User:Anabel.disher/Sandbox/Grade 9 Pascal 1999 Q22

Problem

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$\text{ (A) }\ 1 \qquad\text{ (B) }\ 2 \qquad\text{ (C) }\ 3 \qquad\text{ (D) }\ 4 \qquad\text{ (E) }\ 5$

Solution 1

We can see that $z = \frac{w \times 3 \times 5}{2^4} = \frac{w \times 15}{16} = \frac{15}{16} \times w$ . Since $\frac{15}{16} < 1$ , $z < w$ .

We can also see that $z = \frac{y \times 5}{2} = 2.5y$ . Since the coefficient is greater than $1$ , $y < z$ .

$y = \frac{x \times 3}{2} = 1.5x$ , which gives $x < y$ using similar logic.

Ordering the variables from least

~anabel.disher

Solution 2 (answer choices)

We can use the same logic from solution 1 to conclude that $z < w$ . This only matches answer choices C and D.

Since $x$ is smaller than $y$ in answer choice C but is greater than $y$ in answer choice D, we need to see whether or not $x$ is smaller than $y$ .

$y = \frac{x \times 3}{2} = 1.5x$

Since the coefficient is greater than $1$ , $y > x$ , which matches answer choice

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User:Anabel.disher/Sandbox/Grade 9 Pascal 1999 Q22

Problem

Solution 1

Solution 2 (answer choices)