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DS: xy=1? 1.xyx=x 2.yxy=y [#permalink]
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07 Jul 2004, 00:02
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DS: xy=1?
1.xyx=x
2.yxy=y



SVP
Joined: 03 Feb 2003
Posts: 1604

I want to warn people, D is wrong



Director
Joined: 05 May 2004
Posts: 574
Location: San Jose, CA

will go with E
1 x(xy1)=0 either x=0 or xy=1
2 y(xy1)=0 either y=0 or xy=1



Senior Manager
Joined: 25 Dec 2003
Posts: 359
Location: India

My try
a)X Y X = X, in this case, if X is 1 then Y is 1, and if X is 1 then y is 1. Hence, xy can have 2 values .. xy =1 or xy =1
b) Y X Y=Y, the same as above. Y can be 1, or 1, and x is 1, therefore XY can be 1, or 1.
If x is other 1 and y is 1, then only one statement is satisfied. (Statement  A). And if y is 1 and x is 1, then it satisfies statement B.
Combining both, there is only one value, that is if X is 1, and y is 1 only then both satifies both the statments. If either of them is 1 or if both are 1, we do not satisfy both statements.
Answer is C.
Correct me, if wrong.
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Last edited by carsen on 07 Jul 2004, 05:30, edited 1 time in total.



Senior Manager
Joined: 26 Jan 2004
Posts: 400
Location: India

Will agree with Srijay here, (E) should be it.
(Would like to see how one would refute a common solution to two simultaneous equation, in our case common solution to two equations is xy=1)



Manager
Joined: 16 May 2004
Posts: 64
Location: columbus

[quote="carsen"]My try
a)X Y X = X, in this case, if X is 1 then Y is 1, and if X is 1 then y is 1. Hence, xy can have 2 values .. xy =1 or xy =1
b) Y X Y=Y, the same as above. Y can be 1, or 1, and x is 1, therefore XY can be 1, or 1.
Answer is C.
Correct me, if wrong.[/quote]
carsen : in part A if x =1 then y = 1 and not 1
similarly in part B if y =1 then x = 1 and not 1



Manager
Joined: 16 May 2004
Posts: 64
Location: columbus

MBA,
the only place the common solution (xy = 1 ) failing is when x= y =0
so the answer I think is E



Senior Manager
Joined: 25 Dec 2003
Posts: 359
Location: India

Hi smandalika
I feel that your calculation is wrong.
You have mentioned
in part A if x =1 then y = 1 and not 1 similarly in part B if y =1 then x = 1 and not 1
1.xyx=x
2.yxy=y
If we substitute the values as mentioned by you...
If X is 1, then Y=1, then we get the anser for statement A as 1
Statement 1 = 1 x 1 x 1 = 1 (this violate the original equation)
The same case for Statement 2.
If y=1, and X=1, then the final result will be 1 (1 x 1 x 1 =1). This again will violate the original statement 2.
Hence, if x is 1, then y has to 1, to satisfy statment 1, and similarly, for statement b, if y is 1, then x has to be 1 to satisfy the original statement 2.
Combing both, only one value can satisfy both equations, that is when, x is 1, and y is 1. Hence the answer is C.
I hope, i have explained better in here. If not, let me know, or perhaps, correct me, if my focus is wrong.
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Manager
Joined: 16 May 2004
Posts: 64
Location: columbus

Dude,
You are confusing me even more ....
consider the first eq
XYX = X
if X= 1
(1)Y(1) = 1
then Y = 1 and not 1
similarly
consider the second eq
YXY = Y
if Y= 1
(1)X(1) = 1
then X = 1 and not 1
what am I missing here????



