Last visit was: 19 Nov 2025, 08:14 It is currently 19 Nov 2025, 08:14
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
 1   2   
555-605 Level|   Algebra|   Multiples and Factors|                        
User avatar
AbdurRakib
User avatar
Joined: 11 May 2014
Last visit: 08 Nov 2025
Posts: 465
Own Kudos:
42,847
 [580]
Given Kudos: 220
Status:I don't stop when I'm Tired,I stop when I'm done
Location: Bangladesh
Concentration: Finance, Leadership
Schools: Wharton '20 Yale '20 Tepper '20
GPA: 2.81
WE:Business Development (Real Estate)
Schools: Wharton '20 Yale '20 Tepper '20
Posts: 465
Kudos: 42,847
 [580]
If x and y are positive integers such that y is a multiple of 5 and 3x 14 Jun 2016, 15:38
48
Kudos
Add Kudos
531
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

77% (01:45) correct 23% (01:59) wrong based on 10142 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,994
 [318]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,994
 [318]
If x and y are positive integers such that y is a multiple of 5 and 3x Updated on: 03 Mar 2025, 00:41
Originally posted by KarishmaB on 14 Jun 2016, 22:12.
Last edited by KarishmaB on 03 Mar 2025, 00:41, edited 2 times in total.
183
Kudos
Add Kudos
135
Bookmarks
Bookmark this Post
AbdurRakib
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
Show more

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)

Check out this discussion on numbers and their factors: https://youtu.be/DxIH8rjhpKY

Method 2:

Given: 3x + 4y = 200
y is a multiple of 5 so let's say y = 5a (where a is an integer)

We get: 3x + 4*5a = 200
3x = 200 - 20a
3x = 20(10 - a)

Now, from where do we get this factor of 20? It has to come from x since 3 does not have 20 as a factor. This means x MUST be a multiple of 20 and hence 10 must be a factor of x.

Nothing can be said about the other options.

Answer (E)
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 18 Jul 2025
Posts: 5,934
Own Kudos:
5,327
 [114]
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,934
Kudos: 5,327
 [114]
If x and y are positive integers such that y is a multiple of 5 and 3x 02 Dec 2016, 11:18
84
Kudos
Add Kudos
30
Bookmarks
Bookmark this Post
AbdurRakib
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
Show more

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)
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,739
Own Kudos:
35,343
 [102]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,739
Kudos: 35,343
 [102]
If x and y are positive integers such that y is a multiple of 5 and 3x Updated on: 13 Nov 2019, 17:01
Originally posted by BrentGMATPrepNow on 14 Jun 2016, 15:57.
Last edited by BrentGMATPrepNow on 13 Nov 2019, 17:01, edited 1 time in total.
63
Kudos
Add Kudos
39
Bookmarks
Bookmark this Post
AbdurRakib
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
Show more

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:
Show Spoiler
E
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,977
Own Kudos:
8,389
 [66]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,977
Kudos: 8,389
 [66]
If x and y are positive integers such that y is a multiple of 5 and 3x 02 Dec 2016, 10:45
49
Kudos
Add Kudos
17
Bookmarks
Bookmark this Post
AbdurRakib
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
Show more

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
General Discussion
User avatar
OC2910
User avatar
Joined: 04 Apr 2015
Last visit: 09 Feb 2023
Posts: 230
Own Kudos:
139
 [18]
Given Kudos: 269
GMAT 1: 650 Q49 V31
GPA: 3.59
Products:
My Reviews
GMAT 1: 650 Q49 V31
Posts: 230
Kudos: 139
 [18]
If x and y are positive integers such that y is a multiple of 5 and 3x 14 Jun 2016, 22:25
16
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
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
User avatar
okaypompeii
User avatar
Joined: 23 Nov 2016
Last visit: 15 May 2017
Posts: 1
Own Kudos:
33
 [33]
Given Kudos: 15
GRE 1: Q164 V161
GRE 1: Q164 V161
Posts: 1
Kudos: 33
 [33]
If x and y are positive integers such that y is a multiple of 5 and 3x 28 Nov 2016, 10:32
25
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
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.
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,994
 [6]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,994
 [6]
If x and y are positive integers such that y is a multiple of 5 and 3x 28 Nov 2016, 19:45
5
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
VeritasPrepKarishma
AbdurRakib
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)
Show more

