Bunuel wrote:

If c is the product of a and b, which of the following is the quotient of a and b?

A) \(\frac{b^2}{c}\)

B) \(\frac{c}{b^2}\)

C) \(\frac{b}{c^2}\)

D) \(bc^2\)

E) \(b^2c\)

"The quotient of \(a\) and \(b\)" means "\(a\) divided by \(b\)." In English, if the operation is division,

the quantity mentioned first goes on top.I. AlgebraAnswers have only \(b\) and \(c\)

Define \(a\) in terms of \(b\) and \(c\)

1) \(a*b=c\)

2) \(a=\frac{c}{b}\)

3) \(\frac{a}{b}= ?\)

Substitute \(a\)'s value from (2) above (\(\frac{c}{b}\)) into \(\frac{a}{b}\)

\(\frac{a}{b}= \frac{(\frac{c}{b})}{b} = \frac{c}{b^2}\)

ANSWER B

II. Assign values Almost always, if VICs and division are involved, assign values that are ALL even, and make dividend greater than divisor. Use unusual numbers, but not too hard.*

\((a*b)=c\)

Let

\(a=10\)

\(b=2\), so

\(c=20\)

\((a*b)=c\)

\((10*2)=20\), and

\(\frac{a}{b}=\frac{10}{2}=5\)

Using \(b=2\) and \(c=20\), find the answer choice that yields \(5\)

A) \(\frac{b^2}{c}=\frac{4}{20}=\frac{1}{5}\) REJECT

B) \(\frac{c}{b^2}=\frac{20}{4}=5\) KEEP

C) \(\frac{b}{c^2}=\frac{2}{(20)(20)}\) = tiny. REJECT

D) \(bc^2=(2*20*20)\) = huge. REJECT

E) \(b^2c=(2*2*20)\) = huge. REJECT

ANSWER B

*"Usual" = 0, 1, and 2. If you pick (2 * 1) = 2, answers B and E will be correct. Or usual = only multiples of 2 such as 4, 2, 8. They work here, but often, they will yield more than one correct answer.
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In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"