Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64101

If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
09 Jan 2014, 05:52
Question Stats:
70% (00:56) correct 30% (00:46) wrong based on 651 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionIf both x and y are nonzero numbers, what is the value of y/x? (1) x = 6 (2) y^2 = x^2 Data Sufficiency Question: 28 Category: Arithmetic Powers of numbers Page: 155 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 64101

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
09 Jan 2014, 05:52
SOLUTIONIf 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 \(\sqrt{x^2}=x\).
_________________




Manager
Status: GMATting
Joined: 21 Mar 2011
Posts: 105
Concentration: Strategy, Technology

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
09 Jan 2014, 22:11
Given: x,y<>0; y/x = ?
(1) x=6; No info about y; Insufficient. (2) y^2 = x^2; If we take x,y to be 1, then yes y/x can be determined; But, if we take y as 1 and x as 1, y/x gives 1; Insufficient;
Combining both statements tells us that y is either 6 or 6, thereby giving 2 different values(1 or 1) for y/x; Insufficient.
Hence, Answer is (E).



Director
Joined: 03 Feb 2013
Posts: 836
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
10 Jan 2014, 10:31
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf both x and y are nonzero numbers, what is the value of y/x? (1) x = 6 (2) y^2 = x^2 Data Sufficiency Question: 28 Category: Arithmetic Powers of numbers Page: 155 Difficulty: 600 Statement 1) Value of Y is not specified, we cannot determine  Not Sufficient. Statement 2) y = + (x) so y/x can be + or . Not sufficient Combining the two statements, x can be +6 or 6, so we cannot determine y/x  Option E)



Math Expert
Joined: 02 Sep 2009
Posts: 64101

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
11 Jan 2014, 06:40
SOLUTIONIf 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 \(\sqrt{x^2}=x\).
_________________



Manager
Joined: 12 Jan 2013
Posts: 137

If both x and y are nonzero numbers, what is the value of y/x ?
[#permalink]
Show Tags
12 Jan 2014, 06:42
johnbaker wrote: If both x and y are nonzero numbers, what is the value of y/x ? (1) x = 6 (2) y^2 = x^2 1) only gives us y/6, so clearly insufficient 2) gives us no values at all, so insufficient 1 + 2, only tell us that y is either 6 or 6, but since we have 2 possible values, this is insufficient. answer is E



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16711
Location: United States (CA)

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
12 Mar 2015, 16:39
Hi All, One of the standard Algebraic concepts that you'll see more than once on Test Day is the concept of "squared values." To test your "thoroughness" on this subject, the Test will throw the concept at you in a few different formats. Keep in mind that the rules are the always the same, but you have to pay attention to what you're looking at to get the points. Here, we're told that X and Y are NON0 NUMBERS. We're asked for the value of Y/X. Fact 1: X = 6 This tells us NOTHING about Y. Since Y can be anything except 0, there are an infinite number of different possible values for Y/X. Fact 1 is INSUFFICIENT Fact 2: Y^2 = X^2 Here, we can TEST VALUES to prove a point.... IF.....X = 1, then we have... Y^2 = 1 Since we have a squared value, there are 2 solutions: Y = 1 and Y = 1 IF.... X = 1 Y = 1 The answer to the question is 1/1 = 1 IF.... X = 1 Y = 1 The answer to the question is 1/1 = 1 Fact 2 is INSUFFICIENT Combined, we know.... X = 6 Y^2 = X^2 Notice the issue in Fact 2....it's the same issue here.... We know that X = 6, so Y^2 = 36. But since we have a squared value, there are 2 solutions: Y = 6 and Y = 6. IF.... X = 6 Y = 6 The answer to the question is 6/6 = 1 IF.... X = 6 Y = 6 The answer to the question is 6/6 = 1 Combined, INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Manager
Joined: 07 Apr 2015
Posts: 150

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
21 May 2015, 01:04
I know its wrong, but when we are asked what the value of y/x is, why can't we plug in the information given in statement 2?
y/x = ?
y^2 = x^2  Plug x^2 into the equation:
x^2 / x = x.
It does not answer the question of an exact value, but would it theoretically possible to use this approach?



