GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jan 2019, 13:29

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.

# If x and y are different positive integers, which of the following COU

Author Message
TAGS:

### Hide Tags

CEO
Joined: 11 Sep 2015
Posts: 3344
If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

28 Oct 2018, 14:08
1
Top Contributor
2
00:00

Difficulty:

85% (hard)

Question Stats:

23% (01:41) correct 77% (03:44) wrong based on 70 sessions

### HideShow timer Statistics

If x and y are different positive integers, which of the following COULD be true:
i) When x is divided by y, the remainder is x
ii) When 2x is divided by y, the remainder is x
iii) When x+y is divided by x , the remainder is x-y

A) i only
B) i & ii only
C) i & iii only
D) ii & iii only
E) i, ii & iii

ASIDE: Many Integer Properties questions can be solved by identifying values that satisfy some given conditions. This question is intended to strengthen that skill.

_________________

Test confidently with gmatprepnow.com

Director
Joined: 31 Oct 2013
Posts: 955
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

Updated on: 28 Oct 2018, 17:23
GMATPrepNow wrote:
If x and y are different positive integers, which of the following COULD be true:
i) When x is divided by y, the remainder is x
ii) When 2x is divided by y, the remainder is x
iii) When x+y is divided by x , the remainder is x-y

A) i only
B) i & ii only
C) i & iii only
D) ii & iii only
E) i, ii & iii

ASIDE: Many Integer Properties questions can be solved by identifying values that satisfy some given conditions. This question is intended to strengthen that skill.

First of all this question requires could be true answer.

i) could be.

This statement indicates that x has to be less than y.

x = 3

y = 4

3/4............3 is remainder here. Here the definition of remainder is needed.

So could be true.

ii) could be

iii) x = 2 and y = 1

2 + 1 / 2 = 2 *1 + 1

Remainder is 1

x - y

= 2 - 1 = 1.

Could be .

Actually there is no relationship between x and y is given. Thus any of them could be true in different ways.

Originally posted by selim on 28 Oct 2018, 15:21.
Last edited by selim on 28 Oct 2018, 17:23, edited 1 time in total.
CEO
Joined: 11 Sep 2015
Posts: 3344
Re: If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

28 Oct 2018, 15:56
Top Contributor
Hi selim,

There's an error in one of your calculations.

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com

Director
Joined: 31 Oct 2013
Posts: 955
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

28 Oct 2018, 16:06
GMATPrepNow wrote:
Hi selim,

There's an error in one of your calculations.

Cheers,
Brent

got it . thanks .
Senior Manager
Joined: 07 Jul 2012
Posts: 377
Location: India
Concentration: Finance, Accounting
GPA: 3.5
Re: If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

28 Oct 2018, 21:28
All the options are possible as there is no exact relationship between integer x and y. So E is the answer.
_________________

Kindly hit kudos if my post helps!

Math Expert
Joined: 02 Aug 2009
Posts: 7209
If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

28 Oct 2018, 22:14
GMATPrepNow wrote:
If x and y are different positive integers, which of the following COULD be true:
i) When x is divided by y, the remainder is x
ii) When 2x is divided by y, the remainder is x
iii) When x+y is divided by x , the remainder is x-y

A) i only
B) i & ii only
C) i & iii only
D) ii & iii only
E) i, ii & iii

ASIDE: Many Integer Properties questions can be solved by identifying values that satisfy some given conditions. This question is intended to strengthen that skill.

