It is currently 22 Nov 2017, 02:58

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x and y are positive integers such that y is a multiple of 5 and 3x

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

5 KUDOS received
Director
Director
User avatar
B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 564

Kudos [?]: 2930 [5], given: 220

Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)
If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 14 Jun 2016, 15:38
5
This post received
KUDOS
40
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (01:21) correct 29% (01:33) wrong based on 1114 sessions

HideShow timer Statistics

If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question
[Reveal] Spoiler: OA

_________________

Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

Kudos [?]: 2930 [5], given: 220

Expert Post
Top Contributor
3 KUDOS received
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1850

Kudos [?]: 2621 [3], given: 362

Location: Canada
Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 14 Jun 2016, 15:57
3
This post received
KUDOS
Expert's post
Top Contributor
11
This post was
BOOKMARKED
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question


If y is a multiple of 5, then we know that y = 5k for some integer k.
So, let's take 3x + 4y = 200 and replace y with 5k to get: 3x + 4(5k) = 200
Simplify to get: 3x + 20k = 200 (where k is some integer)
Subtract 20k from both sides to get: 3x = 200 - 20k
Divide both sides by 3 to get: x = (200 - 20k)/3
Now factor the numerator to get: x = (20)(10 - k)/3
Since x must be an integer, and since 20/3 is not an integer, it must be the case that (10 - k)/3 evaluates to be some integer.
In other words, x = (20)(some integer)
So, x must be a multiple of 20. However, 20 is not one of the answer choices.
Then again, we can rewrite x to get: x = (2)(10)(some integer)
This tells us that x must also be a multiple of 10

Answer:
[Reveal] Spoiler:
E


Here are two videos that cover the skills needed to answer this question:


and

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2621 [3], given: 362

Expert Post
16 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7745

Kudos [?]: 17843 [16], given: 235

Location: Pune, India
Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 14 Jun 2016, 22:12
16
This post received
KUDOS
Expert's post
14
This post was
BOOKMARKED
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question


If y is a multiple of 5, 4y must be a multiple of 5 too.

3x = 200 - 4y = Multiple of 5 - Multiple of 5 = Multiple of 5

Since 3 is not a multiple of 5, x MUST be a multiple of 5.

Also, 4y is even. So 3x = Even - Even = Even
Since 3 is not even, x must be even.

Hence x must be a multiple of 10.

Answer (E)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17843 [16], given: 235

1 KUDOS received
Manager
Manager
avatar
S
Joined: 04 Apr 2015
Posts: 133

Kudos [?]: -24 [1], given: 47

CAT Tests
Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 14 Jun 2016, 22:25
1
This post received
KUDOS
its given y is multiple of 5 therefore 4y is even and will end in zero as even multiple of 5 ends in zero(zero at units place)
now equation 3x + 4y =200, as we know 4y ends in zero (zero at units place ) we need to add something that ends in zero (zero at units place) to get to 200,3x can only end in zero if x is multiple of 10

Kudos [?]: -24 [1], given: 47

6 KUDOS received
Intern
Intern
User avatar
Joined: 23 Nov 2016
Posts: 1

Kudos [?]: 6 [6], given: 15

GRE 1: 325 Q164 V161
Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 28 Nov 2016, 10:32
6
This post received
KUDOS
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?
A) 3
B) 6
C) 7
D) 8
E) 10

----------------------
I drowned in these numbers and failed on my first attempt at this question, but I've got it now.

The most simple approach I can think of is to plug in values of y that are multiples of 5.

1) Plug in 5, 10, 15, & 20.

2) These yield equations of:
3x = 180
3x= 160
3x = 140
3x = 120

3) Of our answer choices, (E) 10 is the only # that divides evenly in all these situations, therefore it must be our answer.

Kudos [?]: 6 [6], given: 15

Expert Post
4 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7745

Kudos [?]: 17843 [4], given: 235

Location: Pune, India
Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 28 Nov 2016, 19:45
4
This post received
KUDOS
Expert's post
VeritasPrepKarishma wrote:
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question


If y is a multiple of 5, 4y must be a multiple of 5 too.

3x = 200 - 4y = Multiple of 5 - Multiple of 5 = Multiple of 5

Since 3 is not a multiple of 5, x MUST be a multiple of 5.

Also, 4y is even. So 3x = Even - Even = Even
Since 3 is not even, x must be even.

Hence x must be a multiple of 10.

Answer (E)


Responding to a pm:
Quote:
If 3x has to be even, why can't the answer be B oder D, since 3*6 = even and 3*8 = even?


You are given that y is a multiple of 5. So 4y is a multiple of 10.

Hence 3x = 200 - 4y = Multiple of 10 - Multiple of 10

So 3x would be a multiple of 10 too.

