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

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Math Expert
Joined: 02 Sep 2009
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What is the value of (x - y)^2?  [#permalink]

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25 Dec 2017, 10:35
1
2
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Difficulty:

55% (hard)

Question Stats:

54% (01:45) correct 46% (01:38) wrong based on 60 sessions

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

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

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

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Re: What is the value of (x - y)^2?  [#permalink]

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25 Dec 2017, 10:44
Bunuel wrote:
What is the value of (x - y)^2?

(1) (x + y)^2 = 81
(2) (x + y)(x - y) = 9

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
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Re: What is the value of (x - y)^2?  [#permalink]

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25 Dec 2017, 10:52
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!

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Re: What is the value of (x - y)^2?  [#permalink]

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25 Dec 2017, 10:56
karthikkaushik91 wrote:
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!

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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
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Re: What is the value of (x - y)^2?  [#permalink]

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25 Dec 2017, 10:58
Bunuel wrote:
What is the value of (x - y)^2?

(1) (x + y)^2 = 81
(2) (x + y)(x - y) = 9

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.
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Re: What is the value of (x - y)^2?  [#permalink]

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25 Dec 2017, 11:02
HBSdetermined wrote:
Bunuel wrote:
What is the value of (x - y)^2?

(1) (x + y)^2 = 81
(2) (x + y)(x - y) = 9

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.

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
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Re: What is the value of (x - y)^2?  [#permalink]

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25 Dec 2017, 11:09
niks18 wrote:
HBSdetermined wrote:
Bunuel wrote:
What is the value of (x - y)^2?

(1) (x + y)^2 = 81
(2) (x + y)(x - y) = 9

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.

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

thanks for pointing it out. i agree my bad!
Manager
Joined: 04 Feb 2012
Posts: 156
Location: India
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GRE 1: Q162 V160
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Re: What is the value of (x - y)^2?  [#permalink]

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25 Dec 2017, 11:11
niks18 wrote:
Bunuel wrote:
What is the value of (x - y)^2?

(1) (x + y)^2 = 81
(2) (x + y)(x - y) = 9

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

agree with the solution!
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Re: What is the value of (x - y)^2?  [#permalink]

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27 Dec 2017, 20:35
Bunuel wrote:
What is the value of $$(x - y)^2$$?

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

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

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 $$x-y = ±1$$.
$$(x-y)^2 = 1$$.

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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Re: What is the value of (x - y)^2? &nbs [#permalink] 27 Dec 2017, 20:35
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