Arithmatic problem

[deepak_pathania]

38,69,22,73,31,47,13,82
Which of the following numbers is greater than 3/4 of the numbers but less than one fourth of the numbers in the list above ?
A) 56 B) 68 C) 69 D) 71 E) 73

I could not understand the explanation given in the book.

[anshumishra]

38,69,22,73,31,47,13,82
Which of the following numbers is greater than 3/4 of the numbers but less than one fourth of the numbers in the list above ?
A) 56 B) 68 C) 69 D) 71 E) 73

I could not understand the explanation given in the book.

There are a total of 8 numbers. So the question asks which number is greater than 6 of them and less than 2 of them.
If you write the number in ascending form :

13,22,31,38,47,69,73,82

So, the number should be between 69 and 73. D is the only option which is, right.

[aleph777]

Deepak,

I think the challenging thing about this question is that it's trying to trick you into thinking the number you're looking for is actually featured in the set shown.

Since they're kind enough to give us 8 numbers, we know, then that we are looking for a number greater than 6/8 of the numbers in the set yet less than 2/8 of them. But that means that NONE of the numbers in the actual set can fulfill that goal, since the 6th number in the set is 69 and the 7th number is 73.

Therefore, you need a number that falls between those two numbers, which would be greater than 6 of the numbers in the set, and less than 2 of the numbers in the set.

The only choice: D

[deepak_pathania]

Correct. I could not think that question is not about the values given here and they are talking about the placement of the numbers.

[Brian@VeritasPrep]

Hey guys,

Great question (and terrific answers, anshu and aleph!). It's definitely true that they want you to think that the correct answer choice is one of the numbers in the set - I just looked at this one and that was my first thought, too. But here's how I turned my initial "it's impossible" thought into a correct answer within around 30 seconds:

-I looked at the set of numbers first to see how many values there were and noted that there were 8.

-Before even thinking about numbers, I looked at it this way:

To be greater than 3/4 of the numbers, you have to be bigger than 6 out of 8. So only the 7th and 8th largest numbers need apply...anything less doesn't count.

To be less than 1/4 of the numbers, you have to be smaller than 2 out of 8. So only the 1st through 6th need apply. And there's no overlap between the two sets (1st-6th for "Less" and 7th and 8th for "More").

-So...there are really only two options for solving this one. Either I missed the word "other" in the question stem (so that the number in question doesn't count as one in the denominator..."is greater than 3/4 of the OTHER numbers in the set"), or the correct answer doesn't have to be one of the numbers in question.

-Since 8, the current number of terms in the set, works perfectly with 1/4 and 3/4, I then looked to see if the correct answer were a 9th term to split the set. Like Anshu did, I then noted it had to be between 69 and 73.


You know, I may have just repeated Aleph's explanation in different words, so maybe this doesn't add much new but just in case I'll leave the post up. Great question and discussion, all!