Operator puzzle

for ease of edit i will refer the mentioned operator as 'O'
to satisfy the relation
(6 O 2) O 4=6 O (2 O 4) 'O' has to be either addition or multiplication

now from statement 1 we get
3 O 2>3--this is possible only when 'O' is either addition or mutiplication.hence sufficient

from statement 2
3 O 1=3..this is possible when '0' is either multiplication or division--insuff

Ans is A

(6@2)@4=6@(2@4)
this would be true if,
(A) @ is either + or X (since minus and division wont solve the equation)

statement1: 3@2>3
3+2=5>3 true
3 X 2=6>3 true
3-2=1>3 false
3/2=1.5>3 false

hence @ is either + or X. hence sufficient for (A)


statement2: 3@1=3
this means @ can be X or division..
hence we cant answer (A)

hence A

But the question asks "If the operation TRIANGLE is one of the four arithmetic operations".
From Statement (1) we can select either multiplication or addition, but only Statement (2) in combination with statement (1) would further narrow down to the answer "multiplication". The question says, TRIANGLE is one of the four operators..

ronsom wrote:But the question asks "If the operation TRIANGLE is one of the four arithmetic operations".
From Statement (1) we can select either multiplication or addition, but only Statement (2) in combination with statement (1) would further narrow down to the answer "multiplication". The question says, TRIANGLE is one of the four operators..

it is correct that only combining both we can definitely say the nature of the operator but the question is not 'what is the operator' it is 'using the operator does the given equation hold true'

statement 1 is sufficient to say that the given relation is true we don't need the second statement for it.
Hope it clarifies why it should be A instead of C.

ronsom wrote:But the question asks "If the operation TRIANGLE is one of the four arithmetic operations".
From Statement (1) we can select either multiplication or addition, but only Statement (2) in combination with statement (1) would further narrow down to the answer "multiplication". The question says, TRIANGLE is one of the four operators..

the question never asked about the symbol,
it is asking whether (6@2)@4=6@(2@4)???????
s1) is therfore sufficient as with bth multiplication and addition we get an answer

ronsom wrote:But the question asks "If the operation TRIANGLE is one of the four arithmetic operations".
From Statement (1) we can select either multiplication or addition, but only Statement (2) in combination with statement (1) would further narrow down to the answer "multiplication". The question says, TRIANGLE is one of the four operators..

Especially in yes/no data sufficiency questions, you should always simplify or rephrase the stem.

The question clause asks whether the left hand side (LHS) of the equation equals the right hand side (RHS). We know that the triange is one of the four listed operations. For which of these four operations will the LHS equal the RHS?

Well, since the order in which you add or multiply is not important, the LHS will equal the RHS if the triangle represents either of addition or multiplication.

As you point out, the inequality in (1) is satisfied only if the triangle represents either of addition or multiplication. Thus, regardless of whether it is addition or multiplication the LHS of the equation in the question will definitely equal the RHS. (It matters not that addition and multiplication would lead to different values).

As an aside, please post DS questions in the DS forum (you've posted this one in the PS forum).

I also agree; A is the answer