What is the value of (x - y)^2?

Question

What is the value of  (x - y)^2 ?

(1)  (x + y)^2 = 81

(2)  (x + y)(x - y) = 9

niks18 · Answer

Statement 1:   (x-y)^2=(x+y)^2-4xy . But we do not know the value of  x  &  y .  Insufficient

Statement 2:  implies  (x-y)=\frac{9}{(x+y)} , square both sides to get

=>(x-y)^2=\frac{81}{(x+y)^2} . But we do not know the value of  x  &  y .  Insufficient

Combining 1 & 2:  Statement 1 gives the value of  (x+y)^2 , substitute it in Statement 2 to get the final answer.  Sufficient

Option  C

karthikkaushik91 · Answer

I think it's E, coz statement 1 says x+y could be either 9 or -9 and if we substitute these values in B it gives us either 1 or -1 which leave us with no definitive answer. I hope I m nt wrong fingers crossed, I kinda still learning.
Cheers!

Sent from my iPhone using GMAT Club Forum

niks18 · Answer

Hi  karthikkaushik91

you will get x-y =1 or -1. but the question asks to find  (x-y)^2

therefore you will get only one answer for  (x-y)^2=(1)^2=(-1)^2=1

Hence it will be C

HBSdetermined · Answer

I think the answer should be B. (If its a trap i always fall for these!)

(x-y)^2= (x+y).(x-y) which is given in statement 2 i.e=9 hence sufficient

if we look at statement 1: it says that x+y can be equal to +/-9; but nothing is told about teh condition of x,y if its an integer, fraction, or what-so-ever.. so i think i would go with B as my final answer.

niks18 · Answer

Hi  HBSdetermined

the highlighted portion is wrong.  (x-y)^2=(x-y)(x-y)

and  (x-y)*(x+y)=x^2-y^2 . you have mixed two formulas

HBSdetermined · Answer

thanks for pointing it out. i agree my bad!

HBSdetermined · Answer

agree with the solution!

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables ( x  and  y ) and 0 equations, C is most likely to be the answer and so we should consider 1) & 2) first.

Since  (x+y)^2 = 81 , we have  x+y = ±9 
Since  (x+y)(x-y)=9  and  x+y = ±9 ,we have  x-y = ±1 .
 (x-y)^2 = 1 .

Thus, C is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

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What is the value of (x - y)^2?

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