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If & represents one of the operations +,  and x. Is (a&b) + [#permalink]
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25 Nov 2010, 01:40
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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 2abc = abc, 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?
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Re: If & represents one of the operations +,  and x. Is (a&b) + [#permalink]
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25 Nov 2010, 02:29
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This post received KUDOS
stmnt1: $ is  ==> LHS = ab + ac = 2abc RHS = abc ==> 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?



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Re: If & represents one of the operations +,  and x. Is (a&b) + [#permalink]
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25 Nov 2010, 02:56
but if a = 0 then LHS = RHS in both (1) and (2), so it does not stand true for "all numbers"



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Re: If & represents one of the operations +,  and x. Is (a&b) + [#permalink]
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25 Nov 2010, 03:05
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 2abc = abc, 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 \(2abc=abc\), 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. 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.
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Re: If & represents one of the operations +,  and x. Is (a&b) + [#permalink]
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25 Nov 2010, 03:35
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]
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31 Dec 2010, 11:26
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



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Re: If & represents one of the operations +,  and x. Is (a&b) + [#permalink]
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03 Jul 2014, 05:25
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 2abc = abc, 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 \(2abc=abc\), 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. 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. 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]
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06 Dec 2017, 23:26
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 2abc = abc, 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 = (ab) + (ac) = 2abc and RHS = a  (b+c) = abc. Now obviously 2abc is NOT equal to abc 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




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