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

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

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?

Ⅰ. x#1=x
Ⅱ. x#0=0
Ⅲ. x#y=y#x

A. Ⅰ only
B. Ⅲ only
C. Ⅱ only
D. Ⅰ and Ⅱ only
E. Ⅰ,Ⅱ and Ⅲ

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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?

Ⅰ. x#1=x
Ⅱ. x#0=0
Ⅲ. x#y=y#x

A. Ⅰ only
B. Ⅲ only
C. Ⅱ only
D. Ⅰ and Ⅱ only
E. Ⅰ,Ⅱ and Ⅲ

Ⅰ. 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.

Ⅲ. 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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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

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?

Ⅰ. x#1=x
Ⅱ. x#0=0
Ⅲ. x#y=y#x

A. Ⅰ only
B. Ⅲ only
C. Ⅱ only
D. Ⅰ and Ⅱ only
E. Ⅰ,Ⅱ and Ⅲ

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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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

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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