If p divided by 9 leaves a remainder of 1, which of the following must ... ...
If
p divided by 9 leaves a remainder of 1, which of the following must be true?
I.
p is even.
II.
p is odd.
III.
p = 3 ·
z + 1 for some integer
z.
(A) I only
(B) ...
(C) ...
(D) ...
(E) ...
*This question is included in
Nova Math - Problem Set F: Number Theory
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Posted: 03/28/2013 13:28
Wait why are we assuming 3q=z? Where did that come from?
Contributor
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Posted: 03/28/2013 13:54
Julia, "p divided by 9 leaves a remainder of 1" can be translated mathematically into p/9 = q + 1/9, or p = 9q + 1, for some integer q.
p = p, so 3z + 1 = 9q +1
3z = 9q, or, z = 3q.
Hence, we can say p = 3 (3q) + 1 is a true statement.
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If p divided by 9 leaves a remainder of 1, which of the following must ... ...
Posted: 08/23/2015 01:10
Ok,
P= 10 yield remainder 1. Then obviously 1 is true .
If p=19, then it's also true for 2.
3 is equivalently true for both 1&2. Answer should be 1&2&3.
Am I right?
Admin
Reply 1 of 1
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Posted: 08/23/2015 01:42
Hi Castor,
The question is asking for the answer-choice that MUST always be true.
Your examples show that I may be true or may be false and that II may be true or may be false, which eliminates both.
Only choice III must always be true.
Nova Press
