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If @ represents one of the operations +, , and x, is k@(l+m [#permalink]
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14 Dec 2012, 07:13
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If @ represents one of the operations +, , and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m? (1) k@1 is not equal to 1@k for some numbers k. (2) @ represents subtraction.
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Re: If @ represents one of the operations +, , and x, is k@(l+m [#permalink]
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14 Dec 2012, 07:27
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If @ represents one of the operations +, , and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m?(1) k@1 is not equal to 1@k for some numbers k. @ is neither addition (as \(k+1=1+k\)) nor multiplication (as \(k*1=1*k\)), thus @ represents subtraction. Knowing that we can determine whether \(k(l+m)=(kl)+(km)\) for all numbers k, l,and m. Sufficient. (2) @ represents subtraction. The same here. Sufficient. Answer: D.
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Re: If @ represents one of the operations +, , and x, is k@(l+m [#permalink]
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16 Dec 2012, 12:04
Bunuel wrote: If @ represents one of the operations +, , and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m?
(1) k@1 is not equal to 1@k for some numbers k. @ is neither addition (as \(k+1=1+k\)) nor multiplication (as \(k*1=1*k\)), thus @ represents subtraction. Knowing that we can determine whether \(k(l+m)=(kl)+(km)\) for all numbers k, l,and m. Sufficient.
(2) @ represents subtraction. The same here. Sufficient.
Answer: D. Dear Bunnel, I would like to understand the above question first.. If we take the @ as subtraction from statement 1 and 2 then the equation stands as \(klm=2klm\), which is not equal in both the side. I was wondering whether the question asks about the operation of the @ sign, which makes the equation of k@(l+m)=(k@l)+(k@m) okay from both end. Thanks



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Re: If @ represents one of the operations +, , and x, is k@(l+m [#permalink]
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17 Dec 2012, 00:07
Drik wrote: Bunuel wrote: If @ represents one of the operations +, , and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m?
(1) k@1 is not equal to 1@k for some numbers k. @ is neither addition (as \(k+1=1+k\)) nor multiplication (as \(k*1=1*k\)), thus @ represents subtraction. Knowing that we can determine whether \(k(l+m)=(kl)+(km)\) for all numbers k, l,and m. Sufficient.
(2) @ represents subtraction. The same here. Sufficient.
Answer: D. Dear Bunnel, I would like to understand the above question first.. If we take the @ as subtraction from statement 1 and 2 then the equation stands as \(klm=2klm\), which is not equal in both the side. I was wondering whether the question asks about the operation of the @ sign, which makes the equation of k@(l+m)=(k@l)+(k@m) okay from both end. Thanks No, the question asks: "is k@(l+m)=(k@l)+(k@m) for ALL numbers k, l,and m", where @ represents one of the operations +, , and x.
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Re: If @ represents one of the operations +, , and x, is k@(l+m [#permalink]
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01 Aug 2013, 10:31
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The answer could Option E If we take k=l=m=0 & k=1, l=2, m=3, from statement 1 we will get both "yes" or "no". Similarly Statement 2 also gives the same result. The question doesn't specify anything about k,l,m Could you explain?
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Re: If @ represents one of the operations +, , and x, is k@(l+m [#permalink]
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09 Aug 2013, 02:35
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Qoofi wrote: The answer could Option E
If we take k=l=m=0 & k=1, l=2, m=3, from statement 1 we will get both "yes" or "no". Similarly Statement 2 also gives the same result.
The question doesn't specify anything about k,l,m
Could you explain? From (1) we got that @ is subtraction. So, the question becomes: is k(l+m)=(kl)+(km) for ALL NUMBERS k, l,and m? This equation holds if k=0. Therefore the equation does NOT hold true for ALL NUMBERS (it holds if k=0). The same applies to the second statement. Similar questions to practice: ifrepresentsoneoftheoperationsandxisklm144138.htmlifdenotesoneoftwoarithmeticoperationsadditionor50178.htmlifthesymbolrepresentseitheradditionormultiplication104600.htmliftheoperationisoneofthefourarithmeticoperations101283.htmliftheoperationisoneofthefourarithmeticoperations93966.htmlifdenotesoneofthefourarithmeticoperationsaddition105472.htmlthesymbolrepresentsoneofthefourarithmeticoperation107575.htmlifthesymbolrepresentseitheradditionsubtraction101741.htmlifthesymbolrepresentseitheradditionormultiplication104600.htmlifrepresentsoneoftheoperationsandisa101337.htmltheoperationxnforallpositiveintegersgreaterthan99064.htmlHope it helps.
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Re: If @ represents one of the operations +, , and x, is k@(l+m [#permalink]
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12 Oct 2013, 12:20
The way I approached this question was basically "is @ multiplication"?
That is the only symbol that will make the equation in the question stem equal.
The first statement tells us indeed that @ is not multiplication or even addition. The only other option is subtraction...so we have our answer and it is not multiplication. Sufficient.
The second statement tells us @ is subtraction. Ok so we know it is not multiplication. Sufficient.



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Re: If @ represents one of the operations +, , and x, is k@(l+m [#permalink]
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16 Nov 2013, 21:37
The way i see the question, k o (l +m) = (k o l) + (k o m) is only true where o is x(multiplication) for o = + and o = , it's not true.
1. k o 1 not equal to 1 o k. This statement is true only when o is subtraction (). But we know that the above statement is valid only for multiplication. So this option is SUFFICIENT. 2. o represents subtraction . This statement is SUFFICIENT , as we know that the question is valid only for multiplication.



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Re: If @ represents one of the operations +, , and x, is k@(l+m [#permalink]
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16 Nov 2013, 23:24
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If @ represents one of the operations +, , and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m?
(1) k@1 is not equal to 1@k for some numbers k. (2) @ represents subtraction.
The answer to this question could be a yes or a no. If we can somehow say for sure  yes or no, then we know the option is sufficient. 2) clearly says @ is subtractn. Therefore, the equation in the question is NOT true for all nos. k,l,m. SUFFICIENT.
1)k@1 != 1@k implies that @ s not x . This could be + since if k is neg, k+1 is not equal to 1(k) This could be  since k1 != 1k. substituting in the question, for +: is k+(l+m)=(k+l) + (k+m). NO. for  : is k(lm)= (kl) + (km) . NO.
There the equation is NOT true for all nos. SUFFICIENT.
D it is!



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Re: If represents one of the operations +, , and x, is k(l+m [#permalink]
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13 Jul 2015, 09:07
St1 : @ is substraction
if we take K=5, l=3, m=2 Then 0 is not equal to 5....as per question stem answer is NO.
If we take K=0,l=1,m= 2
Then 3= 3....so answer is YES
Since we get yes and no both....shouldn't this statement be insufficient ?
Where am I doing the mistake ?



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If represents one of the operations +, , and x, is k(l+m [#permalink]
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23 Aug 2015, 00:23
This is a tricky question that troubles a lot of students.
Based on statement 1, the symbol {o} has to be equal to subtraction, because in the case of addition and multiplication the operation k{o}1 is equal to 1{o}k for all all numbers. So the conclusion from statement 1 is that the symbol stands for only subtraction.
Now if we go back to the original question in the main stem, which asks if Does k{o}(l+m) = (k{o}l) + (k{o}m) for all numbers k, l, and m? meaning is the answer to this question a definite Yes or No. If the {o} stands for subtraction then the condition k{l+m} is not equal to (kl) + (km) for all numbers. It may hold true for k=l=m=0, but we need to answer the question if it holds true for all possible values of k, l, and m, and the answer to that is a definite No, which makes it sufficient.
Cheers, Dabral



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