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If x,y,and z are positive numbers,what is the value of the average (ar

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Re: If x,y,and z are positive numbers,what is the value of the average (ar [#permalink] New post   25 Nov 2020, 16:56
chetan2u wrote:
AbdurRakib wrote:
If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z ?

(1) x - y = y - z

(2) x^2 - y^2 = z



Hi,

The info and observations from the Q..
1) all numbers are >0.
2) there is no numeric value at all in the options/statements.

In the given circumstances, you cannot find the value. ANSWER at the best will in variables .

So E


Can't this approach be a little risky as sometimes the variables cancel out? So wouldn't it still be worth it to try and work it out to make sure that we are in fact still only left with variables?
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If x,y,and z are positive numbers,what is the value of the average (ar [#permalink] New post   25 Nov 2020, 18:58
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gd93 wrote:
chetan2u wrote:
AbdurRakib wrote:
If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z ?

(1) x - y = y - z

(2) x^2 - y^2 = z



Hi,

The info and observations from the Q..
1) all numbers are >0.
2) there is no numeric value at all in the options/statements.

In the given circumstances, you cannot find the value. ANSWER at the best will in variables .

So E


Can't this approach be a little risky as sometimes the variables cancel out? So wouldn't it still be worth it to try and work it out to make sure that we are in fact still only left with variables?



You should always try to solve the equations when you have time.
But in case you are short of time and in the given scenarios as in this question, you can mark E.

There is no number in the equations, it just contains variable.
If one of the variables cancel out we will have the other as equal to 0 in most of the cases, but here none can be 0 as all variables are positive integers.
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Re: If x,y,and z are positive numbers,what is the value of the average (ar [#permalink] New post   16 Jan 2021, 01:11
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AbdurRakib wrote:
If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z ?

(1) x - y = y - z

(2) x^2 - y^2 = z


\(Average of x+z=\frac{x+z}{2}\)

(1) \(x-y=y-z\)

\(⇒ x+z=2y\)

\(⇒ \frac{x+z}{2}=\frac{2y}{2}=y\)

(2) Will not give any value for x+z. Insufficient.

The answer is A.
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Re: If x,y,and z are positive numbers,what is the value of the average (ar [#permalink] New post   14 Mar 2021, 16:09
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Re: If x,y,and z are positive numbers,what is the value of the average (ar [#permalink] New post   22 May 2021, 00:57
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AbdurRakib wrote:
If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z ?

(1) x - y = y - z

(2) x^2 - y^2 = z


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Re: If x,y,and z are positive numbers,what is the value of the average (ar [#permalink] New post   21 Feb 2022, 06:42
A lot of people are saying that the statements can not be sufficient since they have no numerical value. This is NOT entirely true, and it is therefore dangerous to make a conclusion on this premise alone even though it is true for this exact question.

For example, IF one of statements where xy+xz=y, this would give us x+z=1. And since we are looking for (x+z)/2, we can conclude that the arithmetic mean of x and z is 1/2.
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Re: If x,y,and z are positive numbers,what is the value of the average (ar [#permalink] New post   19 Jul 2023, 21:24
Q. what is x+z/2 ?

1. after solving, x+z/2 = y. Since we don't know y. (Insufficient)
2. same as a three variables, can't solve for AM
1&2, we have 2 equation but we have 3 variables. Hence E.
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Re: If x,y,and z are positive numbers,what is the value of the average (ar [#permalink]
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