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# 1) In a right triangle x,y and z represent lengths of the

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Manager
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1) In a right triangle x,y and z represent lengths of the [#permalink]  09 Nov 2005, 13:22
1) In a right triangle x,y and z represent lengths of the side such as x<y<z. If n = x^2+y^2+z^2 what is the value of n/x^2+y^2 ?

1) 1
2) z^2
3) 2
4) 2z
5) 2 sqs rt 2

2) what is the alrgest interger N such that 8 is less than 5 times N is less than 43?

Options: 12, 11, 10, 9, 8

3) Two students took science test and received diff scores b/w 10 and 100. If H equals the higher scores and L equals the lower score and the difference b/w the scores equal the average of the two scores. What is the val of H/L?

Options : 3/2, 2, 5/2, 3, 1/3

4) If x = 6/7-5/6+4/5-3/4+2/3-1/2 then x is b/w..
1) -1 and -/2
2) -1/2 and 0
3) 0 and 1/2
4) 1/2 and 1
5) 1 and 3/2
Pls show a simpler way of solving...

PLS SHOW WRKS FOR ALL

Thks
Director
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1. c =2

2. e = 8

let me work on 3rd
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Director
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Re: prob: [#permalink]  09 Nov 2005, 14:16
x<y<z --> n = x^2 + y^2+ z^2.. then n/(x^2+y^2+z^2) = 1+ z^2/(x^2+y^2)

we know that z^2 = x^2 +y^2.. properties of the right traingle.. therefore that is equal to 1.. Hence 1+1 =2

2) what is the alrgest interger N such that 8 is less than 5 times N is less than 43?

Options: 12, 11, 10, 9, 8

8<5n<43... Only number that satisfies this is 8..

3) Two students took science test and received diff scores b/w 10 and 100. If H equals the higher scores and L equals the lower score and the difference b/w the scores equal the average of the two scores. What is the val of H/L?

Options : 3/2, 2, 5/2, 3, 1/3

H - L = (H+L)/2 .. 2H-2L = H+L.. OR H = 3L.. OR H/L = 3/1 which is not right.. what am i missing??

4) If x = 6/7-5/6+4/5-3/4+2/3-1/2 then x is b/w..
1) -1 and -/2
2) -1/2 and 0
3) 0 and 1/2
4) 1/2 and 1
5) 1 and 3/2
Pls show a simpler way of solving...

PLS SHOW WRKS FOR ALL

This one is like.. multiply pairs with common denominators.. so you will end up with something like 36/42-35/42 + 16/20 -15/20 +4/6-1/6
then you can simplify this to 1/42 +1/20 +1/6 and you can clearly see this is between 0 and 1/2
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VP
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Re: prob: [#permalink]  09 Nov 2005, 14:27
bewakoof wrote:

3) Two students took science test and received diff scores b/w 10 and 100. If H equals the higher scores and L equals the lower score and the difference b/w the scores equal the average of the two scores. What is the val of H/L?

Options : 3/2, 2, 5/2, 3, 1/3

H - L = (H+L)/2 .. 2H-2L = H+L.. OR H = 3L.. OR H/L = 3/1 which is not right.. what am i missing??

3/1 = 3 is correct and is in the ans choice.
Senior Manager
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Re: prob: [#permalink]  10 Nov 2005, 00:00
1) C - 2. Z is the hypotenuse. X^2 + Y ^2 = z^2.
so n/(x^2 + Y^2) = ((X^2+Y^2)+Z^2)/(Z^2)
= 2z^2/z^2 = 2

2) 8

3) H-L = (H+L)/2 H=3L => H/L = 3/1 = 3

4) Simplifying we get C.
VP
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IMO the fastest way to solve 1) is to pick numbers: take a right triangle with side relations 1:sqrt3:2 b/c x<y<z. its (1+3+4)/4=2.
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Manager
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Re: prob: [#permalink]  10 Nov 2005, 01:24
sushom101 wrote:
1) In a right triangle x,y and z represent lengths of the side such as x<y<z. If n = x^2+y^2+z^2 what is the value of n/x^2+y^2 ?

1) 1
2) z^2
3) 2
4) 2z
5) 2 sqs rt 2

FYI, one thing you need to be careful of when you post a problem like this is to make sure that you have the proper use of parentheses. The second equation should be stated as n/(x^2 + y^2) in order to get the proper answer. Without that this becomes a messy problem.
Re: prob:   [#permalink] 10 Nov 2005, 01:24
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