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primes again!!!

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primes again!!!

by rajatvmittal » Sat Feb 16, 2013 10:09 pm
If a number is to be randomly selected from Set X, what is the probability that the number will be even?

(1) Set X contains only prime numbers

(2) Set X contains consecutive integers
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by Ian Stewart » Sun Feb 17, 2013 7:35 am
Statement 1 is not sufficient, since the set could be {2, 3}, and the answer is 1/2, or it could be {2, 3, 17}, and the answer is 1/3, among other possibilities.

Statement 2 is not sufficient, since the set could be {1, 2, 3}, and the answer is 1/3, or it could be {2, 3, 4}, and the answer is 2/3, among other possibilities.

Together, we know the numbers in the set are both prime and consecutive. From the wording of the question ('numbers', 'integers'), I assume the set contains more than one number, though the question needs to be more clear about that point. There are only two primes which are consecutive integers: 2 and 3. So the set must be {2, 3}, and the answer is 1/2. So the answer is C.
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by Brent@GMATPrepNow » Sun Feb 17, 2013 7:38 am
rajatvmittal wrote:If a number is to be randomly selected from Set X, what is the probability that the number will be even?

(1) Set X contains only prime numbers

(2) Set X contains consecutive integers
Target question: What is the probability that the selected number will be even?

Statement 1: Set X contains only prime numbers
There are several sets of numbers that meet this condition. Here are two:
Case a: the numbers are {3, 5} in which case P(selected number is even) = 0
Case b: the numbers are {2, 3} in which case P(selected number is even) = 1/2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Set X contains consecutive integers
There are several sets of numbers that meet this condition. Here are two:
Case a: the numbers are {3, 4, 5} in which case P(selected number is even) = 1/3
Case b: the numbers are {2, 3} in which case P(selected number is even) = 1/2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
At this point, the answer boils down to whether or not set X can have only 1 number in it. It could be argued that statement 1 (Set X contains consecutive integers) indicates that set X must contain at least 2 numbers, since "integers" is plural and "consecutive" suggests that we have at least 2 numbers. That said, I think the test-makers would remove any possible ambiguity by adding some wording to that effect.

If we assume that set X must have 2 or more numbers, then the answer is C
Here's why:
If the numbers must be both prime and consecutive, then there are only 2 numbers that meet these criteria: {2,3}. Given this, P(selected number is even) must equal 1/2

Since we can now answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C

-------------------------------------------------------------

If it's possible that set X can have only 1 number, then the answer is E. Consider these two cases:
Case a: the set is {2, 3} in which case P(selected number is even) = 1/2]
Case b: the set is {3} in which case P(selected number is even) = 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

-----------------------------------------------
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by rajatvmittal » Sun Feb 17, 2013 8:11 am
here is what explanation says

Correct Answer: E.

The logic behind this question is apt to trap quite a few test-takers. Note that, while Set X contains only prime numbers AND it contains (some) consecutive integers, it doesn't contain ONLY consecutive integers. Here's where playing devil's advocate helps you. While it's true that Set X could contain just {2, 3} (two consecutive prime numbers), it could also consist of {2, 3, 17, 23}. That set contains only prime numbers and it contains consecutive integers (2 and 3), so it satisfies both statements but gives a different probability (1/4) than the set of just 2 and 3. Accordingly, the correct answer must be E.
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by Ian Stewart » Sun Feb 17, 2013 9:07 am
rajatvmittal wrote:here is what explanation says

Correct Answer: E.

The logic behind this question is apt to trap quite a few test-takers. Note that, while Set X contains only prime numbers AND it contains (some) consecutive integers, it doesn't contain ONLY consecutive integers. Here's where playing devil's advocate helps you. While it's true that Set X could contain just {2, 3} (two consecutive prime numbers), it could also consist of {2, 3, 17, 23}. That set contains only prime numbers and it contains consecutive integers (2 and 3), so it satisfies both statements but gives a different probability (1/4) than the set of just 2 and 3. Accordingly, the correct answer must be E.
When the question writer can't be bothered to make clear whether the set must contain more than one element, which is a crucially important issue here, I hardly expect that they are using language so precisely that we need to pay attention to the distinction between 'contains' and 'consists of'. Real GMAT questions don't contain silly linguistic 'traps' like this. Where is this question from?
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by Tommy Wallach » Sun Feb 17, 2013 11:23 am
Hey Guys,

I'm on the fence on this one. Ian is absolutely right that the GMAT doesn't play linguistic tricks very often. However, I'm not sure I'd call this a linguistic trick. There's a fairly major difference between:

Set X contains consecutive integers
Set X contains only consecutive integers

You could easily write a legitimate question with this language, such as:

If a number is to be randomly selected from Set X, what is the probability that the number will be even, if every number in Set X is prime?

(1) Set X contains consecutive integers
(2) Set X contains only two terms

In this case, the answer would be (C), even though the first statement doesn't have to mean "Set X contains only consecutive integers.

Hope that helps!

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by Ian Stewart » Sun Feb 17, 2013 2:47 pm
Tommy Wallach wrote: I'm on the fence on this one. Ian is absolutely right that the GMAT doesn't play linguistic tricks very often. However, I'm not sure I'd call this a linguistic trick. There's a fairly major difference between:

Set X contains consecutive integers
Set X contains only consecutive integers
This is really an academic discussion, but if I look at the definition of 'contain' in my Mac dictionary (which is based on the New Oxford American Dictionary), the first two definitions read as follows:

contain
verb [ trans. ]
1. have or hold (someone or something) within
2. be made up of (a number of things); consist of

So in the context of this question, the meaning of 'contain' is ambiguous. If you use definition 1 above, then Set X can contain other things. If use definition 2, it can't. There is no way a group of expert mathematicians will agree on the right answer here, and no real GMAT question will ever use this kind of semantic ambiguity as the basis of a 'trap'.
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by Tommy Wallach » Sun Feb 17, 2013 2:56 pm
Hey Ian,

I accept this challenge!

I don't see how the second definition implies that that's all that can be in something. In fact, the second definition you cite is this:

"¢ be made up of (a number of things); consist of: borscht can contain mainly beets or a number of vegetables.

That makes it clear it would be made up of a number of things, but in this list, we only get one thing, implying that this is NOT the definition we should be using (that definition would only apply if there were a number of things after it, as in the example).

That being said, even if the word "contain" could be ambiguous here, the fact that they use the word "only" on one of them makes it pretty clear that we can't take the "only" for granted.

Anyway, who really cares, right? : )

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by Ian Stewart » Sun Feb 17, 2013 3:20 pm
Tommy Wallach wrote:
Anyway, who really cares, right? : )
Yes, this is really the kind of pedantic discussion (meant in a good way - I like pedantic discussions!) that GMAT instructors might enjoy, but which don't really matter to test takers. I understand where you're coming from, but when one possible definition of 'contain' is 'consist of', which means 'entirely made up of', I think the usage is ambiguous.

But my larger issue really was this - the OP posted a few questions from what I assume is the same source. Some of those questions were very careless both with language and with logic. So it seems a bit absurd to me for them to include a 'trap' in a question which hinges on a precise interpretation of the usage of a certain word when they are so cavalier about their use of language everywhere else. How are we to guess that this is the one question where they're using language correctly? :)

And in any case, I think questions like this really mislead test takers into thinking the GMAT is about things the GMAT just isn't about. These aren't the kinds of 'traps' test takers need to care about. So while the question may have produced a fun discussion about semantics, I think it's one that test takers should just ignore.
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by Tommy Wallach » Sun Feb 17, 2013 3:54 pm
Hey Ian,

Agreed on all counts. Good talk. : )

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