WP ed(5) Ch 6, Page 115#3. a, b, and c are integers in the

[georgepa]

a, b, and c are integers in the set {a, b, c, 51, 85, 72}. Is the median of the set greater than 70?

1) b > c > 69
2) a < c < 71

The answer is (A) statement 1 alone is sufficient. I however, had a question on the explanation.

In both statements, the possible values for a in statement 1 and the possible values for b in statement 2 consider an element that already exists in the set (which I believe is wrong)

From the definition of a set, don't the values contained in a set have to be unique? i.e do we even care about the following cases:

For statement 1:
a = 71 (since we already have b as 71 in the set)

For statement 2:
b = 70 (since we already have c as 70 in the set)

I don't think the answer changes since these cases are not valid (and we just don't need to check them) and the explanation still holds true with the other cases.

[supratim7]

Hey..

In both statements, the possible values for a in stmtatement 1 and the possible values for b in statement 2 consider an element that already exists in the set (which I believe is wrong)

There is absolutely nothing in the stem that validates this.
The possible values for "a" in stmt 1 and the possible values for "b" in stmt 2 DOESN'T consider an element that already exists in the set.

As per stmt 1: we know something about "b" & "c", but NOTHING about "a". the stmt DOESN'T consider/assume/indicate any value for "a". So, ANY integer could be "a"

Based on this info and the info already in stem we need to check whether stmt 1 is good to answer "Is the median of the set greater than 70?"

Above explanation is applicable to stmt 2 as well i.e.
As per stmt 2: we know something about "a" & "c", but NOTHING about "b". So, ANY integer could be "b"

For statement 1:
a = 71 (since we already have b as 71 in the set)

For statement 2:
b = 70 (since we already have c as 70 in the set)

As explained, these deductions are plain incorrect.

From the definition of a set, don't the values contained in a set have to be unique?

Nope, values within a set NEED NOT be unique i.e. in *set-land* (2, 2, 2, 2) is as nice/legit/healthy/pretty as (2, 3, 4, 5)

Hope it helps :)

[georgepa]

Hey..

From the definition of a set, don't the values contained in a set have to be unique?

Nope, values within a set NEED NOT be unique i.e. in *set-land* (2, 2, 2, 2) is as nice/legit/healthy/pretty as (2, 3, 4, 5)

Hope it helps :)

Basically this is what I want clarified. If a set is a collection of distinct objects - then {2,2,2,2} is not a set but simply collection of 2s. The set would just be {2}.

See: In mathematics, a set is a collection of distinct objects, ...


Specifically see: Describing Sets

Every element of a set must be unique; no two members may be identical. (A multiset is a generalized concept of a set that relaxes this criterion.) All set operations preserve this property. The order in which the elements of a set or multiset are listed is irrelevant (unlike for a sequence or tuple). Combining these two ideas into an example
{6, 11} = {11, 6} = {11, 6, 6, 11}

- I guess my question is - does the GMAT consider sets to be multisets or the general definition of sets

[messi10]

- I guess my question is - does the GMAT consider sets to be multisets or the general definition of sets

The GMAT will generally specify any restrictions on the set. If nothing is mentioned then assume that the variables can assume any value, including repeated terms.

Also, I would be a bit careful when studying entire subject areas from wikipedia or the web. Sets is a huge topic in mathematics but GMAT only tests certain properties of sets. So if you have a book from a test prep company, then that is a more efficient use of your time in studying the GMAT. Of course, if there are specific doubts with methods on how to do something then you can look up references on the web. But I would steer clear of larger topic areas if I were you.

By the way, even if you were considering the value of integer a in statement 1, (that Supratim has correctly pointed out that you shouldn't), the answer should still have been A.

With b>c>69, the median would always be greater than 70 no matter what you choose integer a to be. So even if you made the mistake of choosing a value for integer a, you should have still got statement 1 as sufficient.

[georgepa]

The GMAT will generally specify any restrictions on the set. If nothing is mentioned then assume that the variables can assume any value, including repeated terms.

By the way, even if you were considering the value of integer a in statement 1, (that Supratim has correctly pointed out that you shouldn't), the answer should still have been A.

Yup - my original post mentioned that the answer doesn't change either way. Thanks for all the tips guys, but I guess, I was looking for an authoritative answer - i.e from the GMAC or at least from one of the instructors

[RonPurewal]

a, b, and c are integers in the set {a, b, c, 51, 85, 72}. Is the median of the set greater than 70?

1) b > c > 69
2) a < c < 71

The answer is (A) statement 1 alone is sufficient. I however, had a question on the explanation.

In both statements, the possible values for a in statement 1 and the possible values for b in statement 2 consider an element that already exists in the set (which I believe is wrong)

From the definition of a set, don't the values contained in a set have to be unique? i.e do we even care about the following cases:

For statement 1:
a = 71 (since we already have b as 71 in the set)

For statement 2:
b = 70 (since we already have c as 70 in the set)

I don't think the answer changes since these cases are not valid (and we just don't need to check them) and the explanation still holds true with the other cases.

well, but those cases certainly are valid possibilities"”at least the way you've transcribed the problem.
i.e., it appears that you have somehow interpreted "b > c > 69" as signifying that b = 71 and c = 70. (!!)
sure, that's one valid case, but hopefully it's clear that b and c don't have to have these values. for instance, it's also possible that, say, b = 1000 and c = 100, in which case a could certainly be 71.

same issue with the other statement"”we just know that a < c < 71, but it doesn't have to be true that a = 69 or that c = 70.