Coordenate problem

[cartera]

Lines n and p lines on the xy-plane, is the slope of n less than the slope of p?

1. n and p intercepts at the point (5,1)
2. the y intercept of the line n is greater than they intercept of line p


C

Can anyone explain the solution?

[mals24]

IMO C

Equation of line n: y=ax+b1
Equation of line p: y=cx+b2

St 1: Lines n and m intersect at point (5,1)

Equ n: 1=5a+b1
Equ p: 1=5c+b2

We still don't know anything about b1, b2, a or c.--->INSUFF

St2: y intercept of 'n' is greater than that of p.

y intercept is (0,y) or when x is 0

Equ n: y=b1
Equ p: y=b2
Hence b1>b2
Still we don't know anything about a and c --->INSUFF

St1 + St2

b1>b2
1-5a>1-5b
-5a>-5b
a<b--->SUFF

Answer should be C

[cartera]

IMO C

Equation of line n: y=ax+b1
Equation of line p: y=cx+b2

St 1: Lines n and m intersect at point (5,1)

Equ n: 1=5a+b1
Equ p: 1=5c+b2

We still don't know anything about b1, b2, a or c.--->INSUFF

St2: y intercept of 'n' is greater than that of p.

y intercept is (0,y) or when x is 0

Equ n: y=b1
Equ p: y=b2
Hence b1>b2
Still we don't know anything about a and c --->INSUFF

St1 + St2

b1>b2
1-5a>1-5b
-5a>-5b
a<b--->SUFF

Answer should be C

how did you get
1-5a>1-5b? I mean 5a and 5b
-5a>-5b

[cartera]

IMO C

Equation of line n: y=ax+b1
Equation of line p: y=cx+b2

St 1: Lines n and m intersect at point (5,1)

Equ n: 1=5a+b1
Equ p: 1=5c+b2

We still don't know anything about b1, b2, a or c.--->INSUFF

St2: y intercept of 'n' is greater than that of p.

y intercept is (0,y) or when x is 0

Equ n: y=b1
Equ p: y=b2
Hence b1>b2
Still we don't know anything about a and c --->INSUFF

St1 + St2

b1>b2
1-5a>1-5b
-5a>-5b
a<b--->SUFF

Answer should be C

how did you get
1-5a>1-5b? I mean 5a and 5b
-5a>-5b

[ronniecoleman]

Easier way is solve them using coordinate geometry

1 point (5, 1) -- infinite lines can pass thru hence INSUFF

2. n has larger intercept greater than p

Insuff... ( you can have test cases)

but with both the things

we can easily prove thru construction...that n has a larger slope...

[Mozartain]

we can easily prove thru construction...that n has a larger slope...

Could you explain what you mean by 'larger slope'?