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

Question

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 +

JenniferClopton · Answer

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)

LM · Answer

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.

Therefore answer should be "E"

Did I miss something?

vaibhavtripathi · Answer

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

vyassaptarashi · Answer

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.

shrouded1 · Answer

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"

Answer : (b)

Bunuel · Answer

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 eq{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. Answer: B. Similar questions: operations-101337.html addition-or-multiplication-104600.html jeff-sackmann-extreme-challenge-q-105352.html Hope it helps.

JenniferClopton · Answer

I have corrected the error in the initial post. Apologies. This question has fooled me twice!

girindra · Answer

BTW WHT'S THE CORRECT ANSWER TO THIS QUESTION I CHOSE

OA-(b)

vyassaptarashi · Answer

Guys consider giving me KUDOS..... i have corrected a question. come on be sporty...

EMPOWERgmatRichC · Answer

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

# means 'add'
(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.

Final Answer:  B 
GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

Check other  Symbols Representing Arithmetic Operation  questions in our  Special Questions Directory .

bumpbot · Answer

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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

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