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Math Expert V
Joined: 02 Sep 2009
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If both x and y are nonzero numbers, what is the value of y/  [#permalink]

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Question Stats: 70% (00:56) correct 30% (00:46) wrong based on 651 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 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

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Math Expert V
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Re: If both x and y are nonzero numbers, what is the value of y/  [#permalink]

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8
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SOLUTION

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.

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/  [#permalink]

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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.

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

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 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 V
Joined: 02 Sep 2009
Posts: 64101
Re: If both x and y are nonzero numbers, what is the value of y/  [#permalink]

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SOLUTION

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.

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 ?  [#permalink]

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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.

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

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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 NON-0 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

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

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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 V
Joined: 02 Sep 2009
Posts: 64101
Re: If both x and y are nonzero numbers, what is the value of y/  [#permalink]

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1
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.
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Re: If both x and y are nonzero numbers, what is the value of y/  [#permalink]

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1
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).

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

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Attached is a visual that should help.
Attachments Screen Shot 2016-03-31 at 1.03.46 AM.png [ 101.05 KiB | Viewed 11740 times ]

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GRE 1: Q169 V154 Re: If both x and y are nonzero numbers, what is the value of y/  [#permalink]

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Here is my approach => In combining both the cases => Y/X can be 1 or -1 => E is the answer
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If both x and y are nonzero numbers, what is the value of y/  [#permalink]

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1
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/  [#permalink]

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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 non-zero 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.

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

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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

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

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

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