GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Aug 2018, 10:16

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

If both x and y are nonzero numbers, what is the value of y/x? (1) x

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 18 Nov 2010
Posts: 10
If both x and y are nonzero numbers, what is the value of y/x? (1) x  [#permalink]

Show Tags

New post 19 Nov 2010, 05:34
3
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

66% (00:37) correct 34% (00:33) wrong based on 167 sessions

HideShow timer Statistics

If both x and y are nonzero numbers, what is the value of y/x?

(1) x = 6
(2) y^2 = x^2

Why isn’t ‘C’ the correct answer? (E is the correct answer here)

If we know that x =6 and
y squared is = square root ( 6 squared) = absolute value (6)
Then absolute value (6)/6 = 1


OPEN DISCUSSION OF THIS QUESTION IS HERE: if-both-x-and-y-are-nonzero-numbers-what-is-the-value-of-y-165767.html
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48106
If both x and y are nonzero numbers, what is the value of y/x? (1) x  [#permalink]

Show Tags

New post 19 Nov 2010, 05:50
1
4
shash wrote:
If both x and y are non zero numbers , what is the value of (y/x)

1) x = 6
2) y square = x square

Why isn’t ‘C’ the correct answer? (E is the correct answer here)

If we know that x =6 and
y squared is = square root ( 6 squared) = absolute value (6)
Then absolute value (6)/6 = 1


If both x and y are nonzero numbers, what is the value of x/y?

Note that \(\sqrt{x^2}=|x|\).

(1) x = 6. Not sufficient.

(2) y^2 = x^2 --> \(|x|=|y|\) --> if \(x\) and \(y\) have the same sign then \(\frac{x}{y}=1\) (for example \(x=y=6\)) but if \(x\) and \(y\) have the opposite signs then \(\frac{x}{y}=-1\) (for example \(x=6\) and \(y=-6\)). Not sufficient.

(1)+(2) We still don't know whether \(x\) and \(y\) have the same sign or not. Not sufficient.

Answer: E.

About \(\sqrt{x^2}=|x|\).

The point here is that as square root function cannot give negative result then \(\sqrt{some \ expression}\geq{0}\).

So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?

Let's consider following examples:
If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);
If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).

So we got that:
\(\sqrt{x^2}=x\), if \(x\geq{0}\);
\(\sqrt{x^2}=-x\), if \(x<0\).

What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8204
Location: Pune, India
Re: If both x and y are nonzero numbers, what is the value of y/x? (1) x  [#permalink]

Show Tags

New post 19 Nov 2010, 07:03
shash wrote:

If we know that x =6 and
y squared is = square root ( 6 squared) = absolute value (6)
Then absolute value (6)/6 = 1


If we know that \(y^2 = 36\), then y can be 6 or -6.
On the other hand, if it is given that y = \(\sqrt{36}\), we only consider the positive value i.e. 6. Here y can only be 6.

It is all in the notation!
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Director
Director
User avatar
B
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 549
If both x and y are nonzero numbers, what is the value of  [#permalink]

Show Tags

New post 20 Feb 2011, 11:15
If both x and y are nonzero numbers, what is the value of x/y?

(1) x = 6
(2) y^2 = x^2

I did wrong doing following:
√y^2 = √x^2
so, y=x
and answer c
What wrong did i do.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48106
Re: QR. 30 Number  [#permalink]

Show Tags

New post 20 Feb 2011, 11:21
Baten80 wrote:
QR. 30 Number
If both x and y are nonzero numbers, what is the value of x/y?
(1) x = 6
(2) y^2 = x^2

I did wrong doing following:
√y^2 = √x^2
so, y=x
and answer c
What wrong did i do.


Note that \(\sqrt{x^2}=|x|\).

If both x and y are nonzero numbers, what is the value of x/y?

(1) x = 6. Not sufficient.

(2) y^2 = x^2 --> \(|x|=|y|\) --> if \(x\) and \(y\) have the same sign then \(\frac{x}{y}=1\) (for example \(x=y=6\)) but if \(x\) and \(y\) have the opposite signs then \(\frac{x}{y}=-1\) (for example \(x=6\) and \(y=-6\)). Not sufficient.

(1)+(2) We still don't know whether \(x\) and \(y\) have the same sign or not. Not sufficient.

Answer: E.

About \(\sqrt{x^2}=|x|\).

The point here is that as square root function can not give negative result then \(\sqrt{some \ expression}\geq{0}\).

So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?

Let's consider following examples:
If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);
If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).

So we got that:
\(\sqrt{x^2}=x\), if \(x\geq{0}\);
\(\sqrt{x^2}=-x\), if \(x<0\).

What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1877
Re: QR. 30 Number  [#permalink]

Show Tags

New post 20 Feb 2011, 11:24
Baten80 wrote:
QR. 30 Number
If both x and y are nonzero numbers, what is the value of x/y?
(1) x = 6
(2) y^2 = x^2

I did wrong doing following:
√y^2 = √x^2
so, y=x
and answer c
What wrong did i do.


\(sqrt(y^2)=\sqrt(x^2)\) may not always mean - y=x

Say
x=6; y=-6; x^2=36, y=36; but x and y are different.
x=6; y=6; x^2=36, y=36; and here x and y are same.

(1) x=6; Nothing about y. Not sufficient.
(2) (y-x) (y+x) = 0
y-x=0 or y+x=0
If former; y=x
Latter; y=-x
Not sufficient.

Combining both;
x=6
y can be 6 or -6.

Ans: "E"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Director
Director
User avatar
B
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 549
Re: QR. 30 Number  [#permalink]

Show Tags

New post 20 Feb 2011, 11:43
fluke wrote:
Baten80 wrote:
QR. 30 Number
If both x and y are nonzero numbers, what is the value of x/y?
(1) x = 6
(2) y^2 = x^2

I did wrong doing following:
√y^2 = √x^2
so, y=x
and answer c
What wrong did i do.


