OG 2nd ed # 83

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joshua868: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon May 09, 2011 1:10 pm

by joshua868 » Wed Jun 01, 2011 10:14 am

If xy is greater than 0, does (x-1)(y-1)=1?

1) x+y=xy
2) x=y

Can someone explain to me why stat 2 is not sufficient? thanks!

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Source: Beat The GMAT — Data Sufficiency | Wed Jun 01, 2011 10:14 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Jun 01, 2011 10:29 am

Hi,
We need to check: Is (x-1)(y-1)=1 =>xy-x-y+1=1 =>xy=x+y
So, in essence we ened to check: Is xy = x+y?
From(1): It is clear
sufficient
From(2)x=y
So, we need to check if x.x=x+x i.e., x^2=2x?
Not sufficient

Hence, A

Cheers!

Things are not what they appear to be... nor are they otherwise

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joshua868: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon May 09, 2011 1:10 pm

by joshua868 » Wed Jun 01, 2011 11:02 am

"So, we need to check if x.x=x+x i.e., x^2=2x?
Not sufficient "

@Frankenstein I'm still kind of lost
so if x^2=2x does that mean that x=0 or X=2

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djiddish98: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Fri Jan 14, 2011 10:01 am; Thanked: 10 times

by djiddish98 » Wed Jun 01, 2011 11:05 am

(x-1)(y-1) = 1?

Statement 2 says x=y. However, x and y could be any number (3,20,-1/2), so we're not sure if it's 1.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jun 01, 2011 11:11 am

joshua868 wrote:If xy is greater than 0, does (x-1)(y-1)=1?

1) x+y=xy
2) x=y

Can someone explain to me why stat 2 is not sufficient? thanks!

I like how Frankenstein rewrote the target question as "Is xy = x+y?"

Statement 1
When we examine statement 1, it is clear that xy does, indeed, equal x+y

Statement 2
If x=y, then when we replace y with x in the target question, we get "Is x(x) = x+(x)?"
In other words, Is x^2 = 2x?
Well, x^2 could equal 2x if x=2 or x=0
But, x^2 doesn't equal 2x for all other values of x

Since we can't answer the target question with certainty, statement 2 is insufficient.

Brent Hanneson - Creator of GMATPrepNow.com

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Jun 01, 2011 11:11 am

joshua868 wrote:"So, we need to check if x.x=x+x i.e., x^2=2x?
Not sufficient "

@Frankenstein I'm still kind of lost
so if x^2=2x does that mean that x=0 or X=2

Hi,
To check whether x^2=2x, we need to know the value of x.We do not know the value of x. So, we cannot surely say if that equality holds or not.

Cheers!

Things are not what they appear to be... nor are they otherwise

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joshua868: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon May 09, 2011 1:10 pm

by joshua868 » Wed Jun 01, 2011 11:12 am

oh okay..Thanks

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