the line n

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue May 26, 2009 12:55 am

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

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Source: Beat The GMAT — Data Sufficiency | Tue May 26, 2009 12:55 am

bluementor: Master | Next Rank: 500 Posts; Posts: 418; Joined: Wed Jun 11, 2008 5:29 am; Thanked: 65 times

by bluementor » Tue May 26, 2009 2:04 am

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-

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2010gmat: Master | Next Rank: 500 Posts; Posts: 371; Joined: Fri Mar 06, 2009 2:48 am; Thanked: 27 times; GMAT Score:740

by 2010gmat » Tue May 26, 2009 2:39 am

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

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue May 26, 2009 2:51 am

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?

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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