The operation # is defined by x # y=x*y for all nonzero numbers x and

Question

The operation # is defined by x # y=x*y for all nonzero numbers x and y, if x and y have the same sign. The operation # is defined by x # y=x/y for all nonzero numbers x and y, if x and y have different sign. If A and B are none zero numbers, which of the following about A and B must be true?

I A#1=A

II A#B=B#A

III (A#B)#A=A#(A#B)

(A) I only

(B) II only

(C) III only

(D) I and II

(E) I and III

I A#1=A

II A#B=B#A

III (A#B)#A=A#(A#B)

(A) I only

(B) II only

(C) III only

(D) I and II

(E) I and III

nishthagupta · Answer

check for both parts (same sign and different signs)

nightvision · Answer

I A#1=A

if same sign, A#1 = A = RHS
IF DIFFERENT SIGN, A#1 = A/1 = RHS

CORRECT

II A#B=B#A
IF SAME SIGN, A#B = AB
B#A = BA

IF DIFFERENT SIGN, A#B = A/B
B#A = B/A

CAN BE FALSE IF A&B ARE DIFFERENT NUMBER -> B IS WRONG

SIMILARLY CHECK FOR III

KarishmaB · Answer

If A and B have same signs, A#B = A*B
If A and B have diff signs, A#B = A/B

I A#1=A

II A#B=B#A

III (A#B)#A=A#(A#B)

It's easy to see that if A#B = A*B, then all 3 will hold.

Check for division assuming A and B have diff signs. Say A is positive and B is negative.

I A#1=A
A/1 = A 
Holds

II A#B=B#A
A/B is not equal to B/A
Does not hold

III (A#B)#A=A#(A#B)
(A/B) / A = A / (A/B)
1/B = B
Does not hold

Answer (A)

ninja_in_progress · Answer

if same sign, A#1 = A
IF DIFFERENT SIGN, A#1 = -A/1 = -A

Hence it is not equal. Why have we ignored the different signs in our calculation?

Bunuel · Answer

Knowing that A is negative does not mean that we should change it to -A. It stays as A; it just stands for a negative number.

The operation # is defined by x # y=x*y for all nonzero numbers x and

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The operation # is defined by x # y=x*y for all nonzero numbers x and

Prep Toolkit

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