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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, 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



Mods, please to DS section...posted by mistake in PS - apologies
[Reveal] Spoiler: OA

Last edited by zisis on 19 Sep 2010, 16:09, edited 1 time in total.
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Re: operations (?) [#permalink] New post 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.

So answer choice D
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Re: operations (?) [#permalink] New post 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.

Hence answer is D
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Re: operations (?) [#permalink] New post 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.

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: operations (?) [#permalink] New post 20 Sep 2010, 00:14
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: operations (?) [#permalink] New post 20 Sep 2010, 03:09
Okay.. I read the question wrong...
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Re: operations (?) [#permalink] New post 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).

Ans D
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Re: operations (?) [#permalink] New post 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.

(D)
Re: operations (?)   [#permalink] 21 Sep 2010, 10:55
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