the line n

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-

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

2010gmat wrote: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?