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



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Re: If both x and y are nonzero numbers, what is the value of y/
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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)
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Re: If both x and y are nonzero numbers, what is the value of y/
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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 \(\sqrt{x^2}=x\).
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If both x and y are nonzero numbers, what is the value of y/x ?
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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



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



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Re: If both x and y are nonzero numbers, what is the value of y/
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21 May 2015, 02:36



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Re: If both x and y are nonzero numbers, what is the value of y/
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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
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Re: If both x and y are nonzero numbers, what is the value of y/
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31 Mar 2016, 00:05
Attached is a visual that should help.
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Screen Shot 20160331 at 1.03.46 AM.png [ 101.05 KiB  Viewed 7572 times ]
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Re: If both x and y are nonzero numbers, what is the value of y/
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04 Apr 2016, 23:51



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



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