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10 Apr 2008, 11:09
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This question came from math bin 3 in the Princeton Review 2008 book.
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.
My reasoning is that each statement alone is sufficient, because...
stmt. 1 - any positive multiple of 3 is included because it could be 0 + 3 = 3, 3 + 3 = 6...., 9 + 3 = 12, etc.
stmt. 2- this could be 3 - 3 = 0, 6 - 3 = 3, and so on. so all positive multiples of 3 should also be included right?
According to the PR explanations, statement 2 gives all the negative multiples of 3 and that the correct answer is:
statement 1 alone is sufficient, but statement 2 alone is not sufficient.
Is this an error in the book or am I completely overlooking something?
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.
My reasoning is that each statement alone is sufficient, because...
stmt. 1 - any positive multiple of 3 is included because it could be 0 + 3 = 3, 3 + 3 = 6...., 9 + 3 = 12, etc.
stmt. 2- this could be 3 - 3 = 0, 6 - 3 = 3, and so on. so all positive multiples of 3 should also be included right?
According to the PR explanations, statement 2 gives all the negative multiples of 3 and that the correct answer is:
statement 1 alone is sufficient, but statement 2 alone is not sufficient.
Is this an error in the book or am I completely overlooking something?
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10 Apr 2008, 13:28
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As per question If P is a set of integers and 3 is in P. Let us assume that to start with P contains only 3.
Statement 1:
Tells us that for any integer in P, the sum of 3 and that integer is also in P. As we already have 3 as part of P, so what follows is we have 3+3 = 6, 6+3 =9, 9+3 = 12...... etc. as part of P. So question is answered.
Statement 2:
Tells us for any integer in P, that integer minus 3 is also in P. As we already have 3 as part of P, so what follows is we have 3-3 = 0, 0-3 = -3, -3-3 = -6,....etc. as part of P. So question is not answered.
Answer A.
Statement 1:
Tells us that for any integer in P, the sum of 3 and that integer is also in P. As we already have 3 as part of P, so what follows is we have 3+3 = 6, 6+3 =9, 9+3 = 12...... etc. as part of P. So question is answered.
Statement 2:
Tells us for any integer in P, that integer minus 3 is also in P. As we already have 3 as part of P, so what follows is we have 3-3 = 0, 0-3 = -3, -3-3 = -6,....etc. as part of P. So question is not answered.
Answer A.
