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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]

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19 Sep 2010, 15:49
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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, 16:09, edited 1 time in total.
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Re: If # represents one of the operations +,- and *, is a # [#permalink]

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19 Sep 2010, 15:58
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.

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Re: If # represents one of the operations +,- and *, is a # [#permalink]

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19 Sep 2010, 16:50
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.

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Re: If # represents one of the operations +,- and *, is a # [#permalink]

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19 Sep 2010, 19:38
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.

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]

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20 Sep 2010, 00:14
Expert's post
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.

Hope it's clear.
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Re: If # represents one of the operations +,- and *, is a # [#permalink]

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20 Sep 2010, 03:09
Okay.. I read the question wrong...
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Re: If # represents one of the operations +,- and *, is a # [#permalink]

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20 Sep 2010, 19:10
(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).

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Re: If # represents one of the operations +,- and *, is a # [#permalink]

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21 Sep 2010, 10:55
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.

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Re: If # represents one of the operations +,- and *, is a # [#permalink]

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03 Jun 2015, 08:54
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]

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03 Jun 2015, 08:58
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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Re: If # represents one of the operations +,- and *, is a # [#permalink]

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03 Jun 2015, 09:07
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, 09:07
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