Equation of a Straight Line

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Aman verma: Master | Next Rank: 500 Posts; Posts: 304; Joined: Wed Jan 27, 2010 8:35 am; Location: International Space Station; Thanked: 11 times; Followed by:3 members

Equation of a Straight Line

by Aman verma » Sat Mar 13, 2010 12:15 pm

Q : What will be the equation of the straight line AB ?

I.The line passes through the point ( 3 , 4).

II.The line has intercepts on the axes such that their sum is 14.

800. Arjun's-Bird-Eye

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Source: Beat The GMAT — Data Sufficiency | Sat Mar 13, 2010 12:15 pm

outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 am; Thanked: 46 times; Followed by:3 members

by outreach » Sat Mar 13, 2010 2:17 pm

answer should be C
option 1 would have been sufficient if we knew the slope and constant
4=3m+c

option 2
let the line be y=mx+c
y intercept is c
x intercept is c/m
c+c/m=14

solve the eq in option 1 and option 2 to get slope and constant.

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kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 am; Thanked: 47 times; Followed by:2 members

by kstv » Sat Mar 13, 2010 10:31 pm

eq of a st line y = mx+c
1) (x,y) is (3,4) m and c still 2 unknown
2) y intercept is c and x intercept is 14-c not sufficient but we know m = c/c-14
combine with 1)
4=(c/c-14)(3) + c
4(c-14) = 3c + c(c-14)
expressio c(c-14) is quadratic so 2 values
still not suff IMO E

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Fiver: Master | Next Rank: 500 Posts; Posts: 114; Joined: Mon Sep 22, 2008 3:51 am; Thanked: 8 times; GMAT Score:680

by Fiver » Sun Mar 14, 2010 12:06 am

agree with E.
Both stmts combined we get c = 8 or c = 7 and thus the value of c and m will change in both cases.

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STEVEN SPIELBERG: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Sat Mar 13, 2010 4:11 am; Thanked: 1 times

by STEVEN SPIELBERG » Sun Mar 14, 2010 3:37 am

What's the OA ?

I want to win an OSCAR on the GMAT !!!

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Aman verma: Master | Next Rank: 500 Posts; Posts: 304; Joined: Wed Jan 27, 2010 8:35 am; Location: International Space Station; Thanked: 11 times; Followed by:3 members

by Aman verma » Mon Mar 15, 2010 2:59 am

Sol: Let the equation of the line in the intercept form be : x/a + y/b = 1, where a and b are the intercepts on the axes.

From statement I. we get :3/a + 4/b = 1 since the line passes through point ( 3 , 4 ) .Not sufficient.

From statment II. we get : a + b = 14 or b = 14 - a. Not sufficient

Combining , we get : 3/a + 4/(14-a) = 1 => a = 6 , 7
so we get two equations : 4x + 3y = 24 and x + y = 7. Still not sufficient.

Hence, AnsE

800. Arjun's-Bird-Eye