Math Expert
Joined: 02 Sep 2009
Posts: 64101

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
21 May 2015, 02:36
noTh1ng wrote: I know its wrong, but when we are asked what the value of y/x is, why can't we plug in the information given in statement 2?
y/x = ?
y^2 = x^2  Plug x^2 into the equation:
x^2 / x = x.
It does not answer the question of an exact value, but would it theoretically possible to use this approach? Official Guide: In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.
_________________



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16711
Location: United States (CA)

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
21 May 2015, 09:40
Hi noTh1ng, noTh1ng wrote: I know its wrong, but when we are asked what the value of y/x is, why can't we plug in the information given in statement 2?
y/x = ?
y^2 = x^2  Plug x^2 into the equation:
x^2 / x = x.
It does not answer the question of an exact value, but would it theoretically possible to use this approach? Fact 2 tells us that Y^2 = X^2. This does NOT tell us the value of Y. Since both terms are 'squared', we don't know if Y = X or Y = X. Since the question asks for the value of Y/X, substituting in (while permissible) does NOT answer the given question (what is the VALUE of Y/X). GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 768
Location: United States (CA)
Age: 40
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
WE: Education (Education)

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
31 Mar 2016, 00:05
Attached is a visual that should help.
Attachments
Screen Shot 20160331 at 1.03.46 AM.png [ 101.05 KiB  Viewed 11740 times ]



Current Student
Joined: 12 Aug 2015
Posts: 2522

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
04 Apr 2016, 23:51
Here is my approach => In combining both the cases => Y/X can be 1 or 1 => E is the answer
_________________



Intern
Joined: 06 May 2017
Posts: 3
Location: Trinidad and Tobago
Concentration: Finance
GPA: 3.65
WE: Analyst (Commercial Banking)

If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
03 Jun 2017, 06:39
Stupid question: So this answer proves that despite x and y being different variables, they can still be the same number. Does this hold for all GMAT questions? (I don't recall reading this anywhere).
My take of the question was that since x^2=y^2, then one must be positive and one must be negative given that they are different variables and therefore the answer is 1.
I.e. for e.g.
x^2=y^2 = 36 x= 6 and y =6; x/y= 6/6= 1 OR x= 6 and y= 6; x/y = 6/6= 1... So we know the value



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16711
Location: United States (CA)

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
03 Jun 2017, 11:40
Hi Graeme520, When dealing with DS questions, you have to consider what you're told and what you're not told. Here, we're told that X and Y are nonzero numbers. That's not particularly 'restrictive' information  it means that X and Y could be ANY number EXCEPT 0 (including integers, fractions, repeating decimals, the SAME number, etc.). IF... a prompt gives you explicit information that X and Y cannot be the same (re: "X is not equal to Y", "X and Y are DISTINCT numbers", X > Y, etc.), then you know that the two variables must be different numbers. Here though, we're given no such information to restrict our work, so we have to consider the possibility that the two values might be the same value. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Senior Manager
Joined: 10 Aug 2018
Posts: 280
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)

Re: If both x and y are nonzero numbers, what is the value of y/
[#permalink]
Show Tags
06 Aug 2019, 23:02
Combining both we can get two answers. If X is 6 and Y is 6 then +1 If X is 6 and Y is 6 then 1 Hence E is the answer.
_________________
On the way to get into the Bschool and I will not leave it until I win. WHATEVER IT TAKES. " I CAN AND I WILL"



NonHuman User
Joined: 09 Sep 2013
Posts: 14969

Re: If both x and y are nonzero numbers, what is the value of
[#permalink]
Show Tags
23 May 2020, 08:21
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: If both x and y are nonzero numbers, what is the value of
[#permalink]
23 May 2020, 08:21




