If the symbol § represents one of the following operations:

Question

If the symbol § represents one of the following operations: addition, subtraction or multiplication, and x≠0, then what is the value of (x§2)§x?

(1) x=5
(2) (−1)§(−2)≠(−2)§(−1)

Hello guys, I can't understand how the answer to this question could be the one indicated.
It would be great if someone would explain me how does it work.

Bunuel · Accepted Answer

If the symbol § represents one of the following operations: addition, subtraction or multiplication, and x≠0, then what is the value of (x§2)§x?

(1) x=5. We need to know what § represents.

(2) (−1)§(−2)≠(−2)§(−1). § is neither addition nor multiplication. Thus it's subtraction: (x§2)§x = (x-2)-x=-2. Sufficient.

Answer: B.

Bunuel · Answer

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Naina1 · Answer

Hi mattycen

1) is definitely insufficient because depending upon what the symbol denotes, the value would change.

2) -a * -b -> this would always be equal to -b * -a
 -a + -b -> this equals -a -b or -b + -a
 the only operation here is subtraction that could change the value of the given expression.
So, using this we can calculate the value of (x§2)§x

BrushMyQuant · Answer

Please move this to DS from PS. Thank you

ENGRTOMBA2018 · Answer

Done. Thankyou for the information.

azamaka · Answer

x can be negative in that case answer B is not right one. Do u agree with that?

Bunuel · Answer

No, that's not right.

From (2) we know that § represents subtraction. We need to find the value of (x§2)§x, thus since § represents subtraction, the value of (x-2)-x. x there cancels out and we get that (x-2)-x=-2. Therefore we get that (x§2)§x = (x-2)-x=-2 irrespective of the value of x, positive or negative.

Hope it's clear.

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If the symbol § represents one of the following operations:

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