Discussion
| (A) | |
| (B) | |
| (C) | |
| (D) | |
| (E) | |
| (F) |
The solution is
Posted: 11/06/2014 20:52
If n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S= n(n+1)/2. Which one of the following statement about S must be true?
A- S is always odd.
B- S always even.
C- S must be a prime number.
D- S must not be a prime number.
E- S must be a perfect square.
A- S is always odd.
B- S always even.
C- S must be a prime number.
D- S must not be a prime number.
E- S must be a perfect square.
Posted: 11/06/2014 22:27
If you try plugging in simple n, like 3, 4, or 5, you can eliminate A, B, C, and E.
Posted: 11/07/2014 13:17
Antonio, S can be either odd or even, so A and B can be eliminated, because they say S must be odd or must be even.
Another way to be sure the answer is D: S is divisible by 2. The definition of a prime number is that it is only divisible by 1 and by itself. By that definition, S cannot be a prime number.
Btw, which problem is this from? We typically only answer questions from our own problem sets.
Another way to be sure the answer is D: S is divisible by 2. The definition of a prime number is that it is only divisible by 1 and by itself. By that definition, S cannot be a prime number.
Btw, which problem is this from? We typically only answer questions from our own problem sets.
Posted: 11/07/2014 14:25
First, thank you so much.
this problem is from number theory, set F from the Nova's prep!
this problem is from number theory, set F from the Nova's prep!
but the other way is could be an even or an odd, that why i got confused, why should only be choice D ?