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If # represents one of the operations +,- and *, is a #

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If # represents one of the operations +,- and *, is a # [#permalink] New post 19 Sep 2010, 14:49
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If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction
[Reveal] Spoiler: OA

Last edited by zisis on 19 Sep 2010, 15:09, edited 1 time in total.
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Re: If # represents one of the operations +,- and *, is a # [#permalink] New post 19 Sep 2010, 14:58
I converted question to 3 euqations where # can be +, - or *

So
I) When # = *
ab-ac = ab-ac (true for all values)

II) When # = +
Is a+b-c=b-c

III) When #=-
Is a-b+c = -b-c?

With option A we know # is not * as 1*a is always equal to a*1. So given equation is not equal
With option B , equation is not equal.

So answer choice D
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Re: If # represents one of the operations +,- and *, is a # [#permalink] New post 19 Sep 2010, 15:50
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction



Mods, please to DS section...posted by mistake in PS - apologies


1. From choice 1 it is clear that # is subtraction. coz a+1=1+1, a*1=1*a but a-1!=(not equal) 1-a.
2. Choice 2 says directly that it is subtraction.

Hence answer is D
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Re: If # represents one of the operations +,- and *, is a # [#permalink] New post 19 Sep 2010, 18:38
vigneshpandi wrote:
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction



Mods, please to DS section...posted by mistake in PS - apologies


1. From choice 1 it is clear that # is subtraction. coz a+1=1+1, a*1=1*a but a-1!=(not equal) 1-a.
2. Choice 2 says directly that it is subtraction.

Hence answer is D



IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?
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Re: If # represents one of the operations +,- and *, is a # [#permalink] New post 19 Sep 2010, 23:14
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BalakumaranP wrote:
IMO, it cannot be "not equal" always.

If # is subtraction,

a#(b-c)=a-(b-c)=a-b+c

(a#b)-(a#c)=(a-b)-(a-c)=a-b-a+c=-b+c

a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?


If # represents one of the operations +, - and *, is \(a#(b-c)=(a#b)-(a#c)\) for all numbers \(a\), \(b\) and \(c\).

(1) \(a#1\) is not equal to \(1#a\) for some numbers \(a\).

\(#\) is neither addition (as \(a+1=1+a\)) not multiplication (as \(a*1=1*a\)), so \(#\) is a subtraction. Then \(LHS=a#(b-c)=a-b+c\) and \(RHS=(a#b)-(a#c)=(a-b)-(a-c)=c-b\), so the question becomes "is \(a-b+c=c-b\) for all numbers \(a\), \(b\) and \(c\)?" --> "is \(a=0\)". So when \(a=0\) (and \(#\) is a subtraction) then \(a#(b-c)=(a#b)-(a#c)\) holds true but not for other values of \(a\), so not for all numbers \(a\), \(b\) and \(c\). Answer to the question is NO. Sufficient.

(2) \(#\) represents subtraction --> the same as above. Sufficient.

Answer: D.

Hope it's clear.
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Re: If # represents one of the operations +,- and *, is a # [#permalink] New post 20 Sep 2010, 02:09
Okay.. I read the question wrong...
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Re: If # represents one of the operations +,- and *, is a # [#permalink] New post 20 Sep 2010, 18:10
(1) a#1 is not equal to 1#a for some numbers a

a + 1 = 1 + a for all a
a*1 = 1*a for all a

a - 1 != 1 - a

Statement (1) implies # is a minus sign, so it has same meaning as (2).

Ans D
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Re: If # represents one of the operations +,- and *, is a # [#permalink] New post 21 Sep 2010, 09:55
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction



Mods, please to DS section...posted by mistake in PS - apologies


You're told that "#" is either addition, subtraction, or multiplication, and then asked if "#" satisfies the distributive property. Of these three, distribution only holds for multiplication, so if "#" is "*", it holds, and if "#" isn't "*", then it does not hold.

All we really need to know is what operation "#" really is.

(1) This is only true of subtraction, so # is subtraction and the distributive property does not hold. Sufficient.
(2) Same as above. Sufficient.

(D)
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Re: If # represents one of the operations +,- and *, is a # [#permalink] New post 03 Jun 2015, 07:54
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction


Could someone edit this question so it will be an actual question? There is no proper question stem.
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Re: If # represents one of the operations +,- and *, is a # [#permalink] New post 03 Jun 2015, 07:58
Expert's post
reto wrote:
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction


Could someone edit this question so it will be an actual question? There is no proper question stem.


What do you mean? Everything is correct there. Similar questions: Operations/functions defining algebraic/arithmetic expressions

Check functions related questions in our Special Questions Directory.

Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions
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COLLECTION OF QUESTIONS:
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Re: If # represents one of the operations +,- and *, is a # [#permalink] New post 03 Jun 2015, 08:07
Bunuel wrote:
reto wrote:
zisis wrote:
If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction


Could someone edit this question so it will be an actual question? There is no proper question stem.


What do you mean? Everything is correct there. Similar questions: Operations/functions defining algebraic/arithmetic expressions

Check functions related questions in our Special Questions Directory.

Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions



The question mark is missing in the question stem.
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Re: If # represents one of the operations +,- and *, is a #   [#permalink] 03 Jun 2015, 08:07
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