Great question !! Brent..
let us see the question

i) When x is divided by y, the remainder is x
Whenever y>x, it will be true
example y=7 x=3, remainder is x or 3..possible

ii) When 2x is divided by y, the remainder is x
so let us make the equation..
$$2x=ny+x......ny=x$$, so x is multiple of y and remainder will always be 0... NOT possible

iii) When x+y is divided by x , the remainder is x-y
when x=y is divided by x, remainder will be y
Now can this y be equal to x-y....y=x-y... x=2y
so possible.. let y = 5, x=10.. remainder = 10-5=5=x-y....
so possible

(i) and (iii)

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 02 Dec 2015
Posts: 3
Re: If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

28 Oct 2018, 23:55
chetan2u wrote:
GMATPrepNow wrote:
If x and y are different positive integers, which of the following COULD be true:
i) When x is divided by y, the remainder is x
ii) When 2x is divided by y, the remainder is x
iii) When x+y is divided by x , the remainder is x-y

A) i only
B) i & ii only
C) i & iii only
D) ii & iii only
E) i, ii & iii

ASIDE: Many Integer Properties questions can be solved by identifying values that satisfy some given conditions. This question is intended to strengthen that skill.

Great question !! Brent..
let us see the question

i) When x is divided by y, the remainder is x
Whenever y>x, it will be true
example y=7 x=3, remainder is x or 3..possible

ii) When 2x is divided by y, the remainder is x
so let us make the equation..
$$2x=ny+x......ny=x$$, so x is multiple of y and remainder will always be 0... NOT possible

iii) When x+y is divided by x , the remainder is x-y
when x=y is divided by x, remainder will be y
Now can this y be equal to x-y....y=x-y... x=2y
so possible.. let y = 5, x=10.. remainder = 10-5=5=x-y....
so possible

(i) and (iii)

C

Hi Chetan, could you spare a few minutes to explain iii again? Thx
Manager
Joined: 29 May 2017
Posts: 130
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

29 Oct 2018, 03:26
Great question !! Brent..
let us see the question

i) When x is divided by y, the remainder is x
Whenever y>x, it will be true
example y=7 x=3, remainder is x or 3..possible

ii) When 2x is divided by y, the remainder is x
so let us make the equation..
$$2x=ny+x......ny=x$$, so x is multiple of y and remainder will always be 0... NOT possible

iii) When x+y is divided by x , the remainder is x-y
when x=y is divided by x, remainder will be y
Now can this y be equal to x-y....y=x-y... x=2y
so possible.. let y = 5, x=10.. remainder = 10-5=5=x-y....
so possible

(i) and (iii)

C[/quote]

Hi chetan...

I dont understand your algebra for the III. can you elaborate please?

regards
Manager
Joined: 28 Jun 2018
Posts: 72
Re: If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

29 Oct 2018, 04:54
Is zero considered a positive integer? Because then X=0 would hold true for II, no?
CEO
Joined: 11 Sep 2015
Posts: 3344
Re: If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

29 Oct 2018, 05:33
Top Contributor
hibobotamuss wrote:
Is zero considered a positive integer? Because then X=0 would hold true for II, no?

Zero is neither positive no negative.

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com

CEO
Joined: 11 Sep 2015
Posts: 3344
If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

29 Oct 2018, 06:27
Top Contributor
varun4s wrote:
All the options are possible as there is no exact relationship between integer x and y. So E is the answer.

If all of the statements are true, then for each statement, you should be able to specify values for x and y that satisfy the statement.

Hint: This is not possible for each statement (i.e., the correct answer is not E)

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com

Manager
Joined: 29 May 2017
Posts: 130
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

29 Oct 2018, 15:27
Algebraic approach to (iii)

x+y divided by x gives remainder of x-y

x+y-->px + x -y
2y-->px, where p is a positive integer. this means:
2y can be: x, 2x, 3x, 4x, ,,, and so on

2y eq x means y is x/2,,,,picking x as 4 gives y as 2 and thus
6/4 gives a remainder of 2 which is 4-2--> x-y

therefore, possible
Intern
Joined: 19 Aug 2018
Posts: 28
Re: If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

29 Oct 2018, 17:00
chetan2u wrote:
GMATPrepNow wrote:
If x and y are different positive integers, which of the following COULD be true:
i) When x is divided by y, the remainder is x
ii) When 2x is divided by y, the remainder is x
iii) When x+y is divided by x , the remainder is x-y

A) i only
B) i & ii only
C) i & iii only
D) ii & iii only
E) i, ii & iii

ASIDE: Many Integer Properties questions can be solved by identifying values that satisfy some given conditions. This question is intended to strengthen that skill.

