It is currently 22 Oct 2017, 20:10

### 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 June
Open Detailed Calendar

# If x and y are integers greater than 1, is x a multiple of y

Author Message
TAGS:

### Hide Tags

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 532

Kudos [?]: 4132 [6], given: 217

Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

29 Jan 2012, 16:21
6
KUDOS
42
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

64% (00:41) correct 36% (00:46) wrong based on 875 sessions

### HideShow timer Statistics

If x and y are integers greater than 1, is x a multiple of y?

(1) 3y^2+7y=x
(2) x^2-x is a multiple of y

[Reveal] Spoiler:
For me its D. Unless someone else thinks otherwise. This is how I solved this:

Statement 1

y is a multiple of 3 and 7

So when y = 2 then x will be 26 and YES x is a multiple of y.
when y = 5 then x will be 110 and YES x is a multiple of y.

Therefore, statement 1 is sufficient to answer this questions.

Statement 2

x^2-x is a multiple of y

x(x-1) is a multiple of y. Sufficient to answer.

Therefore D for me i.e. both statements alone are sufficient to answer this question. Any thoughts guys?
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Last edited by Bunuel on 30 Oct 2012, 01:44, edited 2 times in total.

Kudos [?]: 4132 [6], given: 217

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1377

Kudos [?]: 1681 [29], given: 62

Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: Is x multiple of y? If: 3y^2 + 7y = x? If: x^2-x is mult? [#permalink]

### Show Tags

31 Dec 2012, 21:27
29
KUDOS
5
This post was
BOOKMARKED
x and y are integers > 1. Is x multiple of y?

(1): 3y^2 + 7y = x
(2): x^2 - x is multiple of y

The question is asking whether $$x/y$$ is an integer or not.

Statement 1 can be written as $$y(3y +7)=x$$ or $$3y+7=x/y$$. Since $$y$$ is an integer, therefore 3y+7 must also be an integer. Hence $$x/y$$ will be an integer or x is a multiple of y. Sufficient.

Statement 2 can be written as $$x(x-1)/y$$ is an integer. Notice that we can't deduce that x is a multiple of y because it is quite possible that the product is a multiple of y, but not the individual entities.
ex. 2*3/6 is a mltiple of 6 BUT neither 2 nor 3 is a multiple of 6.
Insufficient.

+1A

_________________

Kudos [?]: 1681 [29], given: 62

Math Expert
Joined: 02 Sep 2009
Posts: 41912

Kudos [?]: 129371 [26], given: 12197

Re: Is x a multiple of y [#permalink]

### Show Tags

29 Jan 2012, 16:31
26
KUDOS
Expert's post
40
This post was
BOOKMARKED
If x and y are integers great than 1, is x a multiple of y?

(1) $$3y^2+7y=x$$ --> $$y(3y+7)=x$$ --> as $$3y+7=integer$$, then $$y*integer=x$$ --> $$x$$ is a multiple of $$y$$. Sufficient.

(2) $$x^2-x$$ is a multiple of $$y$$ --> $$x(x-1)$$ is a multiple of $$y$$ --> $$x$$ can be multiple of $$y$$ ($$x=2$$ and $$y=2$$) OR $$x-1$$ can be multiple of $$y$$ ($$x=3$$ and $$y=2$$) or their product can be multiple of $$y$$ ($$x=3$$ and $$y=6$$). Not sufficient.

Hope it helps.
_________________

Kudos [?]: 129371 [26], given: 12197

Intern
Joined: 21 Apr 2014
Posts: 7

Kudos [?]: 16 [6], given: 1

Re: If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

03 May 2014, 12:26
6
KUDOS
7
This post was
BOOKMARKED

FACTS ESTABLISHED BY STEMS

• $$x$$ is an integer
• $$y$$ is an integer
• $$x > 1$$
• $$y > 1$$

QUESTION TRANSLATED

Since both $$x$$ and $$y$$ are integers the question "is $$x$$ a multiple of $$y$$?" really asks if

$$x = q \cdot y + r$$

where $$q$$ is an integer (the quotient) and $$r$$ is the remainder when you divide $$x$$ by $$y$$ so that $$r = 0$$ which means that

$$x = q \cdot y + 0$$

which implies that

$$x = q \cdot y$$

So the question translates to:

is $$x = q \cdot y$$ when $$x$$, $$q$$ and $$y$$ are all integers, and when $$x>1$$ and $$y > 1$$?

