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Founder  Joined: 18 Apr 2015
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For all integers a and b, a # b = –|a + b| [#permalink]
Expert's post 00:00

Question Stats: 79% (00:29) correct 20% (00:43) wrong based on 139 sessions

For all integers a and b, a # b = –|a + b|

 Quantity A Quantity B (–10) # 7 7 – 10

A) Quantity A is greater.
B) Quantity 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: For all integers a and b, a # b = –|a + b| [#permalink]
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Expert's post
Carcass wrote:

For all integers a and b, a # b = –|a + b|

 Quantity A Quantity B (–10) # 7 7 – 10

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

a # b = –|a + b|
So, (–10) # 7 = –|(-10) + 7|
= -|-3|
= -(3)
= -3

So, we get:
Quantity A: -3
Quantity B: 7 - 10

[Reveal] Spoiler:
C

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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Intern Joined: 08 Dec 2017
Posts: 40
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Kudos [?]: 46  , given: 70

Re: For all integers a and b, a # b = –|a + b| [#permalink]
2
KUDOS
Given that, all integers a and b, a # b = –|a + b|
Q.A (–10) # 7 = - |-10+7| = - |-3| = -3
Q.B 7-10 = -3

Intern Joined: 11 Jan 2018
Posts: 44
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Kudos [?]: 51 , given: 7

Re: For all integers a and b, a # b = –|a + b| [#permalink]
It's an easy question.
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Intern Joined: 17 Feb 2018
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Kudos [?]: 2 , given: 2

Re: For all integers a and b, a # b = –|a + b| [#permalink]
GREMasterBlaster wrote:
It's an easy question.

easy to get tripped up, since the intergers used are A and B, and the option choices are A and B
Intern Joined: 12 Aug 2018
Posts: 9
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Kudos [?]: 3 , given: 3

Re: For all integers a and b, a # b = –|a + b| [#permalink]
Since |a|=-a when a<0, Shouldn't we also test for -(-|-10+7|) which gives us 3. Hence it could be -3 or 3 isn't it? Thanks for the clarification.
Founder  Joined: 18 Apr 2015
Posts: 13371
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Kudos [?]: 3402 , given: 12227

Re: For all integers a and b, a # b = –|a + b| [#permalink]
Expert's post
in a#b you just need to substitute.

a = -10 and b = 7

QA - |a+b|= - |-3|= - |3| (insde the absolute value) = -3

QB is -3

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Intern Joined: 02 Jan 2019
Posts: 14
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Kudos [?]: 7 , given: 9

Re: For all integers a and b, a # b = –|a + b| [#permalink]
I agree with Runnyboy44's doubts about the answer. How are we supposed to know that we do not have to consider the case - -(|-3|) = +3 in this case?

This doubt could be corroborated by looking at exercises where the function is defined as a # b = (+)|a + b|. Then I would seperate between case 1:

a # b = (+)|a + b|

and case 2: a # b = (-)|a + b|

.

how are we supposed to that we should limit our answer strategy to plugging in.
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Joined: 01 Nov 2017
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Kudos [?]: 176 , given: 4

Re: For all integers a and b, a # b = –|a + b| [#permalink]
Expert's post
Zamala wrote:
I agree with Runnyboy44's doubts about the answer. How are we supposed to know that we do not have to consider the case - -(|-3|) = +3 in this case?

This doubt could be corroborated by looking at exercises where the function is defined as a # b = (+)|a + b|. Then I would seperate between case 1:

a # b = (+)|a + b|

and case 2: a # b = (-)|a + b|

.

how are we supposed to that we should limit our answer strategy to plugging in.

Hi..

we have to just read the information given in the question while we solve a question.
The question gives us a function a # b = (-)|a + b|...
Now you have to find (-10)#7, this means a=-10 and b=7, so substitute in the function to get (-10)#7=-|-10+7|=-3

|a|=-a when a<0.. But this is true when you do not know the value of a. Here you know what a and b stands for..

Even here a+b=-10+7=-3<0 so |a+b|=-(a+b) when (a+b)<0 thus |-10+7|=-(-10+7)=-(-3)=3..
But we are looking for -(|a+b|), which will be equal to -(3)
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Re: For all integers a and b, a # b = –|a + b|   [#permalink] 28 Jan 2019, 18:59
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