find the minimum integer value

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karthikgmat: Master | Next Rank: 500 Posts; Posts: 172; Joined: Wed Jul 09, 2008 3:35 amFollowed by: 1 member; Thanked: 3 times; GMAT Score:610

by karthikgmat » Sat May 02, 2009 2:09 am

If 0<x<1 and 0<y<1 and x+y=1, find the minimum integer value of [(x+1/x)pow 2]+[(y+1/y)pow 2]?

A 7

B 9

C 8

D 13

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Source: Beat The GMAT — Problem Solving | Sat May 02, 2009 2:09 am

Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

Re: find the minimum integer value

by Vemuri » Sat May 02, 2009 4:00 am

I have to admit that this one was tricky for me. But, after thinking for a while, it occured to me that if I assume x & y to be equal, I am getting an answer of 6. So, if x & y are slightly different (maybe by a few tenths), then the minimum value of the expression will be 7.

IMO answer should be A. What is the OA?

Last edited by Vemuri on Sat May 02, 2009 4:05 am, edited 1 time in total.

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Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

Re: find the minimum integer value

by Vemuri » Sat May 02, 2009 4:04 am

Vemuri wrote: I have to admit that this one was tricky for me. But, after thinking for a while, it occured to me that if I assume x & y to be equal, I am getting an answer of 6. So, if x & y are slightly different (maybe by a few tenths), then the minimum value of the expression will be 7.

IMO answer should be A. What is the OA?

Damn

....if x & y are equal, I am getting 18 as the answer. I am missing something here.

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Sat May 02, 2009 5:37 am

If 0<x<1 and 0<y<1 and x+y=1, find the minimum integer value of [(x+1/x)pow 2]+[(y+1/y)pow 2]?
================================

x^2 + 1/x^2 + 2 + y^2 + 1/y^2 + 2
=4 + x^2+y^2+ (x^2+y^2)/x^2Y^2
=4 + (x^2+y^2)(x^2y^2 + 1)/(x^2y^2)
=4 + ((x+y)^2 - 2xy) + ((x+y)^2 - 2xy)/(x^2y^2)
=4 + (1 - 2xy)(1+1/x^2y^2)

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dumb.doofus: Master | Next Rank: 500 Posts; Posts: 435; Joined: Sat Sep 27, 2008 2:02 pmFollowed by: 1 member; Location: San Jose, CA; Thanked: 43 times; GMAT Score:720

by dumb.doofus » Sat May 02, 2009 8:18 am

Well, here is the thing..

The lowest value will occur only when x = y. As any of the value increases and so the other one decreases, the more the difference, the higher the value.

A very quick check was to take x = 0.1 this gives 121 as the answer for the equation (x+1)^2/x^2

so I think there should be an option E with value as 18 and that would be the minimum integer value.

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karthikgmat: Master | Next Rank: 500 Posts; Posts: 172; Joined: Wed Jul 09, 2008 3:35 amFollowed by: 1 member; Thanked: 3 times; GMAT Score:610

I found this question in a test on website for CAT

by karthikgmat » Sat May 02, 2009 11:50 pm

It said the answer is 13 ..
I want to know the solution

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PAB2706: Master | Next Rank: 500 Posts; Posts: 260; Joined: Sun Oct 12, 2008 8:10 pm; Thanked: 4 times

by PAB2706 » Mon May 04, 2009 12:14 am

i got answer 13

since 0<x<1 and 0<y<1

we will get the minimum value when x=y

also given is x+y=1

thus the minimum value when x=y and x+y=1 is 0.5

subsituting these values in the given equation you get answer as 12.50

thus the only possible option given is 13 so choose 13.

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