In the rectangular coordinate system, is the point (m, n) farther from the origin than point (p, q)?
(1) mn − pq = 12
(2) p + q = 21.
How do you attack this one
its between A, C and E all of us can conclude that.
do you go the algebraicaly creative 'walah!' approach or
pick numbers to disprove A, C and E conclusively ?
IMO, whenever we encounter a problem which looks very time-consuming, it's highly possible to have E as OA ( this we can conclude if we skillfully substitute numbers)
1) stmt 1: mn-pq= 12 --> we're easily misled to think that m+n > p+q as well. What's about the case of p or q = 0??
Example: p=0 , q= 20 , m=4, n=3 ---> point (p,q) is farther from the origin than (m,n)
p= 1, q=1, m=13,n=1 ---> (m,n) is farther than (p,q)
2) nothing about m,n ---> can't conclude ---> insuff
1) and 2) :
in case: p=0, q=21 , m=4,n=3 ---> (p,q) is farther than (m,n)
in case: p= 15, q= 6, m= 17, n= 6 (satisfy stmt 1) ---> (m,n) is farther than (p,q)
---> E it is.