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Re: If @ represents one of the operations +, -, and x, is k@(l+m [#permalink]
14 Dec 2012, 06:27
2
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Expert's post
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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]
16 Dec 2012, 11:04
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.
Re: If @ represents one of the operations +, -, and x, is k@(l+m [#permalink]
16 Dec 2012, 23:07
Expert's post
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 \(k-(l+m)=(k-l)+(k-m)\) 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. _________________
Re: If @ represents one of the operations +, -, and x, is k@(l+m [#permalink]
09 Aug 2013, 01:35
Expert's post
4
This post was BOOKMARKED
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)=(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]
12 Oct 2013, 11:20
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]
16 Nov 2013, 20:37
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]
16 Nov 2013, 22:24
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.
Re: If @ represents one of the operations +, -, and x, is k@(l+m [#permalink]
27 Nov 2014, 00:08
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If represents one of the operations +, -, and x, is k(l+m [#permalink]
17 Aug 2015, 22:16
Hi Guys,
Please correct me if I'm wrong, but this seems to be a wrong answer for the below question -
Refer the attachment.
I think the answer should be E as the equation has to be true for all numbers x,y, and z. x,y and z considered non-zero give the answer as NO for a "subtraction" sign. x,y and z ,all considered zero give the answer as YES for the same "subtraction" sign.
Attachments
File comment: This is a question.
GMAT Test Prep Wrong Answer.PNG [ 99.24 KiB | Viewed 1662 times ]
Last edited by Engr2012 on 23 Aug 2015, 04:18, edited 2 times in total.
Re: If represents one of the operations +, -, and x, is k(l+m)=(kl)+(k [#permalink]
22 Aug 2015, 23:23
Hi nuttyaks,
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.
If represents one of the operations +, -, and x, is k(l+m [#permalink]
23 Aug 2015, 04:06
nuttyaks wrote:
Hi Guys,
Please correct me if I'm wrong, but this seems to be a wrong answer for the below question -
Refer the attachment.
I think the answer should be E as the equation has to be true for all numbers x,y, and z. x,y and z considered non-zero give the answer as NO for a "subtraction" sign. x,y and z ,all considered zero give the answer as YES for the same "subtraction" sign.
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