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BTG-PQ "K IS A SET OF INTEGERS SUCH THAT" ...

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by gnod » Fri Jun 24, 2011 4:28 pm
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.

I initially thought that X & Y had to be 'set' numbers but the solutions makes it sound like it's not.

Statement 1) if 1 is in K, then 1(2) = 2, and if 1 & 2 are in the set, then 3 is in the set.
I don't get how we're to translate this problem as if X & Y are non-changing numbers.

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by vikram4689 » Fri Jun 24, 2011 5:37 pm
IMO D
1. 1 is in K, so following are in K
1*2 =2
1+2 =3
2+3 =5
2*5 =10
10+3 =13
13+2 =15 ....so 15 is in K
2. 3 is in K,so
3*2=6
3+6=9
9+6=15 ....so 15 is in K
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by Brent@GMATPrepNow » Sat Jun 25, 2011 1:07 pm
gnod wrote: Statement 1) if 1 is in K, then 1(2) = 2, and if 1 & 2 are in the set, then 3 is in the set.
I don't get how we're to translate this problem as if X & Y are non-changing numbers.
thank you
We're not saying that x and y have fixed values here.

Read it as, "If there are two different numbers in a set, then the sum of those two numbers must also be in the set." Don't think about it as a set x-value and a set y-value.

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Brent
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by MM_Ed » Sat Jun 25, 2011 3:36 pm
If 1 is in K, then 2 is in K. If 1 and 2 are in K, then 3 is in K. Therefore statement (1) implies statement (2).

Now, 1+1+...(15x) = 15 and 3+3+...(5x) = 15.

So either statement alone is sufficient to answer the question.
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