If p and q are positive integers, how many integers are larger than pq ... ...
If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 2)?
(A) 3
(B) ...
(C) ...
(D) ...
(E) ...
*This question is included in
Nova Math - Problem Set A: Substitution
Replies to This Thread: 0
|
----
Posted: 09/02/2012 10:33
I don't understand this question. Can someone thoroughly explain it to me.
Admin
Replies to This Thread: 0
|
----
Posted: 09/07/2012 20:12
Jagathi, have you followed the explanation when you tap on Show Correct Answers (before you move on to the Next Question)?
Anyway, we are looking for the count of integers larger than pq and smaller than p(q+2).
p(q+2) = pq + 2p
Think about 2 and 5. How many integers are between 2 and 5? It's not 5 - 2, but (5 - 2) -1 or 2, which are 3 and 4.
Similarly, the count of integers between pq and pq + 2p is pq+2p - pq -1, or 2p - 1.
Replies to This Thread: 0
|
----
Posted: 10/23/2012 20:10
In the question it says that "p" and "q" are positive integers as yet in the example it calls for substituting the variables with 1 and then 2. 1 is odd I thought ?
Contributor
Replies to This Thread: 0
|
----
Posted: 10/23/2012 20:27
Hey there Cody. Yes, 1 is odd and it is a positive integer, so what do you think is the problem?
Replies to This Thread: 0
|
----
Posted: 01/19/2013 15:47
Hi. I do not understand. You make p=1 and q =2 so that the only middle number is 3, but when doing 2p-1, than that equals 2 (1) - 1 which equals 1, not 3.
Replies to This Thread: 0
|
----
Posted: 05/28/2013 18:19
(2)(1)=1 which is not bigger than pq of which pq=2. So how does this work ? My answer Is 3 since pq=2 < 3 < p(q+2)=4
Admin
Replies to This Thread: 0
|
----
Posted: 05/28/2013 20:41
Andres, we are looking not for a specific number, but for the count of integers between pq and p(q+2). Taking p as 1 and q as 2 (you can choose other examples too), we find that there is only 1 integer, which is = 3. We want to express the count, ie, 1, in terms of the variables p and q as in the answer choices. So we plug p and/or q into the expressions in order to find an answer that equals 1. We find it in D, 2p - 1, which equals 1. I hope this helps.
