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Re: If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?
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27 Apr 2019, 10:20

1

Top Contributor

Bunuel wrote:

If xyz ≠ 0, what is the value of \(\frac{x^4z^2}{z^2y^2}\) ?

(1) y^2 = x^4 (2) x = 2 and y = 4

Target question:What is the value of (x⁴z²)/(z²y²)? This is a good candidate for rephrasing the target question. Since z ≠ 0, we know that z² ≠ 0 So, we can safely take (x⁴z²)/(z²y²) and divide top and bottom by z² to get: x⁴/y² REPHRASED target question:What is the value of x⁴/y²?

Aside: The video below has tips on rephrasing the target question

Statement 1: y² = x⁴ Take: x⁴/y² and replace y² with x⁴ to get: x⁴/x⁴, which equals 1 So, the answer to the REPHRASED target question is x⁴/y² = 1 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 2 and y = 4 So, x⁴/y² = 2⁴/4² = 16/16 = 1 Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Re: If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?
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09 May 2019, 19:22

Hi All,

We're told that If (X)(Y)(Z) ≠ 0. We're asked for the value of (X^4)(Z^2) / (Z^2)(Y^2). This question can be approached in a number of different ways, including Algebra and TESTing VALUES.

To start, it's worth noting that none of the given variables can equal 0 and the term (Z^2) appears in both the numerator and denominator (meaning that it essentially 'cancels out' - and we're ultimately asked for the value of (X^4)/(Y^2).

1) Y^2 = X^4

The information in Fact 1 matches the two 'terms' that we need to have values for to answer the given question. Since these two items are equal, the question can be rewritten as "What is the value of (X^4)/(X^4)?" Since the numerator is divided by itself, the answer to the question is clearly "1." You can also use TEST IT to prove that the answer is always 1...

IF... X=2 and Y=4, then the question becomes "What is the value of 16/16?" That fraction simplifies to 1 - and it will always simplify to 1 as long as you choose values that fit the given information. Fact 1 is SUFFICIENT

(2) X = 2 and Y = 4

We can 'plug in' the values from Fact 2 - which would give us 16/16 = 1. Even if we didn't cancel out the Z^2 terms, we would have 16(Z^2)/16(Z^2), which is still 1. Fact 2 is SUFFICIENT

Re: If xyz ≠ 0, what is the value of x^4z^2/z^2y^2 ?
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14 May 2019, 23:26

Solution

Steps 1 & 2: Understand Question and Draw Inferences In this question, we are given

• The value of xyz ≠ 0

We need to determine

• The value of the expression \(\frac{x^4 z^2}{z^2 y^2}\)

As the value of xyz ≠ 0, none of x, y and z are individually 0. Now, simplifying the given expression, we get

• \(\frac{x^4 z^2}{z^2 y^2} = \frac{x^4}{y^2}\) (as z ≠ 0)

Hence, we need to know the values of x and y, or the relationship between x4 and y2 With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1 As per the information given in statement 1, \(y^2 = x^4\)

• Therefore, \(\frac{x^4}{y^2} = 1\)

Hence, statement 1 is sufficient to answer the question.

Step 4: Analyse Statement 2 As per the information given in statement 2, x = 2 and y = 4.

• From this statement, we can determine the values of \(x^4\) and \(y^2\), and also their ratio.

Hence, statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed) Since we can determine the answer from either of the statements individually, this step is not required.