 through 9. But since it's one of multiple adjectives in the introductory clause, I think it's one of the more-likely-to-be-missed (or misunderstood) parts of this problem. My bet is that, simply by adding the answer choice 33% (3 out of 9), the GMAT could make this question a healthy 10-15 percentile points more difficulty by tricking people into thinking that there were only 9 eligible values.

Brain, I am a regular victim of such mistakes (not on this question but on few other probs) . In fact I have started making Quants error logs now. Even though I am strong in Quants all these silly mistakes are ruining my Quants score. Can you suggest any other effective way to avoid doing these?

Brian@VeritasPrep wrote:Nice work on this one, everyone! It looks like you all did this pretty quickly, and in that case one of my favorite activities with GMAT questions is to follow up by proposing a tweak to the problem or creating your own "trap" answer choice. This way you start to anticipate what the authors of the test will do to add difficulty to problems, and you'll be aware of those devices as you're testing.

Here, that word non-negative stands out to me - that means that we're dealing with all single-digit integers 0 through 9. But since it's one of multiple adjectives in the introductory clause, I think it's one of the more-likely-to-be-missed (or misunderstood) parts of this problem. My bet is that, simply by adding the answer choice 33% (3 out of 9), the GMAT could make this question a healthy 10-15 percentile points more difficulty by tricking people into thinking that there were only 9 eligible values.

Hello Brian and Experts,

I'm confused regarding the solution for this one:

P = Favorable/All Possible
So, P = 3 for {6,7,8} divided by 7 [2,3,4,5,6,7,8} = 3/7
The reason for All possible = 7 is that 0, 1, 9 will increase the range.
So, the P should be approx 40%?

I don't understand why you guys included 0,1 in your total possibilities while you did exclude 9 from total as well as favorable?

Please help to elaborate on this

Thanks,
Rohit

rohitd80 wrote:

Brian@VeritasPrep wrote:Nice work on this one, everyone! It looks like you all did this pretty quickly, and in that case one of my favorite activities with GMAT questions is to follow up by proposing a tweak to the problem or creating your own "trap" answer choice. This way you start to anticipate what the authors of the test will do to add difficulty to problems, and you'll be aware of those devices as you're testing.

Here, that word non-negative stands out to me - that means that we're dealing with all single-digit integers 0 through 9. But since it's one of multiple adjectives in the introductory clause, I think it's one of the more-likely-to-be-missed (or misunderstood) parts of this problem. My bet is that, simply by adding the answer choice 33% (3 out of 9), the GMAT could make this question a healthy 10-15 percentile points more difficulty by tricking people into thinking that there were only 9 eligible values.

Hello Brian and Experts,

I'm confused regarding the solution for this one:

P = Favorable/All Possible
So, P = 3 for {6,7,8} divided by 7 [2,3,4,5,6,7,8} = 3/7
The reason for All possible = 7 is that 0, 1, 9 will increase the range.
So, the P should be approx 40%?

I don't understand why you guys included 0,1 in your total possibilities while you did exclude 9 from total as well as favorable?

Please help to elaborate on this

Thanks,
Rohit

The total in the denominator represents the number of options that you're selecting from. In this case, if you're talking about nonnegative digits, we have the following options: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} giving us 10 possibilities. The fact that 0, 1, and 9 increase the range excludes them from the desired possibilities, not from the total.