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

Question

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.

Bunuel · Accepted Answer

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. Similar questions to practice: if-represents-one-of-the-operations-and-x-is-k-l-m-144138.html if-denotes-one-of-two-arithmetic-operations-addition-or-50178.html if-the-symbol-represents-either-addition-or-multiplication-104600.html if-the-operation-is-one-of-the-four-arithmetic-operations-101283.html if-the-operation-is-one-of-the-four-arithmetic-operations-93966.html if-denotes-one-of-the-four-arithmetic-operations-addition-105472.html the-symbol-represents-one-of-the-four-arithmetic-operation-107575.html if-the-symbol-represents-either-addition-subtraction-101741.html if-the-symbol-represents-either-addition-or-multiplication-104600.html if-represents-one-of-the-operations-and-is-a-101337.html the-operation-x-n-for-all-positive-integers-greater-than-99064.html Hope it helps.

Bunuel · Answer

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.

Drik · Answer

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

Bunuel · Answer

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.

Qoofi · Answer

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?

runningguy · Answer

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.

jyotis999 · Answer

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.

surbhi87 · Answer

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!

kshitij89 · Answer

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 ?

dabral · Answer

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.

Cheers,
Dabral

CrackverbalGMAT · Answer

Solution:

St(1):-k@1 is not equal to 1@k for some numbers k.

Commutative property is not satisfied

The operator represents "-"

The rephrased question stem is is k-(l+m)=(k-l)+(k-m) ?

Only at k=0 the question holds good and thus answer is a NO for all numbers

St(2):-Same logic (Sufficient)

(option d)

Devmitra Sen
GMAT SME

Kimberly77 · Answer

Thanks  CrackverbalGMAT  for great explanation. What is the purpose of testing k=0 here and how would we know the requirement to test k=0?
Thanks for your time in advanced.

GMATinsight · Answer

Question: is k@(l+m)=(k@l)+(k@m)?

Let's first think when and how is the given relationship possible. We can easily deeduce that if  SIGN  is replaced with multiplication sign then it's possible 
If  is  addition or subtraction or division then it's not possible for all values of k, l and m

So, Question REPHRASED: Is @ sigh same as Multiplication sign?

Statement 1  : k@1 ≠ 1@k 
i.e. @  is  not addition and not multiplication which clearly mean that answer of the question is DEFINITELY NO as  is  not same as multiplication hence
 SUFFICIENT

Statement 2  : @ represents subtraction.
which clearly mean that answer of the question is DEFINITELY NO as  is  not same as multiplication hence
 SUFFICIENT

Answer: Option D

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

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