the line n

[sanju09]

What is the equation of line n?

(1) The point (6, 8) is on line n.

(2) Sum of the intercepts of the line n, on the coordinate axes is 28.



MBM

[bluementor]

y intercept = c
x intercept = b
slope of line = m

what is the equation of line n?

statement 1: the point (6, 8) is on line n

clearly insufficient, since you would need either the slope or another known point on the line to determine the equation.

statement 2: b + c = 28

actuall values of b and c are unknown. insufficient.

for eg.,

if b = 20, c = 8, the slope = -8/28
if b = 8, c = 20, the slope = -20/8

both statements together:

b + c = 28
b = 28 - c

equation of a straight line : y = mx + c

and the slope, m = -c/b = -c/(28 - c) = c/(c - 28)

so, y = (c/(c - 28))*x + c

we know from statement 1 that line n passes through (6,8). Substituting values for x and y respectively:

8 = (c/(c - 28))*(6) + c
8 - c= (6c)/(c - 28)
c^2 - 30c + 28(8) = 0
c^2 - 30c + 14(16) = 0
(c - 14)(c-16) = 0

c = 14 or c = 16.

if c = 14, b = 28 - 14 = 14, m = -1
if c = 16, b = 28 - 16 = 12, m = -4/3

insufficient since there are two possible slopes.

choose E.

-BM-

[2010gmat]

1. In suff
2. In suff

1 + 2 ...

x/a + y/b = 1; intercept eqn of line

x/a + y/(28-a) = 1; use 1. to solve for a ...

1+2 = suff --> C

[sanju09]

1. In suff
2. In suff

1 + 2 ...

x/a + y/b = 1; intercept eqn of line

x/a + y/(28-a) = 1; use 1. to solve for a ...

1+2 = suff --> C

Will you get a single value of a in this case, 2010gmat?