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x+y+z

by shashank.ism » Wed Feb 10, 2010 12:17 pm
If x + y + z = 1 and x, y, z are non-negative numbers, then what is the minimum possible value of the
following expression: [2 - x + yz]- 1 + [2 - y + xz]-1 + [2 - z + xy]- 1.


a) 27/16
b) 25 / 9
c) 38 / 25
d) 3 / 2
e) 12/ 5
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by rickyishere » Wed Feb 10, 2010 3:56 pm
shashank.ism wrote:If x + y + z = 1 and x, y, z are non-negative numbers, then what is the minimum possible value of the
following expression: [2 - x + yz]- 1 + [2 - y + xz]-1 + [2 - z + xy]- 1.


a) 27/16
b) 25 / 9
c) 38 / 25
d) 3 / 2
e) 12/ 5
[2-x+yz]-1 + [2-y+xz]-1+[2-z+xy] - 1 = 2+ xy+yz+xz. So the answer has to be a value > 2, eliminating options a), c) and d. I go with option e as the answer. What is the OA ?

Thanks
Ricky
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by harsh.champ » Wed Feb 10, 2010 10:34 pm
shashank.ism wrote:If x + y + z = 1 and x, y, z are non-negative numbers, then what is the minimum possible value of the
following expression: [2 - x + yz]- 1 + [2 - y + xz]-1 + [2 - z + xy]- 1.


a) 27/16
b) 25 / 9
c) 38 / 25
d) 3 / 2
e) 12/ 5
The expression can be written as 3 -(x+y+z) +(xy+yz +zx)
= 2 +(xy+yz+zx) Now,since all the no.s are non-negative ,the minimum value will be taken when (xy + yz + zx)
is minimum.
taking the case,x=1,y=0,z=0 xy + yz + zx =0 ,Hence 2.
which does not matches with any of the answer choices.
Did I do something wrong??
Help required!!



Shashank,can you post the OA as well as the soln. approach.
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by harsh.champ » Wed Feb 10, 2010 10:38 pm
rickyishere wrote:
shashank.ism wrote:If x + y + z = 1 and x, y, z are non-negative numbers, then what is the minimum possible value of the
following expression: [2 - x + yz]- 1 + [2 - y + xz]-1 + [2 - z + xy]- 1.


a) 27/16
b) 25 / 9
c) 38 / 25
d) 3 / 2
e) 12/ 5
[2-x+yz]-1 + [2-y+xz]-1+[2-z+xy] - 1 = 2+ xy+yz+xz. So the answer has to be a value > 2, eliminating options a), c) and d. I go with option e as the answer. What is the OA ?

Thanks
Ricky
Hey ricky ,
I just wanted to say isn't that a very wild guess.What should be the guessing approach in the exams??
Help required frm tutors!!!

Also,I think u assumed x,y,z to be positive .But two of them can also be zero,since in the ques. it is written "non-negative"
but it isn't written "positive".I guess you assumed it to be +ve. Just check.This is also one of the common quant trap.

Also,an article was also featured on the BTG home-page about the importance of the cipher.
I also recalled the above point from that article only.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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by gmat800_ » Thu Feb 11, 2010 2:55 pm
My answer is e
but I'm not sure, what is the OA?
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by rickyishere » Thu Feb 11, 2010 3:16 pm
harsh.champ wrote:
rickyishere wrote:
shashank.ism wrote:If x + y + z = 1 and x, y, z are non-negative numbers, then what is the minimum possible value of the
following expression: [2 - x + yz]- 1 + [2 - y + xz]-1 + [2 - z + xy]- 1.


a) 27/16
b) 25 / 9
c) 38 / 25
d) 3 / 2
e) 12/ 5
[2-x+yz]-1 + [2-y+xz]-1+[2-z+xy] - 1 = 2+ xy+yz+xz. So the answer has to be a value > 2, eliminating options a), c) and d. I go with option e as the answer. What is the OA ?

Thanks
Ricky
Hey ricky ,
I just wanted to say isn't that a very wild guess.What should be the guessing approach in the exams??
Help required frm tutors!!!

Also,I think u assumed x,y,z to be positive .But two of them can also be zero,since in the ques. it is written "non-negative"
but it isn't written "positive".I guess you assumed it to be +ve. Just check.This is also one of the common quant trap.

Also,an article was also featured on the BTG home-page about the importance of the cipher.
I also recalled the above point from that article only.
Harsh,

I narrowed down my choices to 2/5. After that, yes, I did make a guess. I based it on the fact that since the question asked for a minimum, I picked the minimum of 2 fractions left. Can someone please explain how this problem needs to be solved ?

Thanks
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by money9111 » Thu Feb 11, 2010 8:48 pm
can you state the source?
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by Osirus@VeritasPrep » Thu Feb 11, 2010 8:55 pm
money9111 wrote:can you state the source?
https://www.scribd.com/doc/15844487/CAT-de-Quant-Test-48

Number 3
https://www.beatthegmat.com/the-retake-o ... 51414.html

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by vscid » Sat Feb 13, 2010 2:48 pm
When you say 'non-negative number', can you assume that number to be zero ? If yes, then the answer will be 2 which is not even in the options.
The GMAT is indeed adaptable. Whenever I answer RC, it proficiently 'adapts' itself to mark my 'right' answer 'wrong'.
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by harsh.champ » Thu Feb 18, 2010 5:41 am
vscid wrote:When you say 'non-negative number', can you assume that number to be zero ? If yes, then the answer will be 2 which is not even in the options.
Well vscid,
According to the mathematical rules "zero" is a non-negative number.
If you look at my post above I also got the same answer "2".Dont know if the answer choices are wrong or my method is??

Harsh,

I narrowed down my choices to 2/5. After that, yes, I did make a guess. I based it on the fact that since the question asked for a minimum, I picked the minimum of 2 fractions left. Can someone please explain how this problem needs to be solved ?

Thanks
Hey ricky,
As I had earlier stated you had picked the opposite choice of the 2 answer choices narrowed down by you.
Just carefully look at the GT and the LT signs in the question.
Anyways what do u say about my approach as I am getting the answer as 2??
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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