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# If abc ≠ 0 is (a/b)/c = a/(b/c)

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Math Expert
Joined: 02 Sep 2009
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If abc ≠ 0 is (a/b)/c = a/(b/c)  [#permalink]

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21 Jan 2014, 04:10
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73% (01:15) correct 27% (01:27) wrong based on 957 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If $$abc\neq{0}$$, is $$\frac{\frac{a}{b}}{c}=\frac{a}{\frac{b}{c}}$$?

(1) a = 1
(2) c = 1

Data Sufficiency
Question: 48
Category: Algebra Fractions
Page: 156
Difficulty: 600

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Re: If abc ≠ 0 is (a/b)/c = a/(b/c)  [#permalink]

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21 Jan 2014, 04:11
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SOLUTION

If $$abc\neq{0}$$, is $$\frac{\frac{a}{b}}{c}=\frac{a}{\frac{b}{c}}$$?

$$\frac{\frac{a}{b}}{c}=\frac{a}{b}*\frac{1}{c}=\frac{a}{bc}$$;

$$\frac{a}{\frac{b}{c}}=a*\frac{c}{b}=\frac{ac}{b}$$.

So, the question becomes: is $$\frac{a}{bc}=\frac{ac}{b}$$? --> reduce by a/b: is $$\frac{1}{c}=c$$? --> is $$c^2=1$$.

(1) a = 1. Not sufficient.

(2) c = 1. Sufficient.

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Intern
Joined: 20 Sep 2016
Posts: 1
GMAT 1: 570 Q45 V24
Re: If abc ≠ 0 is (a/b)/c = a/(b/c)  [#permalink]

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11 Mar 2017, 06:35
Hi all,
Can we use if: a/b = c/d then ad = bc ?

So in this case we will get:
a*c = $$\frac{a}{b}$$ * $$\frac{b}{c}$$
a*c = $$\frac{a}{c}$$

and nowif we know from (1):
a=1 then let's take c=3 as an example:
1*3 ≠ 1/3

(2) c=1
any a we take it always holds true:
4*1 = 4/1
Manager
Joined: 10 Sep 2014
Posts: 78
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WE: Project Management (Manufacturing)
Re: If abc ≠ 0 is (a/b)/c = a/(b/c)  [#permalink]

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30 Sep 2018, 03:42
Senior Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 383
If abc ≠ 0 is (a/b)/c = a/(b/c)  [#permalink]

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06 May 2019, 19:21
I found this confusing so I just used some numbers to see the relationship
Say a=1, b=2, c=3

$$\frac{\frac{1}{2}}{3}=\frac{1}{\frac{2}{3}}$$?

$$\frac{\frac{1}{2}}{3}=\frac{1}{2}*\frac{1}{3}=\frac{1}{6}$$;

$$\frac{1}{\frac{2}{3}}=1*\frac{3}{2}=\frac{3}{2}$$.

(1) a = 1
So the above gives a NO
while if we make a,b,c = 1 then it gives a YES
Not sufficient.

(2) c = 1
a=3, b=2, c=1

$$\frac{\frac{3}{2}}{1}=\frac{3}{2}$$;

$$\frac{3}{\frac{2}{1}}=3*\frac{1}{2}=\frac{3}{2}$$.

This will hold true for any fraction.

An easier way to see it is to convert 3/2 to 1.5 ... so you get 1.5/1 both ways.
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Joined: 30 Jul 2019
Posts: 6
Re: If abc ≠ 0 is (a/b)/c = a/(b/c)  [#permalink]

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04 Aug 2019, 08:51
Could anyone explain the logic of this question? Clearly, it asks whether two equations with same variables in same positions are equal to each other. How, then, could they be different?
Cheers

Posted from my mobile device
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Re: If abc ≠ 0 is (a/b)/c = a/(b/c)  [#permalink]

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04 Aug 2019, 16:30
Oli0139 wrote:
Could anyone explain the logic of this question? Clearly, it asks whether two equations with same variables in same positions are equal to each other. How, then, could they be different?
Cheers

Posted from my mobile device

They are not in the same position. On the left part you are dividing fraction a/b by number c, and on the right you are dividing number a by fraction b/c

The question is asking if c= 1 or -1 because if it is then both sides become equivalent fractions or integer values. If it's not, then you get different fractions, I picked numbers above to show this.

If you look at Bunuel's solution, the actual values of a,b don't matter as they cancel out.

Hope it helps.
Re: If abc ≠ 0 is (a/b)/c = a/(b/c)   [#permalink] 04 Aug 2019, 16:30
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