 It is currently 13 Jul 2020, 08:59 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # The operation [symbol] is deﬁned for all integers x a  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 12080
Followers: 256

Kudos [?]: 3014 , given: 11279

The operation [symbol] is deﬁned for all integers x a [#permalink]
Expert's post 00:00

Question Stats: 54% (01:26) correct 45% (01:05) wrong based on 91 sessions
The operation $$\otimes$$ is deﬁned for all integers x and y as $$x \otimes y = xy - y$$. If x and y are positive integers, which of the following CANNOT be zero?

A) $$x \otimes y$$

B) $$y \otimes x$$

C) $$(x-1)\otimes y$$

D) $$(x+1) \otimes y$$

E) $$x \otimes (y-1)$$

Practice Questions
Question: 22
Page: 463
Difficulty: medium
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Last edited by Carcass on 29 Jan 2020, 18:13, edited 2 times in total.
Updated Founder  Joined: 18 Apr 2015
Posts: 12080
Followers: 256

Kudos [?]: 3014  , given: 11279

Re: The operation * is deﬁned for all integers x and y as x * [#permalink]
2
KUDOS
Expert's post
Solution

Note Our symbol can be $$*$$ or . It does not matter, it is just a placeholder

The question stem says to us that X and Y are positive integers and that the symbol is defined for all integers . So, the best way to tackle the question is picking numbers

X=1 and Y=2

Scanning and substituting in all the answer choices you can reach the correct answer. For D : our (x+1) is = in to our equation to $$XY$$ so we do have that $$1*2=2$$. Then, $$X*Y=XY-Y$$ following that ($$2+1)-2=1$$.

The correct answer is $$D$$

PS: substitute the values in the other answer choices and you will get zero or not. We are searching an answer that CANNOT be zero
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. GRE Instructor Joined: 10 Apr 2015
Posts: 3535
Followers: 133

Kudos [?]: 4009  , given: 65

Re: The operation * is deﬁned for all integers x and y as x * [#permalink]
5
KUDOS
Expert's post
Carcass wrote:
The operation * is deﬁned for all integers x and y as x * y = xy − y. If x and  y are positive integers, which of the following CANNOT be zero?

A) X*Y

B) Y*X

C) (X-1)*Y

D) (X+1)*Y

E) X*(Y-1)

Let's take the formula x * y = xy − y, and rewrite is as x * y = y(x − 1)
Now let's check each answer choice (BEGINNING WITH E, since the test-makers like to place the correct answer
for these questions near the end, since most test-takers will check the answers from A to E.)

E) X*(Y-1)
Apply the formula to get: (Y-1)(X-1)
Can this expression ever equal 0?
Sure, if Y = 1 and X = 1, then (Y-1)(X-1) = (1-1)(1-1) = 0
ELIMINATE E

D) (X+1)*Y
Apply the formula to get: (Y)(X+1-1)
Simplify to get (Y)(X)
Can this expression ever equal 0?
NO.
If X and  Y are positive integers, then (Y)(X) can NEVER equal zero

[Reveal] Spoiler:
D

_________________

Brent Hanneson – Creator of greenlighttestprep.com Intern Joined: 20 Sep 2018
Posts: 14
Followers: 0

Kudos [?]: 1 , given: 0

Re: The operation * is deﬁned for all integers x and y as x * [#permalink] Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 10

Kudos [?]: 166  , given: 4

Re: The operation * is deﬁned for all integers x and y as x * [#permalink]
1
KUDOS
Expert's post
The operation * is deﬁned for all integers x and y as $$x * y = xy - y$$. If x and y are positive integers, which of the following CANNOT be zero?

A) $$X*Y$$......XY-Y=0.....Y(X-1)=0.....$$Y\neq{0}$$ but X can be 1... possible

B) $$Y*X$$......XY-X=0.....X(Y-1)=0.....$$X\neq{0}$$ but Y can be 1... possible

C) $$(X-1)*Y$$......(X-1)Y-Y=Y(X-1-1)=Y(X-2)=0.....$$Y\neq{0}$$ but X can be 2... possible

D) $$(X+1)*Y$$......(X+1)Y-Y=Y(X+1-1)=XY=0.....both X and Y are positive,so $$XY\neq{0}$$.... Not possible

E) $$X*(Y-1)$$......X(Y-1)-(Y-1)=(Y-1)(X-1)=0.....any one or both of Y and X can be 1... possible

D
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 10

Kudos [?]: 166 , given: 4

Re: The operation * is deﬁned for all integers x and y as x * [#permalink]
Expert's post
Reetika1990 wrote:

So x*(y-1)=x(y-1)-(y-1)..
Now let x =2 and y =1..2(1-1)-(1-1)=0-0=0
Or x can be anything positove and y =1 ans is 0
Also when y is anything positive and x=1..
x(y-1)-(y-1)=1*(y-1)-(y-1)=(y-1)-(y-1)=0..

So E is possible
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Re: The operation * is deﬁned for all integers x and y as x *   [#permalink] 27 Oct 2018, 03:00
Display posts from previous: Sort by

# The operation [symbol] is deﬁned for all integers x a  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.