 It is currently 23 Sep 2020, 05:42 ### 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 x2 - y2 = 0 and xy 0, which of the following MUST be true  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2915  , given: 394

If x2 - y2 = 0 and xy 0, which of the following MUST be true [#permalink]
1
KUDOS
Expert's post 00:00

Question Stats: 59% (00:44) correct 40% (00:40) wrong based on 61 sessions
If $$x^2 - y^2 = 0$$ and $$xy \neq 0$$, which of the following MUST be true?
Indicate all such statements.

A. x = y
B. |x| = |y|
C. $$\frac{x^2}{y^2}=1$$
[Reveal] Spoiler: OA Manager Joined: 02 May 2018
Posts: 58
Followers: 0

Kudos [?]: 30  , given: 22

Re: If x2 - y2 = 0 and xy 0, which of the following MUST be true [#permalink]
1
KUDOS
The answers are B and C.

Let's go through each answer one by one.

A. x=y
At first glance, this answer looks correct for the equation $$x^2 - y^2=0$$. However, we have to keep in mind that any number, positive or negative, when squared, is positive. Because the only restriction is that $$xy > 0$$, this means that either x or y could be positive while the other is a negative.

For example,

When x and y are both 5, then $$5^2 - 5^2 = 0$$. However, if x=-5 and y=5, $$(-5)^2 - 5^2 = 0$$

So A is false.

B. |x| = |y|
Using the last example, we can see that this is true. |-5| = |5|
The same goes for any combination of numbers.

B is true.

C. $$\frac{x^2}{y^2}=0$$
Following up from A, we already know that any number, positive or negative squared stays positive. If both numbers when squared, subtracted from each other are zero, then one number over the other will always be 1.

Example.
$$\frac{-5^2}{5^2}$$ = 0
and $$\frac{5^2}{5^2}$$ = 0

C is true.
Intern Joined: 26 May 2018
Posts: 37
Followers: 0

Kudos [?]: 7 , given: 2

Re: If x2 - y2 = 0 and xy 0, which of the following MUST be true [#permalink]
Good one!
Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2915 , given: 394

If x2 – y2 = 0 and xy ≠ 0, which of the following must be tr [#permalink]
Expert's post
If $$x^2$$ – $$y^2$$ = 0 and $$xy \neq 0$$, which of the following must be true?

Indicate all such statements.

A. $$x = y$$
B. $$|x| = |y|$$
C. $$\frac{x^2}{y^2}= 1$$
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2915 , given: 394

Re: If x2 – y2 = 0 and xy ≠ 0, which of the following must be tr [#permalink]
Expert's post
Explanation

Since $$x^2 - y^2 = 0$$, add $$y^2$$ to both sides to get $$x^2 = y^2$$. It might look as though x = y, but this is not necessarily the case. For example, x could be 2 and y could be –2.

Algebraically, taking the square root of both sides of x2 = y2 does not yield x = y, but rather |x| = |y|. Thus, the 1st statement is not necessarily true and the 2nd statement is true. The 3rd statement is also true and can be generated algebraically:

$$x^2 - y^2 = 0$$
$$x^2 = y^2$$
$$\frac{x^2}{y^2}= 1$$.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Manager  Joined: 06 Jun 2018
Posts: 94
Followers: 2

Kudos [?]: 77  , given: 0

Re: If x2 - y2 = 0 and xy 0, which of the following MUST be true [#permalink]
1
KUDOS
sandy wrote:
If $$x^2 - y^2 = 0$$ and $$xy \neq 0$$, which of the following MUST be true?
Indicate all such statements.

A. x = y
B. |x| = |y|
C. $$\frac{x^2}{y^2}=1$$

Given

$$x^2 - y^2 = 0$$

x^2 = y^2

Note: x and y could be negative or positive. Squared value is equal , not their individual value.