STATEMENT 1

$$3y^2 + 7y = x$$

can be rewritten as

$$y(3y + 7) = x$$

however, from the question stems we know that $$y$$ is an integer, which implies $$3y$$ is an integer and that $$3y+7$$ is also an integer:

$$y \cdot integer = x$$

which can be rewritten as

$$x = y \cdot integer$$ or better yet, as

$$x = integer \cdot y$$

which if you notice is an equation of the form $$x = q \cdot y$$ since $$q$$ is an integer which implies that $$x$$ is indeed a multiple of $$y$$.

Therefore, Statement A is sufficient.

STATEMENT 2

the statement "$$x^2 - x$$ is a multiple of $$y$$" must be rewritten as "$$x (x - 1)$$ is a multiple of $$y$$" which implies that

either $$x$$ is a multiple of $$y$$ or $$x-1$$ is a multiple of $$y$$

the sub-statement $$x$$ is a multiple of $$y$$ implies that $$x = q \cdot y$$ which would answer the question, but we still need to figure out if the second sub-statement answers the question with the same answer as the first sub-statement.

the second sub-statement $$x-1$$ is a multiple of $$y$$ implies that

$$x-1 = q \cdot y$$

which can be rewritten as

$$x = q \cdot y + 1$$

which is an equation of the form $$x = q \cdot y + r$$ when $$r=1$$ which implies that when $$x$$ is divided by $$y$$ we get a remainder of 1, meaning that $$x$$ is NOT a multiple of $$y$$.

Since both sub-statements are contradictory, this means that when $$x^2 - x$$ is a multiple of $$y$$, $$x$$ is not always a multiple of $$y$$. meaning that we cannot determine whether $$x$$ is always a multiple of $$y$$ according to Statement 2 alone.

Therefore, Statement 2 is not sufficient.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Kudos [?]: 16 [6], given: 1

Manager
Joined: 09 Apr 2012
Posts: 63

Kudos [?]: 67 [5], given: 29

Re: If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

05 Sep 2012, 14:17
5
KUDOS
4
This post was
BOOKMARKED
for(2)

x(x-1) is multiple of y.
so either x is divisible by y or x-1 is divisible by y.
if x-1 is divisible by y, then x is not divisble by y.

plug in y=8, x=16--->16*15 is divisible by 8 --> yes x is a multiple of y.
plug in y=8,x=17----> 17*16 is still divisible by 8 --> But x is not a multiple of y.

So insufficient.

Kudos [?]: 67 [5], given: 29

Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 223

Kudos [?]: 62 [0], given: 16

Schools: Johnson '15
Re: If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

18 Jun 2012, 07:07
Hi Bunuel,
Can you please explain this problem. I did not understand the explanation above for Point 2.
Sorry for the inconvenience.
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

Satyameva Jayate - Truth alone triumphs

Kudos [?]: 62 [0], given: 16

Math Expert
Joined: 02 Sep 2009
Posts: 41912

Kudos [?]: 129371 [0], given: 12197

Re: If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

18 Jun 2012, 07:10
harshavmrg wrote:
Hi Bunuel,
Can you please explain this problem. I did not understand the explanation above for Point 2.
Sorry for the inconvenience.

Can you please be a little bit more specific? What exactly didn't you understand in the second statement?
_________________

Kudos [?]: 129371 [0], given: 12197

Intern
Joined: 12 Dec 2011
Posts: 9

Kudos [?]: 24 [0], given: 5

Location: Italy
Concentration: Finance, Entrepreneurship
GMAT Date: 04-09-2013
GPA: 4
WE: Management Consulting (Consulting)
Re: If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

05 Sep 2012, 08:00
Hi Bunuel,
I have not understood the answer to the (2) statement, infact we have that x(x-1) = Y*F (because is a multiple), doesn't it depend on the number F if X is a multiple of y? For example:
If x=2, then y could be either 2 or 1; so the answer would be yes;
If x=3, then y could be either 2 or 3; so the answer would be no;

