Good DS question - Cogeo

[austin]

Are lines p (with slope m) and q (with slope n) perpendicular to each other?
1. m + 2 = n
2. m + n = 0

OA in a bit

[bluementor]

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-

[vittalgmat]

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.

[austin]

OA is C...

Great explanations by Vittal and mentor....