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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 \(k-(l+m)=(k-l)+(k-m)\) for all numbers k, l,and m. Sufficient.

(2) @ represents subtraction. The same here. Sufficient.

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 \(k-(l+m)=(k-l)+(k-m)\) 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 \(k-l-m=2k-l-m\), 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.

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 \(k-(l+m)=(k-l)+(k-m)\) 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 \(k-l-m=2k-l-m\), 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.
_________________

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)=(k-l)+(k-m) 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).

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.

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.

Re: If @ represents one of the operations +, -, and x, is k@(l+m [#permalink]

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16 Nov 2013, 23:24

1

This post received KUDOS

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 k-1 != 1-k. substituting in the question, for +: is k+(l+m)=(k+l) + (k+m). NO. for - : is k-(l-m)= (k-l) + (k-m) . NO.

There the equation is NOT true for all nos. SUFFICIENT.

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 (k-l) + (k-m) 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.

Re: If @ represents one of the operations +, -, and x, is k@(l+m [#permalink]

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04 Oct 2017, 05:58

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