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

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==Problem==
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<math> \text{ (A) }\ 1 \qquad\text{ (B) }\ 2 \qquad\text{ (C) }\ 3 \qquad\text{ (D) }\ 4 \qquad\text{ (E) }\ 5</math>
==Solution 1==
We can see that <math>z = \frac{w \times 3 \times 5}{2^4} = \frac{w \times 15}{16} = \frac{15}{16} \times w</math>. Since <math>\frac{15}{16} < 1</math>, <math>z < w</math>.

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

<math>y = \frac{x \times 3}{2} = 1.5x</math>, which gives <math>x < y</math> 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 <math>z < w</math>. This only matches answer choices C and D.

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

<math>y = \frac{x \times 3}{2} = 1.5x</math>

Since the coefficient is greater than <math>1</math>, <math>y > x</math>, which matches answer choice