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The operation # is defined to be multiplication. Which of th

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The operation # is defined to be multiplication. Which of th

by Max@Math Revolution » Tue May 29, 2018 1:32 am

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[GMAT math practice question]

The operation # is defined to be multiplication. Which of the following must be true?

â… . x#1=x
â…¡. x#0=0
â…¢. x#y=y#x

A. â…  only
B. â…¢ only
C. â…¡ only
D. â…  and â…¡ only
E. â… ,â…¡ and â…¢
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by GMATGuruNY » Tue May 29, 2018 2:48 am
Max@Math Revolution wrote:[GMAT math practice question]

The operation # is defined to be multiplication. Which of the following must be true?

â… . x#1=x
â…¡. x#0=0
â…¢. x#y=y#x

A. â…  only
B. â…¢ only
C. â…¡ only
D. â…  and â…¡ only
E. â… ,â…¡ and â…¢
â… . x#1=x
If we replace # with multiplication, we get:
x*1 = x
x = x.
Since the resulting equation is valid, Statement I must be true.
Eliminate B and C, which do not include Statement I.

â…¢. x#y=y#x
If we replace # with multiplication, we get:
x*y = y*x
xy = yx.
Since the resulting equation is valid, Statement III must be true.
Eliminate A and D, which do not include Statement III.

The correct answer is E.
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by Jeff@TargetTestPrep » Wed May 30, 2018 4:19 pm
Max@Math Revolution wrote:[GMAT math practice question]

The operation # is defined to be multiplication. Which of the following must be true?

â… . x#1=x
â…¡. x#0=0
â…¢. x#y=y#x

A. â…  only
B. â…¢ only
C. â…¡ only
D. â…  and â…¡ only
E. â… ,â…¡ and â…¢
Since 1 times any number is that number, I is true.

Since 0 times any number is zero, II is true.

Since multiplication is commutative, III is true.

Answer: E

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by Max@Math Revolution » Thu May 31, 2018 3:25 am
=>

If # is the multiplication operation, then we must have x#1 = x, x#0 = 0 and x#y = y#x.

Therefore, E is the answer.
Answer: E
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