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.
Statement 1: For any integer in P, the sum of 3 and that integer is also in P.
In other words, if we ADD
3 to any integer in P, we get ANOTHER INTEGER in P.
Since 3 is in P, 3
+3=6 also is in P.
Since 6 is in P, 6
+3=9 also is in P.
Since 9 is in P, 9
+3=12 also is in P.
And so on.
Thus, every positive multiple of 3 -- {3, 6, 9, 12...} -- is in P.
SUFFICIENT.
Statement 2: For any integer in P, that integer minus 3 is also in P.
In other words, if we SUBTRACT
3 from any integer in P, we get ANOTHER INTEGER in P.
Since 3 is in P, 3
-3=0 also is in P.
Since 0 is in P, 0
-3=-3 also is in P.
Since -3 is in P, -3
-3=-6 also is in P.
And so on.
Thus:
Every multiple of 3 LESS THAN OR EQUAL TO 3 -- {3, 0, -3, -6...} -- is in P.
No way to determine whether any multiples of 3 GREATER THAN 3 are in P.
INSUFFICIENT.
The correct answer is
A.
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