RE: GMAT Practice Questions

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CrmnKnwls: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Thu Jul 22, 2010 9:32 am

by CrmnKnwls » Mon Aug 09, 2010 10:52 am

I would like to know are there articles regarding these two questions?

In the rectangular coordinate plane system, the area of the triangle PQR is what fraction of the area of the triangle LMN?The following coordinates are given P(6,0) Q(8,4), R(10,0) L(2,0) M(8,12), and N(14,2)
a) 1/9 b) 1/8 c) 1/6 d) 1/5 e) 1/3

An arc is give with 100ft as the legs of the arc. The question states that the figure is a quarter of a circle. Then it goes on to say: If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?
a) 278 b) 341 c) 357 d) 400 e) 441

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Source: Beat The GMAT — Problem Solving | Mon Aug 09, 2010 10:52 am

Maciek: Master | Next Rank: 500 Posts; Posts: 164; Joined: Sun Jul 18, 2010 5:26 amFollowed by: 4 members; Thanked: 49 times; GMAT Score:710

by Maciek » Fri Aug 27, 2010 6:03 am

Hi CrmnKnwls!

IMO B

Formula for the area of the triangle is

A = 0.5 * base * height = 0.5 * b * h

or

A = |( Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By))/2|

Ax and Ay are the x and y coordinates of the point A, Bx and By are the x and y coordinates of the point B, and
Cx and Cy are the x and y coordinates of the point C.

A(PQR)/A(LMN) = ?

The following coordinates are given P(6,0) Q(8,4), R(10,0) L(2,0) M(8,12), and N(14,2)

Triangle PQR:

b = |PR| = 4

h = 4

A(PQR) = 0.5 * 4 * 4 = 8

Triangle LMN:

it is more difficult to calculate height so let us use the second formula

A(LMN) = |( Lx(My - Ny) + Mx(Ny - Ly) + Nx(Ly - My))/2|

A(LMN) = |( 2(12 - 2) + 8(2 - 0) + 14(0 - 12))/2)| = |( 20 + 16 - 14*12)/2| = |(36 - 168)/2| = 66

A(PQR)/A(LMN) = 8/66 = 4/33

the closest answer is b

hope it helps!

Best,
Maciek

An arc is give with 100ft as the legs of the arc. The question states that the figure is a quarter of a circle. Then it goes on to say: If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?
a) 278 b) 341 c) 357 d) 400 e) 441

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BastiG: Master | Next Rank: 500 Posts; Posts: 146; Joined: Sun Jun 13, 2010 5:05 am; Thanked: 7 times

by BastiG » Fri Aug 27, 2010 11:35 am

Can you pls post the source of these questions? I don't think that at least the first question won't be in the GMAT because it takes far too long!

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sun Aug 29, 2010 11:48 am

Maciek wrote:Hi CrmnKnwls!

IMO B

Formula for the area of the triangle is

A = 0.5 * base * height = 0.5 * b * h

or

A = |( Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By))/2|

Ax and Ay are the x and y coordinates of the point A, Bx and By are the x and y coordinates of the point B, and
Cx and Cy are the x and y coordinates of the point C.

A(PQR)/A(LMN) = ?

The following coordinates are given P(6,0) Q(8,4), R(10,0) L(2,0) M(8,12), and N(14,2)
Triangle PQR:

b = |PR| = 4

h = 4

A(PQR) = 0.5 * 4 * 4 = 8

Triangle LMN:

it is more difficult to calculate height so let us use the second formula

A(LMN) = |( Lx(My - Ny) + Mx(Ny - Ly) + Nx(Ly - My))/2|

A(LMN) = |( 2(12 - 2) + 8(2 - 0) + 14(0 - 12))/2)| = |( 20 + 16 - 14*12)/2| = |(36 - 168)/2| = 66

A(PQR)/A(LMN) = 8/66 = 4/33

the closest answer is b

hope it helps!

Best,
Maciek

how come h= 4 here?
An arc is give with 100ft as the legs of the arc. The question states that the figure is a quarter of a circle. Then it goes on to say: If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?
a) 278 b) 341 c) 357 d) 400 e) 441

how come h= 4 here?

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Maciek: Master | Next Rank: 500 Posts; Posts: 164; Joined: Sun Jul 18, 2010 5:26 amFollowed by: 4 members; Thanked: 49 times; GMAT Score:710

by Maciek » Sun Aug 29, 2010 12:37 pm

hi!

h = 4 because points P and R are on X-axis so you can simplify calculation:
h = Qy - 0 = 4

You can still use second formula to calculate the area of triangle PQR
A = |( Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By))/2|
A = |( Px(Qy - Ry) + Qx(Ry - Py) + Rx(Py - Qy))/2|
A = |( 6(4 - 0) + 8(0 - 0) + 10(0 - 4))/2| =
= |( 24 + 0 + -40)/2| = |( -16)/2| = 8

hope it helps!
Best,
Maciek

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