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If @ represents one of the operations +, -, and x, is k@(l+m

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

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New post 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.

Thanks
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New post 16 Dec 2012, 23:07
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 \(k-(l+m)=(k-l)+(k-m)\) 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.
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Re: If @ represents one of the operations +, -, and x, is k@(l+m [#permalink]

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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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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).

The same applies to the second statement.

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

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

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New post 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.
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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 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.

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

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New post 13 Jul 2015, 08:07
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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New post 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.
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Last edited by Engr2012 on 23 Aug 2015, 04:18, edited 2 times in total.
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Re: If represents one of the operations +, -, and x, is k(l+m)=(kl)+(k [#permalink]

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New post 18 Aug 2015, 20:38
Hi nuttyaks,

You'll likely get a much bigger response if you post your question in the DS Forum:

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Also, when you post it, you should physically type out the question (not post a screen-grab; that tends to be frowned-upon).

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New post 21 Aug 2015, 22:50
Thanks for the information.
Going forward I'll post them according to the rules listed :) :)
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Re: If represents one of the operations +, -, and x, is k(l+m)=(kl)+(k [#permalink]

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New post 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.

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

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

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New post 08 Jul 2016, 01:31
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.



From both statement 1 and statment 2 we will get K=0 that means that this k@(l+m)=(k@l)+(k@m) is not true for all numbers. How come D be the solution it should be E?
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New post 08 Jul 2016, 06:17
crunchboss 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.



From both statement 1 and statment 2 we will get K=0 that means that this k@(l+m)=(k@l)+(k@m) is not true for all numbers. How come D be the solution it should be E?


Please read the whole thread: if-represents-one-of-the-operations-and-x-is-k-l-m-144138.html#p1254935
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Re: If represents one of the operations +, -, and x, is k(l+m   [#permalink] 08 Jul 2016, 06:17
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