If @ represents one of the operations +, -, and x, is k@(l+m : GMAT Data Sufficiency (DS)
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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 [#permalink]

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14 Dec 2012, 06:13
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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, 06:27
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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 $$k-(l+m)=(k-l)+(k-m)$$ for all numbers k, l,and m. Sufficient.

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

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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, 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.

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

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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.

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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01 Aug 2013, 09:31
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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, 01:35
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Qoofi wrote:

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

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16 Nov 2013, 22:24
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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 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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27 Nov 2014, 00:08
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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, 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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17 Aug 2015, 22:16
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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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18 Aug 2015, 20:38
Hi nuttyaks,

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

gmat-data-sufficiency-ds-141/

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

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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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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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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.

You must type in the question completely with answer choices provided. Do not post pictures in lieu of the question.

List of all OG quant questions solved: the-official-guide-quantitative-question-directory-143450.html

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

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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.

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

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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.

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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Re: If represents one of the operations +, -, and x, is k(l+m   [#permalink] 08 Jul 2016, 06:17
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