Gmat practice test 1

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vladmire: Master | Next Rank: 500 Posts; Posts: 132; Joined: Tue Oct 07, 2008 4:59 pm; Thanked: 4 times

by vladmire » Tue Oct 14, 2008 4:56 pm

In the rectangular coordinate system above the area of triangle pqr is what fraction of the area triangle lmn?

1/9
1/8
1/6
1/5
1/3

its a triangle within a triangle with the points L= 2,0 P = 6,0 R = 10,0 N = 14,0 Q = 8,4 M = 8,12

can anyone help me

and if this has already been solved what should I have typed in the search field to find it

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Source: Beat The GMAT — Problem Solving | Tue Oct 14, 2008 4:56 pm

Gmatss: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Tue Sep 16, 2008 9:29 pm; Location: new york; Thanked: 2 times

by Gmatss » Tue Oct 14, 2008 5:15 pm

just find the area of 2 triangles.

Pqr=1/2 b.h
1/2 (4)* 4= 8

lmn=1/2 b.h
1/2 (12)* 12)=72

so 8/72= 1/9
A

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gmat009: Master | Next Rank: 500 Posts; Posts: 458; Joined: Sun Aug 31, 2008 10:44 amFollowed by: 1 member; Thanked: 3 times

by gmat009 » Fri Oct 17, 2008 10:01 am

somehow I am getting ans 1/3.
What's OA

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mental: Master | Next Rank: 500 Posts; Posts: 145; Joined: Mon Sep 29, 2008 1:14 am; Thanked: 13 times

by mental » Fri Oct 17, 2008 10:21 am

OA is 1/9

it was posted on forum sometime back with the picture.

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gmat009: Master | Next Rank: 500 Posts; Posts: 458; Joined: Sun Aug 31, 2008 10:44 amFollowed by: 1 member; Thanked: 3 times

by gmat009 » Fri Oct 17, 2008 10:26 am

mental wrote:OA is 1/9

it was posted on forum sometime back with the picture.

I cannot find it. Do you have the link.....

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mental: Master | Next Rank: 500 Posts; Posts: 145; Joined: Mon Sep 29, 2008 1:14 am; Thanked: 13 times

by mental » Fri Oct 17, 2008 10:37 am

I am unable to look for it

anyway will try to give a brief solution

as you see that points L,P,R,N all lie on x-axis

triangle LMN, base = LN = 12 (difference of x-odinates)
height = y-ordinate of m = 12, as the perpencular distance from x-axis
AREA = 12*12/2=72

Triangle PQR, base = PR = 4 (10-6)
height = 4
AREA = 4*4/2=8

ratio = 8/72 = 1/9

...........................
also if you see, they are similar isoceles triangles

also their bases are in ratio 1:3
also heights in 1:3

so area will be 1:9

.......................................
hope that helps

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gmat009: Master | Next Rank: 500 Posts; Posts: 458; Joined: Sun Aug 31, 2008 10:44 amFollowed by: 1 member; Thanked: 3 times

by gmat009 » Fri Oct 17, 2008 10:53 am

mental wrote:I am unable to look for it

anyway will try to give a brief solution

as you see that points L,P,R,N all lie on x-axis

triangle LMN, base = LN = 12 (difference of x-odinates)
height = y-ordinate of m = 12, as the perpencular distance from x-axis
AREA = 12*12/2=72

Triangle PQR, base = PR = 4 (10-6)
height = 4
AREA = 4*4/2=8

ratio = 8/72 = 1/9

...........................
also if you see, they are similar isoceles triangles

also their bases are in ratio 1:3
also heights in 1:3

so area will be 1:9

.......................................
hope that helps

Thanks a lot.......

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