Great question !! Brent..
let us see the question

i) When x is divided by y, the remainder is x
Whenever y>x, it will be true
example y=7 x=3, remainder is x or 3..possible

ii) When 2x is divided by y, the remainder is x
so let us make the equation..
$$2x=ny+x......ny=x$$, so x is multiple of y and remainder will always be 0... NOT possible

iii) When x+y is divided by x , the remainder is x-y
when x=y is divided by x, remainder will be y
Now can this y be equal to x-y....y=x-y... x=2y
so possible.. let y = 5, x=10.. remainder = 10-5=5=x-y....
so possible

(i) and (iii)

C

Excuse me, how dividing 3/7 can give you a remainder of 3?
CEO
Joined: 11 Sep 2015
Posts: 3344
Re: If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

30 Oct 2018, 12:59
1
Top Contributor
jorgetomas9 wrote:
Excuse me, how dividing 3/7 can give you a remainder of 3?

A few examples to set the mood:
25 divided by 8 equals 3 with remainder 1. From this result, we can write (3)(8) + 1 = 25
17 divided by 3 equals 5 with remainder 2. From this result, we can write (5)(3) + 2 = 17
64 divided by 10 equals 6 with remainder 4. From this result, we can write (6)(10) + 4 = 64
And now.....

3 divided by 7 equals 0 with remainder 3. From this result, we can write (0)(7) + 3 = 3

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com

CEO
Joined: 11 Sep 2015
Posts: 3344
Re: If x and y are different positive integers, which of the following COU  [#permalink]

### Show Tags

30 Oct 2018, 13:23
Top Contributor
1
GMATPrepNow wrote:
If x and y are different positive integers, which of the following COULD be true:
i) When x is divided by y, the remainder is x
ii) When 2x is divided by y, the remainder is x
iii) When x+y is divided by x , the remainder is x-y

A) i only
B) i & ii only
C) i & iii only
D) ii & iii only
E) i, ii & iii

i) When x is divided by y, the remainder is x
This occurs any time x < y
For example, if x = 5 and y = 7, then statement i becomes: When 5 is divided by 7, the remainder is 5
So true!

-----------------------------------------------------
ii) When 2x is divided by y, the remainder is x
Nice rule: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, from statement ii, we can say: some possible values of 2x are: x, x + y, x + 2y, x + 3y, . . . etc
Let's examine the first option: 2x = x. Solve to get x = 0, but we're told x is POSITIVE No good.

Check the second option: 2x = x + y. Solve to get x = y. This means the remainder is y (aka x), but the remainder CANNOT be greater than the divisor. See the rule below:

When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0

Check the third option: 2x = x + 2y. Solve to get x = 2y.
This means the remainder = 2y, which means the remainder is greater than the divisor (see rule above). No good.

In fact, we can see that, with all of the possible values of 2x, the remainder will be greater than the divisor.
So, statement ii is NOT true.

Scan the answer choices....eliminate B and E
-----------------------------------------------------
iii) When x+y is divided by x , the remainder is x-y
Some possible values of x+y are: (x-y), (x-y)+x, (x-y)+2x, (x-y)+3x, . . . etc
Let's examine the first option: x+y = x-y
Solve to get y = 0. No good.

Check the second option: x+y = (x-y)+x
Simplify: x+y = 2x - y
Solve to get: x = 2y

So, one possible case is: x = 6 and y = 3
Statement iii becomes: When (6 + 3) is divided by 6, the remainder is 3
So true!
------------------------------

RELATED VIDEO FROM OUR COURSE

_________________

Test confidently with gmatprepnow.com

Re: If x and y are different positive integers, which of the following COU &nbs [#permalink] 30 Oct 2018, 13:23
Display posts from previous: Sort by