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

Question

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

PKN · Answer

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"?

chetan2u · Answer

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}

generis · Answer

"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.

PKN · Answer

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))

generis · Answer

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!

gracie · Answer

ab=c
dividing by b, a=c/b
dividing by b again, a/b=c/b^2
B

780gmatpossible · Answer

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

JeffTargetTestPrep · Answer

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

bumpbot · Answer

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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

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