GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 Jan 2020, 19:58 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x and y are non-zero numbers, adding the reciprocals of x^2 and y^2

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 60647
If x and y are non-zero numbers, adding the reciprocals of x^2 and y^2  [#permalink]

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 66% (01:54) correct 34% (02:31) wrong based on 89 sessions

### HideShow timer Statistics

If x and y are non-zero numbers, adding the reciprocals of x^2 and y^2 and then subtracting 2 times the reciprocal of xy produce which of the following?

A. $$x^2 + y^2 – 2xy$$

B. $$\frac{(x^2y^2 + xy)}{(x + y^2)}$$

C. $$(\frac{1}{y}−\frac{1}{x})$$

D. $$\frac{(x^2 + y^2)}{(x^2y^2)}$$

E. $$(\frac{1}{x} − \frac{1}{y})^2$$

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 8336
Re: If x and y are non-zero numbers, adding the reciprocals of x^2 and y^2  [#permalink]

### Show Tags

Bunuel wrote:
If x and y are non-zero numbers, adding the reciprocals of x^2 and y^2 and then subtracting 2 times the reciprocal of xy produce which of the following?

A. x^2 + y^2 – 2xy
B. (x^2y^2 + xy)/(x + y^2)
C. (1/y−1/x)
D. (x^2 + y^2)/(x^2y^2)
E. (1/x − 1/y)^2

Hi,
The Q may seem complex but in actually is straight forward--
$$\frac{1}{x^2}+\frac{1}{y^2} -\frac{2}{xy}$$

TWO WAYS--

1) substitute
take x = 1/3 and y = 1/2..
$$3^2 +2^2-12$$ = $$1$$
substitute values and see..

A. $$x^2 + y^2 – 2xy$$------- 1/9 +1/4 -1/3 -- NO
B. $$\frac{(x^2y^2 + xy)}{(x + y^2)}$$... (1/36 + 1/6)/(1/3+1/4) --NO
C. $$(\frac{1}{y}−\frac{1}{x}).$$.. 2-3= -1---NO
D. $$\frac{(x^2 + y^2)}{(x^2y^2)-}$$- (1/9+1/4)/(1/36)=13.. NO
E. $$(\frac{1}{x}− \frac{1}{y})^2$$.. (3-2)^2=1.. CORRECT

2) formula
VERY easy if you can see the hidden formula
$$\frac{1}{x^2}+\frac{1}{y^2} -\frac{2}{xy}$$..
$$\frac{1}{x}^2+\frac{1}{y}^2 - 2*\frac{1}{x}*\frac{1}{y}$$..
$$(\frac{1}{x}− \frac{1}{y})^2$$..
same as E
ans E
_________________
Manager  S
Joined: 04 Jun 2015
Posts: 77
Re: If x and y are non-zero numbers, adding the reciprocals of x^2 and y^2  [#permalink]

### Show Tags

Bunuel wrote:
If x and y are non-zero numbers, adding the reciprocals of x^2 and y^2 and then subtracting 2 times the reciprocal of xy produce which of the following?

A. $$x^2 + y^2 – 2xy$$

B. $$\frac{(x^2y^2 + xy)}{(x + y^2)}$$

C. $$(\frac{1}{y}−\frac{1}{x})$$

D. $$\frac{(x^2 + y^2)}{(x^2y^2)}$$

E. $$(\frac{1}{x} − \frac{1}{y})^2$$

Putting x=1, y=2 in $$\frac{1}{x^2} + \frac{1}{y^2} - \frac{2}{xy}$$ we get $$\frac{1}{4}$$
Now TEST THE ANSWERS only E fits in.
_________________
Sortem sternit fortem! Re: If x and y are non-zero numbers, adding the reciprocals of x^2 and y^2   [#permalink] 27 Jan 2017, 13:05
Display posts from previous: Sort by

# If x and y are non-zero numbers, adding the reciprocals of x^2 and y^2  