akhp77 wrote:Statement 1:
Q, R, and S occur at 2 places. So these cannot be even
yeah.
in more detail:
a product of integers will be even if any of the integers is/are even.
the product is odd only if all of the integers are odd.
so, it's impossible for q, r, or s to be even:
* if q were even, then pq, qr, and qs would all be even.
* if r were even, then both qr and rs would be even.
* if s were even, then both rs and qs would be even.
so the only way to satisfy statement (1) is to make 'p' even. (if p were also odd, then
none of the products would be even.)
as akhilesh says, this statement gives no clues as to whether p is prime.
--
statement 2:
says nothing about p.
--
together:
examine statement 2.
you could do this algebraically, as done by akhilesh, or you could just make a list:
15, 21, 27, 33, 39, ...
if you make a list, it becomes pretty clear that all of these numbers are divisible by 3, so none of them will be prime.
therefore, S is the non-prime number.
so, from statement 1, p is even.
from statement 2, p is prime.
sufficient.
Ron has been teaching various standardized tests for 20 years.
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
