Discussion
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.
*This question is included in Nova Math - Problem Set F: Number Theory, question #8
I. p is even.
II. p is odd.
III. p = 3 · z + 1 for some integer z.
| (A) | I only |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 03/28/2013 13:28
Wait why are we assuming 3q=z? Where did that come from?
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.
p = p, so 3z + 1 = 9q +1
3z = 9q, or, z = 3q.
Hence, we can say p = 3 (3q) + 1 is a true statement.
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?
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?
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
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