x and y is y

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue May 26, 2009 12:34 am

For the non zero integers x and y, what is the value of {(x/y) + (y/x)}?

(1) x, y are roots of the equation 16 t^2 – 24 t + 9.

(2) The least common multiple of x and y is y, the same as their greatest common divisor.

MBM

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Source: Beat The GMAT — Data Sufficiency | Tue May 26, 2009 12:34 am

eyoussef: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Fri May 01, 2009 12:15 pm; Thanked: 1 times

by eyoussef » Tue May 26, 2009 1:29 am

I think the answer to this question is D
statment 1: by examining the discriminant of the given equation.. it will be equal to 0; which means one single repeated root, in other words, x=y

statement 2: also states that x=y because for the GCD both numbers to be equal to the HCF, they have to be equal

Please correct me if i'm wrong

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2010gmat: Master | Next Rank: 500 Posts; Posts: 371; Joined: Fri Mar 06, 2009 2:48 am; Thanked: 27 times; GMAT Score:740

by 2010gmat » Tue May 26, 2009 3:12 am

IMO B

1st does not give integer values for x and y..

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TryHarder: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Fri Feb 27, 2009 8:38 pm

by TryHarder » Tue May 26, 2009 3:15 pm

I am confused about the justification to say that (1) in Insufficient.

Should'nt we say that 16t^2 -24t + 9 =0 has a singular non-integer root t=3/4 and hence the values of x and y remain undecided?

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subha_sri8: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Tue Jan 08, 2008 11:13 am; Thanked: 2 times

by subha_sri8 » Wed May 27, 2009 9:34 pm

On resolving the first equation we get the roots as 12 and 12.
Therefore statement 1 is sufficient.

Also from statement 2 if LCD = GCD then the numbers must be equal so we can calculate the value of the expression.

therefore the answer is D.

Please post the OA?

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

Re: x and y is y

by Vemuri » Wed May 27, 2009 11:29 pm

IMO D.

The first statement essentially leads to the root 3/4, which is the same for x & y. The second statement is also saying that the roots are equal by telling us that the LCM & GCD are the same.

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sacx: Master | Next Rank: 500 Posts; Posts: 139; Joined: Wed Oct 22, 2008 4:36 am; Thanked: 17 times

by sacx » Thu May 28, 2009 2:43 am

shouldn't the question say non-zero non-integers

Stmt I gives us x = y = 3/4, and hence the value of the expression 2
Stmt II says x = y, hence value of the expression = 2

D

SACX

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