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# If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a

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If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  29 Nov 2010, 21:09
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If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for all numbers a, b, and c?

(1) 1#c = c#1
(2) # represents +
[Reveal] Spoiler: OA

Last edited by JenniferClopton on 30 Nov 2010, 06:55, edited 1 time in total.
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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  29 Nov 2010, 21:21
I initially chose D. Working quickly, I reasoned that both + and * would satisfy the distributive equation for all a, b, and c. But, when you write it out, this is obviously not the case...

(a+b)+c ≠ (a+c) + (b+c)

(a+b)*c = (a*c) + (b*c)
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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  29 Nov 2010, 22:41
From Statement (1)

# could be

# = + ( for any c )

# = - ( for c = 1)

# = * ( for any c )

# = / ( for c = 1, -1 )

Therefore, # could be + or *

+ doesn't satisfy the equation (a+b)#c = (a#b) + (b#c)

It will satisfy only if b =0

* also doesn't satisfy the equation (a+b)#c = (a#b) + (b#c)

It will satisfy only if a = 0 or b = c

From Statement (2)

# = +

Even after combining the (1) and (2), we can't say that equation will be satisfied for all the values of a,b, and c.

Did I miss something?
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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  29 Nov 2010, 22:55
From both the options we can not say that equation will be satisfied for all the values of a,b, and c...
BUT we can say that equation will NOT be satisfied for all the values of a,b, and c.

IMO D
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PS: Correct me if I am wrong.

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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  29 Nov 2010, 23:16
Jennifer is this question write or it is (a+b)#c = (a#c) + (b#c)

Because if it is (a+b)#c = (a#b) + (b#c) as u have mentioned in the question then..
Statement 1 does not satisfy the condition in any way. Therefore (a+b)#c = (a#b) + (b#c) does not stand and this statement gives us the answer that condition is not possible.

Statement 2 also provide that (a+b)#c = (a#b) + (b#c) does not stand and this statement again gives us answer that condition is not possible.

And therefore answer will be "D"

But OA is "B" ... and for that the condition should be (a+b)#c = (a#c) + (b#c) and not as u mentioned in the question.
In this Statement 1 will satisfy in * and / conditions and will not in + and - conditions
But statement 2 will satisfy the condition and the answer will be "B"

Plz recheck ur question.
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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  29 Nov 2010, 23:49
JenniferClopton wrote:
From Grockit:

If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for all numbers a, b, and c?

1. 1#c = c#1

2. # represents +

I think the correct question ought to be as above

Statement 1 : 1#c=c#1 ... means # is either + or * ... If it is +, the answer is "no" ... If it is *, the answer is "yes"
Statement 2 : Sufficient to answer "no"

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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  29 Nov 2010, 23:50
Expert's post
JenniferClopton wrote:
From Grockit:

If # represents +, -, *, or /, then does (a+b)#c = (a#b) + (b#c) for all numbers a, b, and c?

1. 1#c = c#1

2. # represents +

It should be: (a+b)#c = (a#c) + (b#c) instead of (a+b)#c = (a#b) + (b#c)

(1) 1#c = c#1 --> # can be either addition or multiplication: $$1*c=c*1$$ and $$1+c=c+1$$ (true for ALL numbers of a, b, and c). Now, if it's addition then we'll have: $$a+b+c\neq{a+c+b+c }$$ (so it's doesn't hold true for ALL numbers a, b, and c, it holds true when c=0) and if it's multiplication then we'll have: $$ac+bc={ac+bc }$$ (so it's holds true for ALL numbers of a, b, and c). Not sufficient.

(2) # represents + --> if # represents addition then given equation doesn't hold true for all numbers a, b, and c, it holds true when c=0. So we have the answer No to the question. Sufficient.

Similar questions:
operations-101337.html
jeff-sackmann-extreme-challenge-q-105352.html

Hope it helps.
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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  30 Nov 2010, 06:57
Bunuel wrote:
It should be: (a+b)#c = (a#c) + (b#c) instead of (a+b)#c = (a#b) + (b#c)

I have corrected the error in the initial post. Apologies. This question has fooled me twice!
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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  30 Nov 2010, 07:05
BTW WHT'S THE CORRECT ANSWER TO THIS QUESTION I CHOSE

OA-(b)
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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  30 Nov 2010, 07:43
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Guys consider giving me KUDOS..... i have corrected a question. come on be sporty...
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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  08 Jan 2014, 18:32
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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  11 Feb 2015, 11:44
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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  11 Feb 2015, 13:00
Expert's post
Hi All,

This is an example of a "symbolism" question - it involves a "made up" math symbol which you'll be asked to use to perform a basic set of calculations. You'll likely see 1 such question on the GMAT and it almost always involves some type of arithmetic or algebra.

We're told that the symbol # is one of 4 possible math functions: add, subtract, multiply, or divide.

We're asked if (A+B)#C = (A#C) + (B#C) for all numbers A, B, and C? This is a YES/NO question. The answer will depend on the actual 'meaning' of the symbol.

In these types of questions, it might be tempting to do a lot of pre-work before dealing with the two Facts. However, much of that work is NOT necessary, so in this case it would be a waste of time.

Fact 1: 1#C = C#1

This means that the symbol can be 1 of 2 possibilities: either 'add' or 'multiply'

Let's TEST VALUES to see what happens in each case:

IF.....
A=1
B=2
C=3

(A+B)#C = (A#C) + (B#C) =
(1+2)+3 = (1+3) + (2+3)?
6 = 4 + 5?
The answer to the question is NO.

IF...# means 'multiply'
(A+B)#C = (A#C) + (B#C) =
(1+2)(3) = (1)(3) + (2)(3)?
9 = 3 + 6?
The answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: # represents "+"

Since we know the symbol can only represent one symbol, then we CAN answer the question.
Fact 2 is SUFFICIENT.

[Reveal] Spoiler:
B

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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a [#permalink]  13 Feb 2015, 03:42
Expert's post
JenniferClopton wrote:
If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for all numbers a, b, and c?

(1) 1#c = c#1
(2) # represents +

Check other Symbols Representing Arithmetic Operation questions in our Special Questions Directory.
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Re: If # represents +, -, *, or /, then does (a+b)#c = (a#c) + (b#c) for a   [#permalink] 13 Feb 2015, 03:42
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