If & represents one of the operations +, - and x. Is (a&b) +

Question

If & represents one of the operations +, - and x. Is (a&b) + (a&c) = a&(b + c) for all numbers a, b, and c ?

(1) & represents subtraction. 
(2) m&2 is not equal to 2&m for some numbers m.

Don't get how it can be D. Shouldn't it be E? in 2a-b-c = a-b-c, a can be 0 when there would in fact be a "Yes" answer, while it would also be possible to get "No" with other values?

muralimba · Answer

stmnt1: $ is -
==> LHS = a-b + a-c = 2a-b-c
 RHS = a-b-c ==> LHS not = RHS answer to the question is NO..hence, SUFF.

stmnt2:m&2 is not equal to 2&m for some numbers m.
this can happen only when & is - as m+2=2+m and 2*m=m*2
which is again stmnt 1 hence SUFF.

answer D

Regards,
Murali.
kudos?

gmat1011 · Answer

but if a = 0 then LHS = RHS in both (1) and (2), so it does not stand true for "all numbers"

Bunuel · Answer

The point here is that the question asks whether  (a@b)+(a@c)=a@(b+c)  is true  FOR ALL NUMBERS a, b, and c ?

(1)  @  represents subtraction --> the question becomes is  2a-b-c=a-b-c , or is  a=0 ? So  (a@b)+(a@c)=a@(b+c)  is NOT true for all numbers a, b, and c (so the answer to the question is NO), for this expression to be true  a  must equal to zero (so not for all values of  a ). Sufficient.

(2)  m@2
eq{2@}  -->  @  represents subtraction (as it can not be addition or multiplication), so we have the the same info as above. Sufficient.

Answer: D.

Alternately you can see that  (a@b)+(a@c)=a@(b+c)  to be true  FOR ALL NUMBERS a, b, and c  then  @  must represent multiplication as only for multiplication it's true for all numbers:  ab+ac=ab+ac . So the question basically ask whether  @  represents multiplication, both (1) and (2) give answer No toth is question.

Hope it's clear.

gmat1011 · Answer

yes - thanks Bunuel and Murali - +1 to both...

for some reason i was misinterpreting the expression "all numbers".. this makes sense - the equation is not valid for all values of a,b,c so both are in fact sufficient. thanks.

rojans · Answer

Statement 1- tells us exact nature of sign( subtraction). therefore,sufficient
Statement 2- 2@m not equal to m@2 
 take the values m=6,5. and solve and we get what the mean of sign. sufficient
 so, Answer is D

Bunuel · Answer

Check  Arithmetic Operation Functions Questions  in  Special Questions Directory .

amanvermagmat · Answer

Is (a&b) + (a&c) = a&(b + c) for all numbers a, b, and c ?

(1) if & represents subtraction, then LHS = (a-b) + (a-c) = 2a-b-c and RHS = a - (b+c) = a-b-c. Now obviously 2a-b-c is NOT equal to a-b-c for all numbers a, b, c. So we get our definite answer as NO for the question stem. Sufficient.

(2) m&2 is NOT equal to 2&m. Now if & is '+', then m+2 = 2+m, for all values of m. So & cannot be '+'. If & is 'x', then also mx2 = 2xm, for all values of m. So & cannot be 'x'. Thus & can only represent subtraction '-'. In which case it becomes same as first statement. Sufficient.

Hence  D answer

bumpbot · Answer

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If & represents one of the operations +, - and x. Is (a&b) +

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