Kudos [?]: 24 [0], given: 5

Director
Joined: 25 Apr 2012
Posts: 724

Kudos [?]: 850 [0], given: 724

Location: India
GPA: 3.21
Re: Is x multiple of y? If: 3y^2 + 7y = x? If: x^2-x is mult? [#permalink]

### Show Tags

31 Dec 2012, 22:41
x and y are integers > 1. Is x multiple of y?

(1): 3y^2 + 7y = x
(2): x^2 - x is multiple of y

The Questions asks whether x/y is an integer or not.

from St 1 we have 3y^2 +7y=x ---> x/y= 3y+7 if y=2, x=13 and 13/2 is not an integer.
If y=7, then x/y=4 which is an integer.
So St1 alone not sufficient

From St 2 we have x^2-x is multiple of y ----> x(x-1)/y= Integer value
Now we know x-1 and x are consecutive integers

X2-x is even because if x is odd then x2-x (odd-odd)=even and if x is even then x2-x is even. Now x can be odd or even and hence alone not sufficient.

Combining both statement,we get for x/y to be an integer y has to be 7 and x will be have to be multiple of 7.
But we are not sure from above statement so ans should be E.

What is OA??

Thanks
Mridul
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 850 [0], given: 724

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1377

Kudos [?]: 1681 [0], given: 62

Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: Is x multiple of y? If: 3y^2 + 7y = x? If: x^2-x is mult? [#permalink]

### Show Tags

31 Dec 2012, 22:59
mridulparashar1 wrote:
x and y are integers > 1. Is x multiple of y?

(1): 3y^2 + 7y = x
(2): x^2 - x is multiple of y

The Questions asks whether x/y is an integer or not.

from St 1 we have 3y^2 +7y=x ---> x/y= 3y+7 if y=2, x=13 and 13/2 is not an integer.
If y=7, then x/y=4 which is an integer.
So St1 alone not sufficient

From St 2 we have x^2-x is multiple of y ----> x(x-1)/y= Integer value
Now we know x-1 and x are consecutive integers

X2-x is even because if x is odd then x2-x (odd-odd)=even and if x is even then x2-x is even. Now x can be odd or even and hence alone not sufficient.

Combining both statement,we get for x/y to be an integer y has to be 7 and x will be have to be multiple of 7.
But we are not sure from above statement so ans should be E.

What is OA??

Thanks
Mridul

if x/y=3y+7, then taking y as 2 will yield x/y as 13 and not 13/2.
_________________

Kudos [?]: 1681 [0], given: 62

Senior Manager
Joined: 15 Aug 2013
Posts: 302

Kudos [?]: 83 [0], given: 23

Re: If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

18 Sep 2014, 18:36
Bunuel wrote:
If x and y are integers great than 1, is x a multiple of y?

(1) $$3y^2+7y=x$$ --> $$y(3y+7)=x$$ --> as $$3y+7=integer$$, then $$y*integer=x$$ --> $$x$$ is a multiple of $$y$$. Sufficient.

(2) $$x^2-x$$ is a multiple of $$y$$ --> $$x(x-1)$$ is a multiple of $$y$$ --> $$x$$ can be multiple of $$y$$ ($$x=2$$ and $$y=2$$) OR $$x-1$$ can be multiple of $$y$$ ($$x=3$$ and $$y=2$$) or their product can be multiple of $$y$$ ($$x=3$$ and $$y=6$$). Not sufficient.

Hope it helps.

Hi Bunuel,

Two questions:
1) If x = 2 and y = 2, does that mean that x is a multiple of y? I always thought that x needed to be 1 multiple greater, meaning, x=4 and y=2 etc?
2) In situations like these, I usually stumble with either starting off with factoring(like you did above) or some other method. What do you suggest?
3) Lastly, the way I solved statement 1 was -- I saw it as (y)(multiple of y) = x, and the rule states that if i multiply two numbers that are multiples of y, then the result will be a multiple of y. Is that correct to assume?(I know that we can assume that with addition, right?)

