Discussion
Which of the following must be true.
I. pq + 1 is even.
II. pq/2 is an integer.
III. pq is a multiple of 12.
*This question is included in Nova Math - Problem Set F: Number Theory, question #11
I. pq + 1 is even.
II. pq/2 is an integer.
III. pq is a multiple of 12.
| (A) | I only |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 05/14/2012 16:13
If p=5 and q=7 then pq+1=31
If p=q=1 then pq/2=1/2
If p=3 and q=7 then pq= 21
The answer should none of the above right? Or am I missing something?
If p=q=1 then pq/2=1/2
If p=3 and q=7 then pq= 21
The answer should none of the above right? Or am I missing something?
Posted: 05/14/2012 16:27
Alex, in your first example, pq + 1 = 35 + 1 = 36, not 31.
Acc to the facts given, p and q are odd numbers (since there is a remainder of 1 when they are divided by 2 or 6). The product of odd numbers are always odd numbers, so when you add 1, you always get an even number.
Acc to the facts given, p and q are odd numbers (since there is a remainder of 1 when they are divided by 2 or 6). The product of odd numbers are always odd numbers, so when you add 1, you always get an even number.