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a ≠ b

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a ≠ b [#permalink]  23 Jun 2018, 12:28
Expert's post
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Question Stats:

62% (00:34) correct 37% (00:34) wrong based on 95 sessions
$$a \neq b$$

 Quantity A Quantity B $$\frac{a-b}{b-a}$$ 1

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: a ≠ b [#permalink]  26 Jun 2018, 07:51
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sandy wrote:
$$a \neq b$$

 Quantity A Quantity B $$\frac{a-b}{b-a}$$ 1

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

From the statement; statement B > Statement 1

If we put any values in Statement 1 it will always result = -1 which is less than statement 2
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Re: a ≠ b [#permalink]  27 Jun 2018, 17:01
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(a-b)/(b-a)=(a-b)/-(a-b)=-1<1 -> B
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Retired Moderator
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Kudos [?]: 3041 [1] , given: 394

Re: a ≠ b [#permalink]  18 Jul 2018, 07:38
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Expert's post
Explanation

Plug in any two unequal values for a and b, and Quantity A will always be equal to –1. This is because a negative sign can be factored out of the top or bottom of the fraction to show that the top and bottom are the same, except for their signs:

$$\frac{a-b}{b-b}=\frac{a-b}{-(a-b)}=-1$$
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Re: a ≠ b [#permalink]  10 Apr 2019, 06:20
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@ScottTargetTestPrep @Sandy

I was trying a different approach, but I does not work, why?

I did the following:

Quant A
a-b/b-a

Quant B
1 is the same as b-a/b-a

so, I need to compare a-b (Quant A) with b-a (Quant B)

Just I pick some numbers, but the answer is D:

Option 1: a=2, b=-3

QA: a-b = -1
QB: b-a = -3-2 = -5
so QA>QB

Option 1: a=-2, b=3

QA: a-b = 1
QB: b-a = 3+2 =5
so QB>QA

Why?
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Re: a ≠ b [#permalink]  10 Apr 2019, 06:40
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Expert's post
dcmartinezp wrote:
@ScottTargetTestPrep @Sandy

I was trying a different approach, but I does not work, why?

I did the following:

Quant A
a-b/b-a

Quant B
1 is the same as b-a/b-a

so, I need to compare a-b (Quant A) with b-a (Quant B)

Just I pick some numbers, but the answer is D:

Option 1: a=2, b=-3

QA: a-b = -1
QB: b-a = -3-2 = -5
so QA>QB

Option 1: a=-2, b=3

QA: a-b = 1
QB: b-a = 3+2 =5
so QB>QA

Why?

You got here:
QUANTITY A: (a-b)/(b-a)
QUANTITY B: (b-a)/(b-a)

From here, you basically multiplied both quantities by (b-a) to get:
QUANTITY A: (a-b)
QUANTITY B: (b-a)

This is where the problem lies.
We don't know whether (b-a) is POSITIVE or NEGATIVE.

As such, we cannot multiply both quantities by (b-a)

For more on this, watch the following:

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Re: a ≠ b [#permalink]  10 Apr 2019, 07:00
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Hi @GreenlightTestPrep Brent, thank you by your message!

It's a little confuse for me that I have just the option provided by Sandy/MGRE. Just I imagine myself doing the test and no be sure that I could use picking numbers or another strategy..

How do you do this exercise using picking numbers without a err as I had?
I tried two options, just because I was conscious that I do not know whether the values of a and b are positive or negative, integers of fractions.

Thank you
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Re: a ≠ b [#permalink]  10 Apr 2019, 09:22
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Expert's post
dcmartinezp wrote:
Hi @GreenlightTestPrep Brent, thank you by your message!

It's a little confuse for me that I have just the option provided by Sandy/MGRE. Just I imagine myself doing the test and no be sure that I could use picking numbers or another strategy..

How do you do this exercise using picking numbers without a err as I had?
I tried two options, just because I was conscious that I do not know whether the values of a and b are positive or negative, integers of fractions.

Thank you

It's totally fine to test values. HOWEVER, you cannot first simplify the quantities as you did the first time.

QUANTITY A: (a-b)/(b-a)
QUANTITY B: 1

Case 1
If a = 2, and b = -3, we get:
QUANTITY A: (2 - -3)/(-3 - 2) = 5/-5 = -1
QUANTITY B: 1
Quantity B is greater

Case 2
If a = -2, and b = 3, we get:
QUANTITY A: (-2 - 3)/(3 - -2) = -5/5 = -1
QUANTITY B: 1
Quantity B is greater

Case 3
If a = 1, and b = 7, we get:
QUANTITY A: (1 - 7)/(7 - 1) = -7/7 = -1
QUANTITY B: 1
Quantity B is greater

Case 4
If a = 11, and b = 2, we get:
QUANTITY A: (11 - 2)/(2 - 11) = 9/-9 = -1
QUANTITY B: 1
Quantity B is greater

Etc...

Does that help?

Cheers,
Brent
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Re: a ≠ b [#permalink]  08 May 2020, 03:51
Why not just factor a -1 out of the denominator or numerator to get -1 * 1? Worked for me and super fast!
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Re: a ≠ b [#permalink]  09 May 2020, 04:05
Didnt understand the condition a negative or b negative
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Re: a ≠ b [#permalink]  09 May 2020, 05:50
Expert's post
NickBass wrote:
Why not just factor a -1 out of the denominator or numerator to get -1 * 1? Worked for me and super fast!

Exactly.
That's how @leanhdung and @sandy (above) answered the question.
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Re: a ≠ b [#permalink]  09 May 2020, 05:52
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Expert's post
Nikhil4GRE wrote:
Didnt understand the condition a negative or b negative

I'm not too sure what you're asking. Can you elaborate?
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Re: a ≠ b   [#permalink] 09 May 2020, 05:52
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