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Question 2

by cans » Sat May 28, 2011 11:24 am
IF P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

1) For any integer in P, the sum of 3 and that integer is also in P.

2) For any integer in P, that integer minus 3 is also in P.
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by maihuna » Sat May 28, 2011 11:40 am
is 3^1, 3^2, 3^3 etc all there.
1. 3+x is there for all any x so 3, 3+3, 3+3+3 will all be there...since all positive power of 3 can be represented in sum of 3, it suffice.

2. since 3 is there it means 3-3 is there, 0-3 si there etc ..so all non-positive integers are there including 3, but no way to determing higher power of 3 r there..

i will choose A.
cans wrote:IF P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

1) For any integer in P, the sum of 3 and that integer is also in P.

2) For any integer in P, that integer minus 3 is also in P.
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by vzzai » Sat May 28, 2011 4:23 pm
IMO, It is A.

Please publish the OA.
Thank you,
Vj
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by cans » Sat May 28, 2011 8:37 pm
OA A
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by amar66 » Sat May 28, 2011 11:02 pm
To solve this problem, it is better to start with the member that we already have: 3 in this case.

(1) For any integer in P, we have also (that integer + 3). So, for 3 that we already have, we have also 6. For 6, we have 9....So, P={3, 6, 9, ...}. Sufficient.

(2) For 3, we have 0. For 0, we have -3. So, P={3, 0, -3, ....}. Insufficient.

A is it.
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