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Difficulty:
25%
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Question Stats:
74% (01:37) correct
26%
(01:43)
wrong
based on 361
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If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 2)?
A. 3
B. P + 2
C. p – 2
D. 2p – 1
E. 2p + 1
A. 3
B. P + 2
C. p – 2
D. 2p – 1
E. 2p + 1
jamesphw
Joined: 21 Nov 2013
Last visit: 18 Jun 2016
Posts: 8
Location: Canada
Concentration: Strategy, Technology
Schools: Ross '18 (M)
If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 2)?
First, we notice that:
p(q+2) = pq + 2p
So we are asking how many integers are larger than pq but smaller than pq+2p. Notice that the range of this is 2p, so our answer should be around 2p. When you count the number of integers in between two other integers, you take high number - low number - 1.
Answer: pq + 2p - pq - 1 = 2p -1
To see why this counting formula works, try it out.
How many numbers between 1 and 3? 3-1-1 = 1
How many numbers between 1 and 4? 4-1-1 = 2
-2 and 2? 2-(-2)-1=3
First, we notice that:
p(q+2) = pq + 2p
So we are asking how many integers are larger than pq but smaller than pq+2p. Notice that the range of this is 2p, so our answer should be around 2p. When you count the number of integers in between two other integers, you take high number - low number - 1.
Answer: pq + 2p - pq - 1 = 2p -1
To see why this counting formula works, try it out.
How many numbers between 1 and 3? 3-1-1 = 1
How many numbers between 1 and 4? 4-1-1 = 2
-2 and 2? 2-(-2)-1=3
03 Dec 2013, 02:21
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smartyman
The number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is (5-1)-1=3: 2, 3, and 4.
Thus, the number of integers between pq and p(q+2)=pq+2p is (pq+2p-pq)-1=2p-1.
Answer: D.
