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

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Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
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gmat1011 wrote:
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.

C/right Jeff Sackmann. Just posting it here for educational purposes.

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?

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

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.
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Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
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.
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Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
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
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Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
Bunuel wrote:
gmat1011 wrote:
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.

C/right Jeff Sackmann. Just posting it here for educational purposes.

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?

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

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.

Check Arithmetic Operation Functions Questions in Special Questions Directory.
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Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
gmat1011 wrote:
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?

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.

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Re: If & represents one of the operations +, - and x. Is (a&b) + [#permalink]
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