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Math Expert V
Joined: 02 Sep 2009
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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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Difficulty:   15% (low)

Question Stats: 77% (01:33) correct 23% (02:04) wrong based on 59 sessions

### HideShow timer Statistics 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) $$b^2c$$

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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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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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Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: If c is the product of a and b, which of the following is the quotient  [#permalink]

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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..
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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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 $$\frac{a}{b}$$

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

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

*"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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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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Regards,

PKN

Rise above the storm, you will find the sunshine
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3080
If c is the product of a and b, which of the following is the quotient  [#permalink]

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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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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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GMAT 1: 660 Q44 V37 Re: If c is the product of a and b, which of the following is the quotient  [#permalink]

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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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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.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. 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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