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# Two tough Q's:

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Intern
Joined: 17 Feb 2008
Posts: 28
Two tough Q's:  [#permalink]

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01 Mar 2009, 20:14
Q.1: 'For all positive integers m, m = 3m when m is odd and m=1/2m when m is even. Which of the following is equivalent to 9 x 6 =?

Ans. is 27

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Can someone please explain how they get 27 from above.

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Q. 2: The Perimeter of a certain isosceles triangle is 16+ 16sqrt2. What is the length of Hypotenuse?

Ans: 16

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using x : x :sqrt2x

I would take it that we get x=8, and thus hyp should be srt2*8? but ans is 16? why?

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Current Student
Joined: 03 Aug 2006
Posts: 112
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Re: Two tough Q's:  [#permalink]

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01 Mar 2009, 23:57
I am not sure if I understand the first problem so I am going to skip that.

For the second: It says it's an isosceles triangle and it's asking for the hypotenuse. This leads us to say that it's a right angled isosceles triangle. For such a triangle with 2 equal sides 'x' the hypotenuse is

sqrt( x^2 + x^2)
= sqrt(2*x^2)
= x*sqrt(2)

The perimeter would be x + x + x*sqrt(2) = 2x + x*sqrt(2)

It states in the problem that the perimeter is 16+16*sqrt(2)

That would mean

=> 2x + x*sqrt(2) = 16 + 16*sqrt(2)
=> x*sqrt(2) (sqrt(2) + 1) = 16 (1 + sqrt(2))
Cancel (1 + sqrt(2)) on both sides
=> x*sqrt(2) = 16
=> x = 16/sqrt(2)

Hypotenuse = x*sqrt(2) = (16/sqrt(2))*sqrt(2) = 16
CEO
Joined: 17 Nov 2007
Posts: 3484
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: Two tough Q's:  [#permalink]

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02 Mar 2009, 00:24
Forrester300 wrote:
Q.1: 'For all positive integers m, m = 3m when m is odd and m=1/2m when m is even. Which of the following is equivalent to 9 x 6 =?

Ans. is 27

Maybe it was:
Q.1: 'For all positive integers m, [m] = 3m when m is odd and [m]=1/2m when m is even. Which of the following is equivalent to [9] x [6] =?

Ans. is [27]

P.S. Please, post problems separately!
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Manager
Joined: 27 Feb 2009
Posts: 57
Re: Two tough Q's:  [#permalink]

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02 Mar 2009, 08:39
1, 9*6 = 54, 54 is even, so m = 1/2*m
1/2*54 = 27

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: Two tough Q's: &nbs [#permalink] 02 Mar 2009, 08:39
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# Two tough Q's:

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