So the answer cannot be (B) or (D)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17843 [4], given: 235

Expert Post
5 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1684

Kudos [?]: 910 [5], given: 5

Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 02 Dec 2016, 10:45
5
This post received
KUDOS
Expert's post
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10


We are given that x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200. We need to determine which answer choice MUST be a multiple of x.

Because y is a multiple of 5, we can represent y as 5k, in which k is an integer, and we have:

3x + 4(5k) = 200

3x + 20k = 200

Since the sum of 3x and 20k is 200 (or a number that has a units digit of zero), and since 20k has a units digit of zero, 3x must also contain a units digit of zero. The only way for 3x to contain a units digit of zero is if it’s multiplied by a multiple of 10. Thus, x must be a multiple of 10.

Answer: E
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 910 [5], given: 5

4 KUDOS received
Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3102

Kudos [?]: 1116 [4], given: 327

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 02 Dec 2016, 11:18
4
This post received
KUDOS
2
This post was
BOOKMARKED
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question


Plug in values and check -

Let y = 5 ; 3x + 4y = 200

So, 3x + 20 = 200

Or, x = 60 ( Options C & D rejected , Left with options A, B & E )


Let y = 20 ; 3x + 4y = 200

So, 3x + 80 = 200

Or, x = 40 ( Options A &B rejected , Left with option E )

Hence, answer will be optin (E)

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1116 [4], given: 327

Intern
Intern
avatar
B
Joined: 28 Aug 2016
Posts: 2

Kudos [?]: 5 [0], given: 296

Location: India
Concentration: General Management, Technology
WE: Engineering (Computer Software)
Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 25 Mar 2017, 06:08
We know: 1. x and y are positive integers
2. y is a multiple of 5
3. 3x + 4y = 200

3x + 4y = 200

=> 3x = 200 - 4y

It's known that if we add or subtract multiples of N, the result is a multiple of N. Here, both 200 and 4y are multiple of 10(20 actually). So 3x is a multiple of 10.
And therefore x is a multiple of 10.

Regards,
GJ

Kudos [?]: 5 [0], given: 296

Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 838

Kudos [?]: 268 [0], given: 15

Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 25 Mar 2017, 09:40
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10


let y=35
x=20
only E works

Kudos [?]: 268 [0], given: 15

Intern
Intern
avatar
B
Joined: 30 Mar 2017
Posts: 4

Kudos [?]: 0 [0], given: 3

Location: United States
GMAT 1: 650 Q39 V41
GPA: 3.9
Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 28 Apr 2017, 10:49
I approached this in a different style I think than the other posters - is this way correct as well?

First, 200 factors down to \(2^3 * 5^2\)

Looking at the information we know that from the equation \(3x + 4y\), where y is a multiple of 5, we have the factors of \(2^2\) (from the 4), 3, and 5. Given this, we can then determine that we need one more factor of both 2 and 5. E - 10 is the only answer choice that provides those two factors.

Kudos [?]: 0 [0], given: 3

Intern
Intern
User avatar
B
Joined: 07 May 2015
Posts: 23

Kudos [?]: 4 [0], given: 51

Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 01 May 2017, 10:54
GMATPrepNow wrote:
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question


If y is a multiple of 5, then we know that y = 5k for some integer k.
So, let's take 3x + 4y = 200 and replace y with 5k to get: 3x + 4(5k) = 200
Simplify to get: 3x + 20k = 200 (where k is some integer)
Subtract 20k from both sides to get: 3x = 200 - 20k
Divide both sides by 3 to get: x = (200 - 20k)/3
Now factor the numerator to get: x = (20)(10 - k)/3
Since x must be an integer, and since 20/3 is not an integer, it must be the case that (10 - k)/3 evaluates to be some integer.
In other words, x = (20)(some integer)
So, x must be a multiple of 20. However, 20 is not one of the answer choices.
Then again, we can rewrite x to get: x = (2)(10)(some integer)
This tells us that x must also be a multiple of 10

Answer:
[Reveal] Spoiler:
E



Here we say that (10-k)/3 = (some-int) => (10-k) = 3*(some-int)
and x = 20*(10-k)/3
x = 20*3*(some-int)
so x is a multiple of 3 as well.

Where am I going wrong?

