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

Hi Bunuel,
I couldn't figure out "what is quotient of a and b". I know "quotient concept is related to a division operation. Is it "which of the following is quotient of a/b"?
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The question means quotient/value when a is divided by b..
Thus ‘Our answer’ * b = a..

Let is check the choices..

A) \(\frac{b^2}{c}\)....\(b^2/c * b=b^3/c=b^2/a\)…..NO

B) \(\frac{c}{b^2}\).......\(c/b^2*b=c/b=a\)..YES


B


Algebraic

c is the product of a and b means \(c=a*b……a=\frac{c}{b}\)

We are looking for value of \(\frac{a}{b}=\frac{\frac{c}{b}}{b}=\frac{c}{b^2}\)
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"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. Algebra
Answers 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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Hi Bunuel,
My doubt is cleared. Thanks to Quant mega-thread.

In the following cases, order is important:
‘quotient/ratio of’ construction
If a problems says ‘the ratio of x and y’, it means ‘x divided by y’ NOT 'y divided by x'.

Thanks generis for elaborating it. Your last line may be a typo(Ans. (C))
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PKN , thank you! Indeed it is a typo. Maybe now my pals on the verbal forums will believe me when I say that I never edit my own work!
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ab=c
dividing by b, a=c/b
dividing by b again, a/b=c/b^2
B

c=a*b
Thus, a = c/b
We need to find a/b
therefore, (c/b)/b
Thus, a= c/b^2

We are given that c = ab. We need to find a/b in terms of b and c as we can see from the given choices. We can multiply a/b by b/b and obtain:

a/b * b/b = ab/b^2 = c/b^2

Alternate Solution:

We know that ab = c. Dividing each side of the equation by b^2, we get a/b = c/b^2.

Answer: B
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