Kudos [?]: 83 [0], given: 23

Math Expert
Joined: 02 Sep 2009
Posts: 41912

Kudos [?]: 129371 [0], given: 12197

Re: If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

19 Sep 2014, 02:31
russ9 wrote:
Bunuel wrote:
If x and y are integers great than 1, is x a multiple of y?

(1) $$3y^2+7y=x$$ --> $$y(3y+7)=x$$ --> as $$3y+7=integer$$, then $$y*integer=x$$ --> $$x$$ is a multiple of $$y$$. Sufficient.

(2) $$x^2-x$$ is a multiple of $$y$$ --> $$x(x-1)$$ is a multiple of $$y$$ --> $$x$$ can be multiple of $$y$$ ($$x=2$$ and $$y=2$$) OR $$x-1$$ can be multiple of $$y$$ ($$x=3$$ and $$y=2$$) or their product can be multiple of $$y$$ ($$x=3$$ and $$y=6$$). Not sufficient.

Hope it helps.

Hi Bunuel,

Two questions:
1) If x = 2 and y = 2, does that mean that x is a multiple of y? I always thought that x needed to be 1 multiple greater, meaning, x=4 and y=2 etc?
2) In situations like these, I usually stumble with either starting off with factoring(like you did above) or some other method. What do you suggest?
3) Lastly, the way I solved statement 1 was -- I saw it as (y)(multiple of y) = x, and the rule states that if i multiply two numbers that are multiples of y, then the result will be a multiple of y. Is that correct to assume?(I know that we can assume that with addition, right?)

1. The least multiple of a positive integer is that integer itself. So, the least multiple of 2 is 2.
2. I suggest the way I used.
3. 3y+7 is not necessarily a multiple of y but it does not need to be. y*integer=x implies that x is a multiple of y.
_________________

Kudos [?]: 129371 [0], given: 12197

Manager
Joined: 13 Aug 2015
Posts: 205

Kudos [?]: 68 [0], given: 64

GMAT 1: 710 Q49 V38
GPA: 3.82
WE: Corporate Finance (Retail Banking)
If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

20 Aug 2016, 19:46
x,y are integers>1, is x multiple of y?

x multiple of y is same as x/y=integer

1. 3y^2+7y=x
y(3y+7)=x
dividing both sides by y, we get:
(3y+7)=x/y
x/y=int as question stem says y is integer
statement 1. is sufficient

2. x^2-x is a multiple of y
x(x-1) is a multiple of y
i.e {x(x-1)}/y must be integer
x/y say 4/2 =integer or 4-1/2=3/2 not integer
Thus, statement 2 is insufficient.

Hence, A
_________________

If you like my posts, please give kudos. Help me unlock gmatclub tests.

Kudos [?]: 68 [0], given: 64

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 845 [0], given: 595

Re: If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

21 Aug 2016, 01:59
Awesome Question .
Here we need to prove if x=y*I for some integer I
Statement 1=> x=y[3y+y]=y*I => Sufficient
Statement 2 => x(x-1) is a multiple of y let x=7 x-1=6 and y =6 here clearly the answer is NO
now let y=7 => the answer will be YES
hence Insufficient
Smash that A
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 845 [0], given: 595

Director
Joined: 26 Oct 2016
Posts: 691

Kudos [?]: 180 [0], given: 855

Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

26 Jan 2017, 19:34
Statement 1: x = y(3y + 7) = y*(Some integer)
Therefore, x is a multiple of y

Sufficient

Statement 2: x(x - 1) is a multiple of y.
Therefore, either x or (x - 1) or none of them is multiple of y.

Not sufficient

_________________

Thanks & Regards,
Anaira Mitch

Kudos [?]: 180 [0], given: 855

Intern
Joined: 24 Oct 2015
Posts: 3

Kudos [?]: [0], given: 20

Re: If x and y are integers greater than 1, is x a multiple of y [#permalink]

### Show Tags

16 Oct 2017, 06:13
What if we change the question stem to factors... is B the answer?

If x and y are integers greater than 1, is x a factor of y?

(1) 3y^2+7y=x
(2) x^2-x is a multiple of y

Kudos [?]: [0], given: 20

Re: If x and y are integers greater than 1, is x a multiple of y   [#permalink] 16 Oct 2017, 06:13
Display posts from previous: Sort by