What is the value of (x y)^2 ? (1) x and y are integers (2) xy = 3

Question

What is the value of (x − y)^2 ?

(1) x and y are integers
(2) xy = 3

Archit3110 · Answer

#1
x and y are integers
x=y then target is 0
or any value of x,y
insufficient
#2
xy=3
no limitation that x, y are integers of same sign ( +,-)
or x is fraction 1/3 and y is 9
insufficient
from 1 &2
x,y can be ( 1,3 ) or ( -1,-3)
target is always +4
OPTION C

gmatophobia · Answer

Statement 1

(1) x and y are integers

This statement is clearly insufficient. x and y can hold any value and hence we can not get an unique value of  (x-y)^2  using statement 1.

Eliminate A and D

Statement 1

(2) xy = 3

While one might get tempted to consider integers as possible values, x and y infact can be fractions.

In fact, statement 1 safeguard us from making that incorrect assumption.

Hence, statement 2 is not sufficient.

Combined

As x and y can only be integers , the product of which is 3. The following possibility exists

x = 1 ; y = 3 
 x = 3 ; y = 1 
 x = -1 ; y = -3 
 x = -3 ; y = -1

In all cases, (x-y)^2 is 4.

Sufficient.

Option C

What is the value of (x y)^2 ? (1) x and y are integers (2) xy = 3

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