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# Assuming that x and y are the same.

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Assuming that x and y are the same. [#permalink]  16 Nov 2011, 11:46
Assuming that we have a certain GMAT question and it mentions that there are two variables, x and y. Does the variables, having two different names, mean that they must be different? or could x and y be sometimes disguised to be the same variable?

In other words, is it safe to always assume that x and y must be different numbers since they are named x and y? The same applies to any two different variable names, k and n, m and n etc etc.
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Re: Assuming that x and y are the same. [#permalink]  16 Nov 2011, 23:45
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That's a good question.

Whenever the question explicitly mentions two variables, say x and y, you are supposed to assume that x and y are numbers with different values. Although, on solving for the answer, you might realize that they both have same values i.e. a single number can be the value for both x and y such that the given system of equations/inequalities/conditions are satisfied.

For example, consider the two equations
x + y = 9 and
x - y = 1
We can solve these two equations to get the unique answer as x = 5 and y = 4.

However, consider the following equation
(x^2)/(y^2) = 1
The above equation means that both x and y have the same absolute value i.e. |x| = |y|
Consider the values x = 2 and y = -2 --> These values satisfy the equation
So does the values x = 3 and y = 3

So, we can say that, for the purpose of solving the question, we have to assume that the values of x and y are different. However, in cases such as inequalities, wherein you need to consider varied values, it might so happen that the same value for x and y will satisfy the given equation/inequality.

Hope this helps

Cheers!
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Manager
Joined: 08 Jun 2011
Posts: 98
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Kudos [?]: 11 [0], given: 65

Re: Assuming that x and y are the same. [#permalink]  17 Nov 2011, 03:28
sudish wrote:

That's a good question.

Whenever the question explicitly mentions two variables, say x and y, you are supposed to assume that x and y are numbers with different values. Although, on solving for the answer, you might realize that they both have same values i.e. a single number can be the value for both x and y such that the given system of equations/inequalities/conditions are satisfied.

For example, consider the two equations
x + y = 9 and
x - y = 1
We can solve these two equations to get the unique answer as x = 5 and y = 4.

However, consider the following equation
(x^2)/(y^2) = 1
The above equation means that both x and y have the same absolute value i.e. |x| = |y|
Consider the values x = 2 and y = -2 --> These values satisfy the equation
So does the values x = 3 and y = 3

So, we can say that, for the purpose of solving the question, we have to assume that the values of x and y are different. However, in cases such as inequalities, wherein you need to consider varied values, it might so happen that the same value for x and y will satisfy the given equation/inequality.

Hope this helps

Cheers!

Thanks for the help. Very clear
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Re: Assuming that x and y are the same. [#permalink]  18 Nov 2011, 01:00
1
KUDOS
Assuming that we have a certain GMAT question and it mentions that there are two variables, x and y. Does the variables, having two different names, mean that they must be different? or could x and y be sometimes disguised to be the same variable?

In other words, is it safe to always assume that x and y must be different numbers since they are named x and y? The same applies to any two different variable names, k and n, m and n etc etc.

'there are two variables, x and y' - Do not assume that they must have different values. It is possible that they are distinct, it is also possible that they have the same value.

'there are two distinct variables, x and y' - The value of the two variables must be different.
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Re: Assuming that x and y are the same.   [#permalink] 18 Nov 2011, 01:00
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