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

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If c is the product of a and b, which of the following is the quotient  [#permalink]

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New post 17 Aug 2018, 05:59
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Re: If c is the product of a and b, which of the following is the quotient  [#permalink]

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New post 17 Aug 2018, 06:21
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) \(b^2c\)


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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Re: If c is the product of a and b, which of the following is the quotient  [#permalink]

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New post 17 Aug 2018, 06:30
2
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 question must be meaning quotient when a is divided by b..
Our answer *b=a..
See the choices..

A) \(\frac{b^2}{c}\)....\(b^2/c * b=b^3/c=b^2/a\)

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

B
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If c is the product of a and b, which of the following is the quotient  [#permalink]

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New post 17 Aug 2018, 20:25
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. 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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Re: If c is the product of a and b, which of the following is the quotient  [#permalink]

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New post 17 Aug 2018, 23:19
PKN wrote:
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) \(b^2c\)


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"?


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

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If c is the product of a and b, which of the following is the quotient  [#permalink]

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New post 17 Aug 2018, 23:45
PKN wrote:

generis Your last line may be a typo(Ans. (C))

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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Re: If c is the product of a and b, which of the following is the quotient  [#permalink]

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New post 18 Aug 2018, 07:30
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) \(b^2c\)


ab=c
dividing by b, a=c/b
dividing by b again, a/b=c/b^2
B
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Re: If c is the product of a and b, which of the following is the quotient  [#permalink]

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New post 18 Aug 2018, 07:36
c=a*b
Thus, a = c/b
We need to find a/b
therefore, (c/b)/b
Thus, a= c/b^2
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Re: If c is the product of a and b, which of the following is the quotient  [#permalink]

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New post 20 Aug 2018, 11:33
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) \(b^2c\)



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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Re: If c is the product of a and b, which of the following is the quotient   [#permalink] 20 Aug 2018, 11:33
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