If x and y are non zero integers, Is x=y ?

Question

I. x=1/y
II. (x+y)^2 = 4xy

medic19 · Answer

Nice question testing different things, namely number properties and factorisation.

1. Re-arrange for xy=1. The only possibility here is that x and y are each 1 or each -1 - therefore are equal. Worth setting up two columns for x and y and take it from there.

2. Expand and factorise which comes out to (x-y)(x-y)=o which in effect means x=y, x=y.

mangamma · Answer

How OA is D? Experts please explain.

BrentGMATPrepNow · Answer

Given : x and y are  non-zero integers

Target question :    Is x=y ?

Statement 1 : x = 1/y  
Multiply both sides by y to get:  xy = 1 
The key information is that x and y are  non-zero integers 
So, there are only TWO possible solutions for the equation  xy = 1 
 Case a : x = 1 and y = 1. In this case, the answer to the target question is  YES, x DOES equal y 
 Case b : x = -1 and y = -1. In this case, the answer to the target question is  YES, x DOES equal y 
So, it MUST be the case that  x = y 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : (x+y)² = 4xy 
Expand left side to get: x² + 2xy + y² = 4xy
Subtract 4xy from both sides to get: x² - 2xy + y² = 0
Factor: (x - y)(x - y) = 0
So, it must be the case that x - y = 0, which means  x = y 
The answer to the target question is  YES, x DOES equal y 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Archit3110 · Answer

given x&y are non zero integers 
#1
x*y=1
x=y=1
sufficeint
#2

(x+y)^2 = 4xy
or say
x^2+y^2=2xy
or say (x-y)^2=0
only possible when x=y=1
sufficient
IMO D

If x and y are non zero integers, Is x=y ?

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GMAT Data Sufficiency (DS) Questions

If x and y are non zero integers, Is x=y ?

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