Author 
Message 
TAGS:

Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 518
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
14 Jun 2016, 14:38
Question Stats:
75% (01:44) correct 25% (01:56) wrong based on 3187 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
Official Answer and Stats are available only to registered users. Register/ Login.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10105
Location: Pune, India

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
14 Jun 2016, 21:12
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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4843
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
02 Dec 2016, 10:18
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)
_________________




GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4320
Location: Canada

If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
Updated on: 13 Nov 2019, 16:01
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 If y is a multiple of 5, then we know that y = 5k for some integer k. So, let's take 3x + 4 y = 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:
_________________
Test confidently with gmatprepnow.com
Originally posted by GMATPrepNow on 14 Jun 2016, 14:57.
Last edited by GMATPrepNow on 13 Nov 2019, 16:01, edited 1 time in total.



Senior Manager
Joined: 03 Apr 2015
Posts: 251
GPA: 3.59

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
14 Jun 2016, 21:25
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



Intern
Joined: 23 Nov 2016
Posts: 1

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
28 Nov 2016, 09:32
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.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10105
Location: Pune, India

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
28 Nov 2016, 18:45
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) 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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2801

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
02 Dec 2016, 09:45
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
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 28 Aug 2016
Posts: 29
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
25 Mar 2017, 05:08
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



VP
Joined: 07 Dec 2014
Posts: 1235

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
25 Mar 2017, 08:40
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



Intern
Joined: 30 Mar 2017
Posts: 4
Location: United States
GPA: 3.9

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
28 Apr 2017, 09:49
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.



Manager
Joined: 06 May 2015
Posts: 62
Location: India
GPA: 4

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
01 May 2017, 09:54
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 + 4 y = 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: Here we say that (10k)/3 = (someint) => (10k) = 3*(someint) and x = 20*(10k)/3 x = 20*3*(someint) so x is a multiple of 3 as well. Where am I going wrong?



Director
Joined: 29 Jun 2017
Posts: 957

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
30 Jun 2017, 01:46
this is hard
3x+4y=200 y=(2003x)/4
= 503x/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



Director
Joined: 02 Sep 2016
Posts: 633

If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
07 Sep 2017, 22:50
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= (20020k)/3
x= 20(10k)/3
As x is an integer, the above equation has to be an integer. As 20 is not divisible by 3, (10k) must be divisible by 3 to make RHS an integer.
Looking at the options, E works.



VP
Joined: 07 Dec 2014
Posts: 1235

If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
09 Sep 2017, 09:01
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(50y) because y is a multiple of 5, and 4 is even, 4(50y) will always have a units digit of 0 10 E



Manager
Joined: 07 Jun 2017
Posts: 159
Location: India
Concentration: Technology, General Management
GPA: 3.6
WE: Information Technology (Computer Software)

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
14 Sep 2017, 22:07
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



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 260

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
22 Sep 2017, 08:45
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



VP
Joined: 07 Dec 2014
Posts: 1235

If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
22 Sep 2017, 09:23
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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10105
Location: Pune, India

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
26 Sep 2017, 00:37
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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 01 Dec 2016
Posts: 101
Concentration: Finance, Entrepreneurship
GMAT 1: 650 Q47 V34
WE: Investment Banking (Investment Banking)

Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
Show Tags
22 Oct 2017, 16:59
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




Re: If x and y are positive integers such that y is a multiple of 5 and 3x
[#permalink]
22 Oct 2017, 16:59



Go to page
1 2 3
Next
[ 48 posts ]