Kudos [?]: 4 [0], given: 51

Manager
Manager
avatar
B
Joined: 29 Jun 2017
Posts: 156

Kudos [?]: 10 [0], given: 364

Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 30 Jun 2017, 02:46
this is hard

3x+4y=200
y=(200-3x)/4

= 50-3x/4

because y is divisible by 5, 3x/5 is divisible by 5

3x/4=5a
x=20a/3

a must divisible by 3, so that x can be interger, so x= multiple of 20

x divisible by 10

hard one

Kudos [?]: 10 [0], given: 364

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 788

Kudos [?]: 43 [0], given: 274

Premium Member CAT Tests
If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 07 Sep 2017, 23:50
x and y are positive integers

This is the most important information that will help us find the answer.

y=5k (k is a positive constant)

3x+4*5k= 200
3x+20k= 200
x= (200-20k)/3

x= 20(10-k)/3

As x is an integer, the above equation has to be an integer. As 20 is not divisible by 3, (10-k) must be divisible by 3 to make RHS an integer.

Looking at the options, E works.
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Kudos [?]: 43 [0], given: 274

Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 838

Kudos [?]: 268 [0], given: 15

If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 09 Sep 2017, 10:01
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question


3x+4y=200➡3x=4(50-y)
because y is a multiple of 5, and 4 is even,
4(50-y) will always have a units digit of 0
10
E

Kudos [?]: 268 [0], given: 15

Manager
Manager
User avatar
G
Joined: 07 Jun 2017
Posts: 176

Kudos [?]: 90 [0], given: 59

Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 14 Sep 2017, 23:07
3x + 4y = 200
y is a multiple of 5 so go for the trail and error
1. 3x+4*5 = 200
3x = 180, it is mutiple of both 3 and 10
2. 3x+4*(5*2) = 200
3x = 160, 3 can be eliminated so answer should be 10
E
_________________

Regards,
Naveen
email: nkmungila@gmail.com
Please press kudos if you like this post

Kudos [?]: 90 [0], given: 59

Manager
Manager
User avatar
B
Status: love the club...
Joined: 24 Mar 2015
Posts: 199

Kudos [?]: 17 [0], given: 451

Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 22 Sep 2017, 09:45
VeritasPrepKarishma wrote:
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question


If y is a multiple of 5, 4y must be a multiple of 5 too.

3x = 200 - 4y = Multiple of 5 - Multiple of 5 = Multiple of 5

Since 3 is not a multiple of 5, x MUST be a multiple of 5.

Also, 4y is even. So 3x = Even - Even = Even
Since 3 is not even, x must be even.

Hence x must be a multiple of 10.

Answer (E)



hi mam

The way I approached the problem is as under:

3x + 4y = 200
Now, as, y = 5k

3x + 20k = 200

x = 20(10 - k)/3
Now, (10 - k) must be 3n

So, x = 60n

Thus answer choice E must be true, and other choices could be true ....

please say to me whether it is okay...

thanks in advance, mam

Kudos [?]: 17 [0], given: 451

Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 838

Kudos [?]: 268 [0], given: 15

If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 22 Sep 2017, 10:23
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question


3x/4+y=50
x=either 20 or 40
10
E

Kudos [?]: 268 [0], given: 15

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7745

Kudos [?]: 17843 [1], given: 235

Location: Pune, India
Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 26 Sep 2017, 01:37
1
This post received
KUDOS
Expert's post
gmatcracker2017 wrote:
VeritasPrepKarishma wrote:
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question


If y is a multiple of 5, 4y must be a multiple of 5 too.

3x = 200 - 4y = Multiple of 5 - Multiple of 5 = Multiple of 5

Since 3 is not a multiple of 5, x MUST be a multiple of 5.

Also, 4y is even. So 3x = Even - Even = Even
Since 3 is not even, x must be even.

Hence x must be a multiple of 10.

Answer (E)



hi mam

The way I approached the problem is as under:

3x + 4y = 200
Now, as, y = 5k

3x + 20k = 200

x = 20(10 - k)/3
Now, (10 - k) must be 3n

So, x = 60n

Thus answer choice E must be true, and other choices could be true ....

please say to me whether it is okay...

thanks in advance, mam


Yes, perfectly fine.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17843 [1], given: 235

Manager
Manager
User avatar
S
Joined: 01 Dec 2016
Posts: 118

Kudos [?]: 13 [0], given: 32

Location: Cote d'Ivoire
Concentration: Finance, Entrepreneurship
WE: Investment Banking (Investment Banking)
GMAT ToolKit User
Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

Show Tags

New post 22 Oct 2017, 17:59
I think the trick here is to use unit digit concept.
3X+20K=200 means 3X must have 0 as unit digit.
from the answer choices, only E works.

Thanks
_________________

What was previously considered impossible is now obvious reality.
In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them

Kudos [?]: 13 [0], given: 32

Re: If x and y are positive integers such that y is a multiple of 5 and 3x   [#permalink] 22 Oct 2017, 17:59
Display posts from previous: Sort by

If x and y are positive integers such that y is a multiple of 5 and 3x

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.