\(sqrt(y^2)=\sqrt(x^2)\) may not always mean - y=x

Say
x=6; y=-6; x^2=36, y=36; but x and y are different.
x=6; y=6; x^2=36, y=36; and here x and y are same.

(1) x=6; Nothing about y. Not sufficient.
(2) (y-x) (y+x) = 0
y-x=0 or y+x=0
If former; y=x
Latter; y=-x
Not sufficient.

Combining both;
x=6
y can be 6 or -6.

Ans: "E"


But as x= 6 (positive) so why i will consider √y^2 i.e., √36=-6 other than 6. [for ans c.] please help.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48106
Re: QR. 30 Number  [#permalink]

Show Tags

New post 20 Feb 2011, 11:49
Baten80 wrote:
But as x= 6 (positive) so why i will consider √y^2 i.e., √36=-6 other than 6. [for ans c.] please help.


Read my post above: \(\sqrt{x^2}=|x|\).

\(x^2=y^2\) means \(|x|=|y|\) as from (1) \(x=6\) then \(|y|=6\) --> \(y=6\) or \(y=-6\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48106
Re: QR. 30 Number  [#permalink]

Show Tags

New post 20 Feb 2011, 11:53
Manager
Manager
avatar
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 205
Schools: Johnson '15
if both x and y are non-zero numbers, what is the value of  [#permalink]

Show Tags

New post 25 Jun 2011, 23:02
if both x and y are non-zero numbers, what is the value of y/x?
1. x=6
2. ysquare = xsquare
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat ;)

Satyameva Jayate - Truth alone triumphs

Manager
Manager
avatar
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 205
Schools: Johnson '15
Re: Prep Test DS-9  [#permalink]

Show Tags

New post 25 Jun 2011, 23:04
initially i had selected B as the answer...

now i realize

1. x=6
this does not give any information about the value of y. hence no

2. ysquare=xsquare

ysquare
--------- = 1
xsquare

taking square-roots on both sides

+or- y/x = +or-1

hence No

Taking together, it does not give better answer either as

+or- y/6 = +or-1

is my understanding correct about the right answer?
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat ;)

Satyameva Jayate - Truth alone triumphs

Senior Manager
Senior Manager
User avatar
Joined: 03 Mar 2010
Posts: 395
Schools: Simon '16 (M)
Re: Prep Test DS-9  [#permalink]

Show Tags

New post 26 Jun 2011, 00:26
Value of y/x?

Stmt1: x=6. Not sufficient.
Stmt2: \(y^2 = x^2\)
x can be +6
y can be +6
Value \(y/x = 6/6 =1\)
OR
x can be -6
y can be +6
Value of \(y/x=-1\) Not sufficient.

Take (1) and (2) together, x=+6. y can be +6 or -6, giving value of y/x as 1 or -1 respectively.
Hence not sufficient together.

OA E.
_________________

My dad once said to me: Son, nothing succeeds like success.

Manager
Manager
avatar
Joined: 18 May 2014
Posts: 61
Location: United States
Concentration: General Management, Other
GMAT Date: 07-31-2014
GPA: 3.99
WE: Analyst (Consulting)
Re: If both x and y are nonzero numbers, what is the value of  [#permalink]

Show Tags

New post 18 May 2014, 11:00
1
st(1) no info about y Insuff
st(2) |x|=|y| Insuff
combined st(1&2): |6|=|6| Insuff
Hence E
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 397
If both x and y are nonzero numbers, what is the value of  [#permalink]

Show Tags

New post 17 Sep 2016, 06:27
Bunuel -

I'm confused on why B isn't the correct answer. The problem says at the beginning ..."If both x and y are nonzero numbers..."

So when I went to set up (2), it eliminated the negative root possibility on either side of the eq and I arrived at y = x. This makes the main statement = 1

Did I misread the question?

Thank you in advance for your help!
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3690
Premium Member Reviews Badge CAT Tests
Re: If both x and y are nonzero numbers, what is the value of  [#permalink]

Show Tags

New post 17 Sep 2016, 06:35
lawiniecke wrote:
Bunuel -

I'm confused on why B isn't the correct answer. The problem says at the beginning ..."If both x and y are nonzero numbers..."

So when I went to set up (2), it eliminated the negative root possibility on either side of the eq and I arrived at y = x. This makes the main statement = 1

Did I misread the question?

Thank you in advance for your help!


I think you are missing something here. Note that Non Zero means either positive or negative but not Zero.

So, \(y^2 = x^2\) means y is + or - x. Hence x/y will be either 1 or -1. Hence, B is insufficient.

What do you mean by Negative root possibility. Note that we are not given sqrt(y)=sqrt(x). So, you need to be very careful while solving such type of questions.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place
Blog: Subscribe to Question of the Day Blog

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.

New! Best Reply Functionality on GMAT Club!



Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 397
If both x and y are nonzero numbers, what is the value of  [#permalink]

Show Tags

New post 17 Sep 2016, 06:43
Hi abhimahna -

I misread the question. I was under the impression we were dealing with non-negative integers. Problem resolved.

Thank you!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48106
Re: If both x and y are nonzero numbers, what is the value of y/x? (1) x  [#permalink]

Show Tags

New post 04 Dec 2017, 10:27
Re: If both x and y are nonzero numbers, what is the value of y/x? (1) x &nbs [#permalink] 04 Dec 2017, 10:27
Display posts from previous: Sort by

If both x and y are nonzero numbers, what is the value of y/x? (1) x

  post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.