A. clearly out. x=2 , y = -2. Squared value is equal.

B. Squared value has no difference with absolute value. both show the positive answer.

C. True. both x^2 and y^2 have equal value. at the very beginning we got it.

So, B and c are true in all aspects.
Director  Joined: 22 Jun 2019
Posts: 517
Followers: 4

Kudos [?]: 104 , given: 161

Re: If x2 - y2 = 0 and xy 0, which of the following MUST be true [#permalink]
sandy wrote:
If $$x^2 - y^2 = 0$$ and $$xy \neq 0$$, which of the following MUST be true?
Indicate all such statements.

A. x = y
B. |x| = |y|
C. $$\frac{x^2}{y^2}=1$$

Why We can't take a different value for x and y.? Like: x=2 and y=3, if we so then B. must not be an answer. Only answer C.

_________________

New to the GRE, and GRE CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All In One Resource's | All Quant Questions Collection | All Verbal Questions Collection | Manhattan 5lb All Questions Collection
Books: All GRE Best Books
Scores: Average GRE Score Required By Universities in the USA
Tests: All Free & Paid Practice Tests | GRE Prep Club Tests
Extra: Permutations, and Combination
Vocab: GRE Vocabulary

Manager Joined: 22 May 2019
Posts: 58
Followers: 0

Kudos [?]: 30 , given: 194

Re: If x2 - y2 = 0 and xy 0, which of the following MUST be true [#permalink]
huda wrote:
sandy wrote:
If $$x^2 - y^2 = 0$$ and $$xy \neq 0$$, which of the following MUST be true?
Indicate all such statements.

A. x = y
B. |x| = |y|
C. $$\frac{x^2}{y^2}=1$$

Why We can't take a different value for x and y.? Like: x=2 and y=3, if we so then B. must not be an answer. Only answer C.

If you take different values for x andy, then will their square difference yields 0? Certainly not!!
? Manager Joined: 22 May 2019
Posts: 58
Followers: 0

Kudos [?]: 30  , given: 194

Re: If x2 - y2 = 0 and xy 0, which of the following MUST be true [#permalink]
1
KUDOS
sandy wrote:
If $$x^2 - y^2 = 0$$ and $$xy \neq 0$$, which of the following MUST be true?
Indicate all such statements.

A. x = y
B. |x| = |y|
C. $$\frac{x^2}{y^2}=1$$

Let's think this way...
x^2 - y^2 =0
=> (x+y) (x-y)=0
=> x=y or x = -y
So we can eliminate option A. But their absolute value must be equal. We must take B as an answer.

Again,
x^2 - y^2 =0
=> x^2 = y^2
x^2/y^2=1

Definitely C is also our answer! So B,C.
Manager Joined: 02 Mar 2020
Posts: 55
Followers: 0

Kudos [?]: 7 , given: 2

Re: If x2 - y2 = 0 and xy 0, which of the following MUST be true [#permalink]
PIneappleBoy2 wrote:
The answers are B and C.

Let's go through each answer one by one.

A. x=y
At first glance, this answer looks correct for the equation $$x^2 - y^2=0$$. However, we have to keep in mind that any number, positive or negative, when squared, is positive. Because the only restriction is that $$xy > 0$$, this means that either x or y could be positive while the other is a negative.

For example,

When x and y are both 5, then $$5^2 - 5^2 = 0$$. However, if x=-5 and y=5, $$(-5)^2 - 5^2 = 0$$

So A is false.

B. |x| = |y|
Using the last example, we can see that this is true. |-5| = |5|
The same goes for any combination of numbers.

B is true.

C. $$\frac{x^2}{y^2}=0$$
Following up from A, we already know that any number, positive or negative squared stays positive. If both numbers when squared, subtracted from each other are zero, then one number over the other will always be 1.

Example.
$$\frac{-5^2}{5^2}$$ = 0
and $$\frac{5^2}{5^2}$$ = 0

C is true.

You accidentally set C. equal to zero instead of 1. Might wanna fix that just so someone on the fence can follow. Thanks! Re: If x2 - y2 = 0 and xy 0, which of the following MUST be true   [#permalink] 08 May 2020, 04:55
Display posts from previous: Sort by

# If x2 - y2 = 0 and xy 0, which of the following MUST be true  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.