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If 1@1 = 1, is −2@−2 = 1 ? (1) 1@-1 = 1 (2) 0@0 = 0

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Bunuel
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If 1@1 = 1, is −2@−2 = 1 ? (1) 1@-1 = 1 (2) 0@0 = 0 [#permalink] New post   06 Apr 2020, 04:04
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If \(1@1= 1\), is \(-2@-2= 1\)?


(1) \(-1@-1=1\)

(2) \(0@0=0\)


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If 1@1 = 1, is −2@−2 = 1 ? (1) 1@-1 = 1 (2) 0@0 = 0 [#permalink] New post   06 Apr 2020, 04:16
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Bunuel wrote:
If \(1@1= 1\), is \(-2@-2= 1\)?


(1) \(-1@-1=1\)

(2) \(0@0=0\)



Given:
\(1@1= 1\); so \(@\) can be multiplication or division.

statement 1:
\(-1@-1=1\)
\(@\) can be multiplication or division.
\(-2*-2= 1\) (No)
\(\frac{-2}{-2}= 1\) (Yes)
not sufficient

statement 2:
\(0@0=0\)
\(@\) can be addition, subtraction or multiplication.
constraint: \(@\) can only be multiplication or division, so \(@\) is multiplication.
\(-2*-2= 1\) (No)
sufficient

Ans: B
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If 1@1 = 1, is −2@−2 = 1 ? (1) 1@-1 = 1 (2) 0@0 = 0 [#permalink] New post   06 Apr 2020, 07:17
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2nd statement alone is sufficient
1@1=1, it means @ = division OR multiplication.
-2@-2=1 , it is only possible when @= division.

Now find whether is Division or not ?


(1) −1@−1=1

@= multiplication or division

Not sufficient

(2) 0@0=0

@= multiplication, subtraction and addition. Except division, every other thing is possible.
We can't divide 0 with 0

Sufficient.

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Re: If 1@1 = 1, is −2@−2 = 1 ? (1) 1@-1 = 1 (2) 0@0 = 0 [#permalink] New post   06 Apr 2020, 08:26
\(1@1= 1\)
can be division or multiplication ;
#1
\(-1@-1=1\)
can be division or multiplication ;
we get yes and no to our target is \(-2@-2= 1\)
#2
\(0@0=0\)
it can be addition, subtraction or multiplication
so \(-2@-2= 1\) always NO
; sufficient
IMO B

Bunuel wrote:
If \(1@1= 1\), is \(-2@-2= 1\)?


(1) \(-1@-1=1\)

(2) \(0@0=0\)


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Re: If 1@1 = 1, is −2@−2 = 1 ? (1) 1@-1 = 1 (2) 0@0 = 0 [#permalink] New post   08 May 2020, 13:29
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Why is everyone assuming that @ represents a single operation? Based on the prompt, couldn't x@y = x*y +100x - 100y for example?

Would the problem normally state that @ represents a single operation?
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Re: If 1@1 = 1, is −2@−2 = 1 ? (1) 1@-1 = 1 (2) 0@0 = 0 [#permalink] New post   19 Sep 2021, 05:24
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Bunuel: We need to add following to the question. "@ represents one of the operations +, -, and *"

can be anything otherwise.

Example
a@b = a + b - \(\frac{ab}{2}\)
Bunuel wrote:
If \(1@1= 1\), is \(-2@-2= 1\)?


(1) \(-1@-1=1\)

(2) \(0@0=0\)


Project DS Butler Data Sufficiency (DS3)


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Re: If 1@1 = 1, is 2@2 = 1 ? (1) 1@-1 = 1 (2) 0@0 = 0 [#permalink] New post   26 Jun 2023, 17:25
Yes, otherwise the correct alternative should be E.

BrushMyQuant wrote:
Bunuel: We need to add following to the question. "@ represents one of the operations +, -, and *"

can be anything otherwise.

Example
a@b = a + b - \(\frac{ab}{2}\)
Bunuel wrote:
If \(1@1= 1\), is \(-2@-2= 1\)?


(1) \(-1@-1=1\)

(2) \(0@0=0\)


Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here



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Re: If 1@1 = 1, is 2@2 = 1 ? (1) 1@-1 = 1 (2) 0@0 = 0 [#permalink]
26 Jun 2023, 17:25
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