Gmatprep3 Problem

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Sun Sep 22, 2013 12:48 am

No Idea how to solve this.

A good question also deserves a Thanks.

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Source: Beat The GMAT — Problem Solving | Sun Sep 22, 2013 12:48 am

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Sep 22, 2013 5:25 am

Edited:
Area of the BCE = âˆš2/4

Answer [spoiler][/spoiler]

Sorry, earlier I made a wrong diagram which resulted in answer 1/2

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Last edited by theCodeToGMAT on Sun Sep 22, 2013 7:24 am, edited 1 time in total.

R A H U L

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Sun Sep 22, 2013 5:33 am

I am not sure what the logic you have used but the answer is incorrect.

OA is B

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Sep 22, 2013 5:53 am

faraz_jeddah wrote:I am not sure what the logic you have used but the answer is incorrect.

OA is B

Really??????? Can you please share the explanation.. I was very convinced that I was correct

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Sep 22, 2013 7:03 am

faraz_jeddah wrote:I am not sure what the logic you have used but the answer is incorrect.

OA is B

yes, correct.. the answer is indeed .. small mistake

I have edited my post which is just below the question.

R A H U L

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runningguy: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Jul 22, 2013 4:40 pm; Thanked: 1 times

by runningguy » Sun Sep 22, 2013 7:25 am

I'm confused as to why the answer is not 1/2 (A=1/2(b)(h)).

b=1
h=1

A=1/2(1)(1)=1/2

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Sep 22, 2013 7:32 am

runningguy wrote:I'm confused as to why the answer is not 1/2 (A=1/2(b)(h)).

b=1
h=1

A=1/2(1)(1)=1/2

How did you find that base and height are 1?? that's not possible

if you say that you drew a perpendicular on BE from C and that weighted 1.. then the triangle is not possible as BC & CE are 1.. so perpendicular to BE from C must be less than 1.

if you say that you extended the C and dropped a perpendicular from E on the extended C line.. then also similar rule applies..

Refer my solution just below the question..

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by [email protected] » Sun Sep 22, 2013 12:33 pm

Hi All,

You might find this approach to be a bit easier; it's based on spotting a "hidden" 45/45/90 triangle...

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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runningguy: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Jul 22, 2013 4:40 pm; Thanked: 1 times

by runningguy » Sun Sep 22, 2013 3:27 pm

theCodeToGMAT wrote:
runningguy wrote:I'm confused as to why the answer is not 1/2 (A=1/2(b)(h)).

b=1
h=1

A=1/2(1)(1)=1/2
How did you find that base and height are 1?? that's not possible

if you say that you drew a perpendicular on BE from C and that weighted 1.. then the triangle is not possible as BC & CE are 1.. so perpendicular to BE from C must be less than 1.

if you say that you extended the C and dropped a perpendicular from E on the extended C line.. then also similar rule applies..

Refer my solution just below the question..

I had incorrectly assumed that one of the legs that was equal to 1 was the height. After looking at my flash cards, I see that for an isosceles triangle, you can divide the hypotenuse by sqrt2 to find the length. This was a very tricky question for me.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Sep 23, 2013 2:41 am

In square ABCD, since s=1, BD = âˆš2 and CF = âˆš2/2.
It is given that CE=1.
Thus, EF = âˆš2/2 + 1.

âˆ†BED = (1/2)(BD)(EF) = (1/2)(âˆš2)(âˆš2/2 + 1) = (1/2)(1 + âˆš2) = 1/2 + âˆš2/2.

âˆ†BCD = (1/2)(square ABCD) = 1/2.

Quadrilateral BEDC = âˆ†BED - âˆ†BCD = (1/2 + âˆš2/2) - 1/2 = âˆš2/2.

âˆ†BCE = (1/2)(quadrilateral BEDC) = (1/2)(âˆš2/2) = âˆš2/4.

The correct answer is B.

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Mon Sep 23, 2013 2:51 am

GMATGuruNY wrote:

In square ABCD, since s=1, BD = âˆš2 and CF = âˆš2/2.
It is given that CE=1.
Thus, EF = âˆš2/2 + 1.

âˆ†BED = (1/2)(BD)(EF) = (1/2)(âˆš2)(âˆš2/2 + 1) = (1/2)(1 + âˆš2) = 1/2 + âˆš2/2.

âˆ†BCD = (1/2)(square ABCD) = 1/2.

Quadrilateral BEDC = âˆ†BED - âˆ†BCD = (1/2 + âˆš2/2) - 1/2 = âˆš2/2.

âˆ†BCE = (1/2)(quadrilateral BEDC) = (1/2)(âˆš2/2) = âˆš2/4.

The correct answer is B.

Thanks Mitch! I must say it would be hard to figure this question out in less than 3 minutes.

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shinys: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Mon Jul 06, 2009 2:08 am

by shinys » Tue Sep 24, 2013 6:19 pm

Rich,
Can you please help me understand how you figured out that 135 deg angle?

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by [email protected] » Tue Sep 24, 2013 6:36 pm

Hi shinys,

We're told that the sides BC=CD=CE=1 and we're told that BE=DE. This info tells us that the 2 triangles are IDENTICAL.

Since they're identical, their two "big angles" + the corner of the square = 360 degrees

2(Big angle) + 90 = 360
2(Big angle) = 270
Big angle = 135

Be on the lookout for the "special" right triangles in GMAT Quant questions; sometimes they're obvious, sometimes they're hidden.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Resp007: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Sat Aug 31, 2013 1:29 pmFollowed by: 1 member; Thanked: 2 times; GMAT Score:680

by Resp007 » Thu Sep 26, 2013 4:38 am

HI Rich,
I used GMATGuruNY approach and solved it correctly but as pointed its bit time consuming,
So looked into yours and couldn't understand how you found H.
How you were able to conclude its a 45-45-90 triangle please?

[email protected] wrote:Hi All,

You might find this approach to be a bit easier; it's based on spotting a "hidden" 45/45/90 triangle...

GMAT assassins aren't born, they're made,
Rich

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Resp007: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Sat Aug 31, 2013 1:29 pmFollowed by: 1 member; Thanked: 2 times; GMAT Score:680

by Resp007 » Thu Sep 26, 2013 4:39 am

repeat post...

Last edited by Resp007 on Thu Sep 26, 2013 4:42 am, edited 1 time in total.

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