Senior Manager
Joined: 25 Dec 2003
Posts: 359
Location: India

Hi Smandalika
Got ya point.
You know, I got my mind fixed to this equation instead ..
1.xyx=x => my mind got fixed to this equation as xyx=1
2.yxy=y => my mind got fixed this equation as yxy=1
My mistake. I did crap on the above explaination, with the misinterptn. Sorry about girl. I need to reread the whole thing again. Thanks for correcting me.
The answer is E. (Man, i need to focus, and I have just 2 weeks to go).
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Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Entrepreneurship, International Business
GMAT 3: 740 Q40 V50 GMAT 4: 700 Q48 V38 GMAT 5: 710 Q45 V41 GMAT 6: 680 Q47 V36 GMAT 9: 740 Q49 V42 GMAT 11: 500 Q47 V33 GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)

that is OK Carsen.Dont worry too much about the test. Take a deep breath. Relax . you will do just fine.
Good luck with the test . Let us all know how it went.



Manager
Joined: 19 Jun 2003
Posts: 151

I think it is E. But OA was not posted..
Can some expert please comment?



Director
Joined: 20 Jul 2004
Posts: 592

DS: xy=1?
1.xyx=x
2.yxy=y
My answer is C.
(1)
xyx = x
xyx  x = 0
x (xy1) = 0
x = 0 OR xy = 1
Cannot say. Insufficient.
(2)
yxy = y
yxy  y = 0
y (xy1) = 0
y = 0 OR xy = 1
Cannot say. Insufficient.
(Together)
xy = 1 is the solution present in both statements. So, I can give a certain answer ("Yes") with C.
My asnwer = C.
(Did I miss anything?)



Senior Manager
Affiliations: CFA Level 2
Joined: 05 May 2004
Posts: 264
Location: Hanoi

Answer is E for sure.
(1) xyx = x > xy = 1 or x = 0 > insufficient
(2) yxy = y > xy = 1 or y = 0 > insufficient
(1)+(2) > xy = 1 or x=y=0 > insufficient.
hardworker_indian: In your approach, you should take the combination of the 2 statements rather than the interception.
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Intern
Joined: 12 Aug 2004
Posts: 33

Is it possible that A and B. tells use that all the signs are the same?
Ex. 5 * 1/5 * 5 = 5 or 5 *  1/5 * 5 = 5 (XYX=X)
Ex. 1/5 * 5 * 1/5 = 1/5 or 1/5 * 5 * 1/5 = 5 (YXY=Y)
Can we say for sure that x = y or x = 1/y (or the inverse of this), either way X * Y would = 1
I might be wrong, this is my first post so go easy on me.
But this would rule out E ?



Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Entrepreneurship, International Business
GMAT 3: 740 Q40 V50 GMAT 4: 700 Q48 V38 GMAT 5: 710 Q45 V41 GMAT 6: 680 Q47 V36 GMAT 9: 740 Q49 V42 GMAT 11: 500 Q47 V33 GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)

Answer is E.
From 1) x = 0 OR xy = 1. Not sufficient. Rule out A and D.
From 2) y = 0 OR xy = 1. Again Not sufficient. Rule out B.
Combining the 2. xy = 1 OR xy = 0 (since x and y can both be 0). Again Not sufficient. Rule out C.
A, B, C, D are ruled out. We are left with E.



Senior Manager
Joined: 07 Oct 2003
Posts: 350
Location: Manhattan

bigtooth81 wrote: Answer is E for sure.
(1) xyx = x > xy = 1 or x = 0 > insufficient (2) yxy = y > xy = 1 or y = 0 > insufficient
(1)+(2) > xy = 1 or x=y=0 > insufficient.
hardworker_indian: In your approach, you should take the combination of the 2 statements rather than the interception.
I have a fundamental difficulty accepting E here. I could've sworn that Kaplan teaches you to look for interception  hence my thoughtflow was same as hardworking indian's.
What am I missing here?



Senior Manager
Joined: 07 Oct 2003
Posts: 350
Location: Manhattan

alright, I finally realized why answer is E here
x and y could both be zeros in both equations (thus eliminating the possibility that xy=1), and both equations would still equal 0.
the lesson learned here is that interception method does not apply when alternative solutions exist



Intern
Joined: 12 Aug 2004
Posts: 33

YES!!!!!!!!!!!!!! X & Y could be zero!!
Thanks guys










