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BTG practice question -- sets

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BTG practice question -- sets

by aleph777 » Tue Feb 15, 2011 4:24 am
Another BTG question I'm not so sure about re: phrasing.

K is a set of integers such that

i) if x is in K, then 2x is in K

ii) if each of x and y is in K, then x + y is in K

Is 15 in K?

(1) 1 is in K.

(2) 3 is in K.


OA is D. I saw the potential for that answer, but I also thought, "hmm, maybe it's a trap," and I was stuck between choosing D and E because I think I've seen OG questions before with a similar phrasing where you aren't allowed to think beyond the first instance of x and 2x, etc. Is this confusingly worded or will any question on the GMAT expect you to think infinitely unless otherwise told?
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by ankur.agrawal » Tue Feb 15, 2011 7:01 am
IMO D.
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by Night reader » Tue Feb 15, 2011 7:42 am
i) K {i ... integers} {i, 2i ...}
ii) K {i ... integers} (i, i+i ...}
Is 15 in K?

st(1) x=1, K {1, 2, 3, 4 ...15} Sufficient
st(2) x=3, K {3, 6, 9, 12, 15...} Sufficient
IOM D

it's very unlikely that we will see this kind of wording, because this question is in our thread

aleph777 wrote:Another BTG question I'm not so sure about re: phrasing.
K is a set of integers such that

i) if x is in K, then 2x is in K
ii) if each of x and y is in K, then x + y is in K
Is 15 in K?

(1) 1 is in K.
(2) 3 is in K.

OA is D. I saw the potential for that answer, but I also thought, "hmm, maybe it's a trap," and I was stuck between choosing D and E because I think I've seen OG questions before with a similar phrasing where you aren't allowed to think beyond the first instance of x and 2x, etc. Is this confusingly worded or will any question on the GMAT expect you to think infinitely unless otherwise told?
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by Geva@EconomistGMAT » Tue Feb 15, 2011 12:35 pm
aleph777 wrote:Another BTG question I'm not so sure about re: phrasing.

K is a set of integers such that

i) if x is in K, then 2x is in K

ii) if each of x and y is in K, then x + y is in K

Is 15 in K?

(1) 1 is in K.

(2) 3 is in K.


OA is D. I saw the potential for that answer, but I also thought, "hmm, maybe it's a trap," and I was stuck between choosing D and E because I think I've seen OG questions before with a similar phrasing where you aren't allowed to think beyond the first instance of x and 2x, etc. Is this confusingly worded or will any question on the GMAT expect you to think infinitely unless otherwise told?
Every question will expect you to follow the statements wherever they go, even recursively, as this one. Very few questions will use the concept to infinity, though. In this particular case, though, there's no ambiguity:
if x is in K, then 2x is in K.
So if according to (1), 1 is in K, this means that 2*1=2 is in K.
If 2 is in K, then 4 is in K.
If 4 is in K, then 8 is in K.
If 8 is in K, then 16 is in k.
etc. etc.
recursivity follows from the definition of the question stem, and there's no limit - nothing stopping (such as K only includes 2 terms, or some other limiting factor).
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