If lines p and q are perpendicular to each other, then the following must be true:
m = -1/n
Statement 1: m + 2 = n
if m = 0, then n = 2. NO
if m = -1, then n = 1. YES. Insufficient.
Statement 2: m + n = 0
m = -n
if m=1, then n=-1. YES
if m = 2, then n=-2. NO. Insufficient.
Both statements together: Add both statements
m + 2 + m + n = n + 0
2m = -2
m = -1
substituting m into one of the statements and we'll get n=1. if m=1, and n=1, lines p and q are perpendicular to each other. Sufficient.
Choose C.
-BM-
Good DS question - Cogeo
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IMO C as well.
my approach is similar to BM.
Important points to remember:
- 2 lines are perpendicular to each other if product of their slopes = -1.
ie m*n = -1.
this implies that m = -1/n
Trivially, if m = 1, then n should be -1 if the two lines are perpendicular.
stmt1:
m+2 = n.
this is insufficient. coz we cant find values of m and n. so cannot determine if the lines are perpendicular or parallel or whatever.
stmt2:
m+n = 0.
=> m = -n.
Still not sufficient coz the lines are perpendicular if m = 1 else we dont know.
Combining 1 and 2.
solving the simultaneous equations we get
m= -1 and n= 1.
Hence product of m and n = -1
So C is my answer.
my approach is similar to BM.
Important points to remember:
- 2 lines are perpendicular to each other if product of their slopes = -1.
ie m*n = -1.
this implies that m = -1/n
Trivially, if m = 1, then n should be -1 if the two lines are perpendicular.
stmt1:
m+2 = n.
this is insufficient. coz we cant find values of m and n. so cannot determine if the lines are perpendicular or parallel or whatever.
stmt2:
m+n = 0.
=> m = -n.
Still not sufficient coz the lines are perpendicular if m = 1 else we dont know.
Combining 1 and 2.
solving the simultaneous equations we get
m= -1 and n= 1.
Hence product of m and n = -1
So C is my answer.
