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GRE Math Challenge #2 (170 level question)

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GRE Math Challenge #2 (170 level question) [#permalink] New post 06 Aug 2014, 13:38
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This is the type of question you have to answer correctly to get a perfect score of 170 in GRE Math
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Re: GRE Math Challenge #2 (170 level question) [#permalink] New post 06 Aug 2014, 23:22
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Re: GRE Math Challenge #2 (170 level question) [#permalink] New post 02 Jul 2017, 12:55
the key to solve this question is that. put y coordinate=0 in the parabola equation to get the x coordinate(half the lenght of the base) .in terms of k. then find the value of k
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Re: GRE Math Challenge #2 (170 level question) [#permalink] New post 11 Jul 2017, 02:46
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Re: GRE Math Challenge #2 (170 level question) [#permalink] New post 16 Aug 2017, 10:49
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Re: GRE Math Challenge #2 (170 level question) [#permalink] New post 20 Sep 2018, 04:29
Tough question.

The first part of the solution:

Let the origin be O.

The area of the triangle ABC is 1/8.
The area of the triangle ABC = the area of the triangle AOB*2
The area of the triangle AOB = (distance between Origin and B * distance between Origin and A)/2
The area of the triangle ABC = ((distance between Origin and B * distance between Origin and A)/2)*2 =>
The area of the triangle ABC = distance between Origin and B * distance between Origin and A = 1/8

The second part of the solution:

Point A is the point when x=0
If x=0, then y=k-0 => y=k
So, we now know that the distance between the origin and the point A is k.

Points B and C are points when y=0
0=k-x^2 => x^2 = k => x = +- sqrt(k)

So, we now know that the distance between the origin and the point B is sqrt(k)

The third part of the solution:
k*sqrt(k) = 1/8
k^3 = 1/64
k = 1/sqrt(8)
k = 0.35

Kudos if you liked this solution :)
Re: GRE Math Challenge #2 (170 level question)   [#permalink] 20 Sep 2018, 04:29
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GRE Math Challenge #2 (170 level question)

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