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

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

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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
[Reveal] Spoiler: OA

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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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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
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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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New post 01 Jul 2017, 03:00
If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z ?

All are positive integers.

Both statement (1) and statement (2) do not give us any values, for x, y or z and hence, we will not be able to arrive at a certain value for the average of x & z.

Hence, Answer is 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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We need to find (x+z)/2

Statement 1. x-y = y-z . this means z, y, x are in Arithmetic Progression (increasing order also)..
And x+z = 2y or (x+z)/2 = y. But we don't know the value of y, so insufficient.

Statement 2. Clearly insufficient.

Combining the two statements: Let the three AP terms: z = z, y = z+d, x = z+2d
Now from second statement we are given that x^2 - y^2 = z
or (z+2d)^2 - (z+d)^2 = z
Solving we get 2zd + 3d^2 = z.. But this is NOT sufficient to find the value of z/d (thus that of y too) so the question cannot be answered.

Hence E answer
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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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New post 13 Jul 2017, 08:34
Clumsy question right?

Like from 1 we get that the question is y=?

Then from 2 the info is something that has nothing to do with nothing.

So I chose E because the the question was a complete mess and I couldn't evaluate anything essentially.
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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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New post 17 Aug 2017, 01:33
Clearly E since we have 3 variables and only 2 equations
moreover

1) x-y=y-z
y= (x+z) /2 we dont know x,y,z A,D gone

2) x^2-y^2 = z
(x-y) (x+y) =z. we dont know x,y,z B gone

put y = x+z /2 in 2nd equation
which will give quadratic but mean of x and z will be impossible to obtain... Insufficient C GONE

Remaining E is answer
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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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New post 17 Aug 2017, 08:48
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GMAT normally ask
What or IS type of question .

When "What " type of question , then the ans is a definite numeric answer .
When " IS " type of question ,then the ans is yes or no .

So the answer to this question is E . As this a what type of question .

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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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New post 31 Aug 2017, 10:32
Statement (1) can be simplified and looked at conceptually. No need to pick numbers.

(x + z)/2 = y

Since we have no idea what y is, statement (1) is insufficient.

Statement (2) tempts us to use the difference of squares common equation.

(x + y)(x – y) = z

Since x, y and z are all positive, we know x – y must be positive, or x – y > 0. So x > y. But this is about all we can get with this approach, and this is something we could have observed from x^2 – y^2 = z, since z is positive.

The fact that there are no values in x^2 – y^2 = z is a clue that there are many possible combinations of x, y and z that could work. In picking numbers, I always like to start with simple numbers that fit the situation. So since x > y, here are some numbers that fit:

x = 2
y = 1
z = 2^2 – 1 = 3
(x + z)/2 = 2.5

OR

x = 3
y = 2
z = 3^2 – 2^2 = 5
(x + z)/2 = 4

Since we get two possible values for (x + z)/2, statement (2) is insufficient.

For (1) and (2) together, here’s an alternative to picking numbers. Notice that (1) tells us that y is the midpoint of x and z. Since (2) tells us that x > y, we know that z < y < x, and they are all evenly spaced. I like the idea of representing the spacing as d, so y = z + d, and x = z + 2d. Therefore, (2) gives us:

(z + 2d)^2 – (z + d)^2 = z
z^2 + 4dz + 4d^2 – z^2 – 2dz – d^2 = z
2dz + 3d^2 = z
3d^2 = z – 2dz = z(1-2d)
z = 3d^2/(1-2d)

In order to keep z positive, we must have d < ½, but as long as we do that, z could be lots of numbers, and therefore y and x could also be lots of numbers. Since (1) showed that our question is equivalent to y = ?, (1) and (2) together are insufficient.
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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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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


We need to determine (x + z)/2.

Statement One Alone:

x - y = y - z

Simplifying the equation, we have:

x - y = y - z

x + z = 2y

Since x + z = 2y, we have:

(x + z)/2 = 2y/2 = y

However, since we do not know the value of y, we cannot determine the average. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x^2 - y^2 = z

This does not provide enough information to determine the average of x and z. For example, if x = 3 and y = 2, then z = 5, and the average of x and z would be 4. However, if x = 4 and y = 2, then z = 12, and the average of x and z would be 8. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

From statement one, we see that z = 2y - x, and from statement two, we have z = x^2 - y^2. Thus, we have 2y - x = x^2 - y^2.

Notice that the equation above has two variables; thus, there are infinitely many solutions. That is, we won’t have a unique value for x or y, and hence we don’t have a unique value for z, either. The two statements together are still not sufficient to answer the question.

Answer: 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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New post 19 Nov 2017, 12:48
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Hi All,

We're told that X, Y and Z are POSITIVE numbers. We're asked for the average of X and Z. This question can be solved with a bit of math and TESTing VALUES.

1) X - Y = Y - Z

We can simplify this equation...
X + Z = 2Y

IF.... X=1, Z=1, Y=1, then the answer to the question is... (1+1)/2 = 1
IF.... X=2, Z=4, Y=3, then the answer to the question is... (2+4)/2 = 3
Fact 1 is INSUFFICIENT

2) X^2 - Y^2 = Z

IF.... X=2, Y=1, Z=3, then the answer to the question is... (2+3)/2 = 2.5
IF.... X=3, Y=1, Z=8, then the answer to the question is... (3+8)/2 = 5.5
Fact 2 is INSUFFICIENT

Combined, we can combine the two given equations....
X + Z = 2Y
X^2 - Y^2 = Z
into....
X + (X^2 - Y^2) = 2Y
X + X^2 = Y^2 + 2Y

Given that last equation - and since all 3 variables are POSITIVE - as X gets bigger, Y will ALSO get bigger. Since X could become a huge number (and Z is positive so it cannot 'offset' the increase in X'), the answer to the question "what is the average of X and Z?" will vary.
Combined, INSUFFICIENT

Final Answer:
[Reveal] Spoiler:
E


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Re: If x,y,and z are positive numbers,what is the value of the average (ar   [#permalink] 19 Nov 2017, 12:48
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