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?
Show more

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)
User avatar
wvu
User avatar
Joined: 30 Mar 2017
Last visit: 08 Oct 2025
Posts: 17
Own Kudos:
11
 [7]
Given Kudos: 9
Location: United States (NY)
Schools: Stanford '25 (D) Wharton '25 (A$) HBS '25 (D)
GMAT 1: 730 Q44 V45 (Online)
GPA: 3.9
Schools: Stanford '25 (D) Wharton '25 (A$) HBS '25 (D)
GMAT 1: 730 Q44 V45 (Online)
Posts: 17
Kudos: 11
 [7]
If x and y are positive integers such that y is a multiple of 5 and 3x 28 Apr 2017, 10:49
7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
mrdlee23
User avatar
Joined: 29 Jan 2017
Last visit: 02 Dec 2018
Posts: 31
Own Kudos:
41
Given Kudos: 13
Posts: 31
Kudos: 41
If x and y are positive integers such that y is a multiple of 5 and 3x 09 Feb 2018, 17:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone pls verify if this method will work for all similar question types? This is the way I approached as well

wvu
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.
Show more
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,994
 [1]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,994
 [1]
If x and y are positive integers such that y is a multiple of 5 and 3x 12 Feb 2018, 04:38
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
mrdlee23
Can someone pls verify if this method will work for all similar question types? This is the way I approached as well

wvu
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.
Show more

Since y is a factor of 5, 4y will end in 0.
So get the sum of 200, 3x should end in 0 as well. So x should be a multiple of 10.
User avatar
SVaidyaraman
User avatar
Joined: 17 Dec 2012
Last visit: 11 Jul 2025
Posts: 576
Own Kudos:
1,795
Given Kudos: 20
Location: India
Expert
Expert reply
Posts: 576
Kudos: 1,795
If x and y are positive integers such that y is a multiple of 5 and 3x 06 Aug 2018, 18:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
i. We see that 4y is always a multiple of 10 when y is a multiple of 5 . So 3x is a multiple of 10 or x is a multiple of 3.33.
ii. However x is an integer . So x has to be a multiple of 3.33*3=10 since that is the minimum value that makes x an integer.
iii. So a multiple of 10.
Hence E.
avatar
sadikabid27
avatar
Joined: 10 Sep 2014
Last visit: 23 Jul 2021
Posts: 59
Own Kudos:
32
Given Kudos: 417
Location: Bangladesh
GPA: 3.5
WE:Project Management (Manufacturing)
Posts: 59
Kudos: 32
If x and y are positive integers such that y is a multiple of 5 and 3x 01 Oct 2018, 09:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel, VeritasKarishma anyway to do it using number testing ? Thanks.
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,994
 [1]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,994
 [1]
If x and y are positive integers such that y is a multiple of 5 and 3x Updated on: 17 Oct 2022, 03:30
Originally posted by KarishmaB on 02 Oct 2018, 04:24.
Last edited by KarishmaB on 17 Oct 2022, 03:30, edited 1 time in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sadikabid27
Bunuel, VeritasKarishma anyway to do it using number testing ? Thanks.
Show more


You can use number testing here though it could end up eating too much of your time.

y is a multiple of 5
3x + 4y = 200

Put y = 5, you get x = 60
Two options (C) and (D) are eliminated because 60 is not a multiple of 7 and 8.

Put y = 10 or 15, x is not an integer.

Put y = 20, you get x = 40
Options (A) and (B) are eliminated because 40 is not divisible by 3 and 6.

Answer must be (E)

Note: For x to be an integer, y must increase in multiples of 3 and y is already a multiple of 5 so you know that y must increase in multiples of 15 for x to be an integer. This can help skipping the y = 10 and y = 15 steps. If you are not sure why, think of integer solutions to equations in 2 variables.
User avatar
vanam52923
User avatar
Joined: 17 Jul 2017
Last visit: 12 Jun 2025
Posts: 202
Own Kudos:
102
 [1]
Given Kudos: 228
Posts: 202
Kudos: 102
 [1]
If x and y are positive integers such that y is a multiple of 5 and 3x 08 Oct 2019, 23:59
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATPrepNow
AbdurRakib
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:
Show Spoiler
E




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


and
Show more
but my doubut is :
but my doubt is :
x = (20)(10 - k)/3
so this can b integer only if k =1 or 4 or 7 ,so 10-k will be =9 or 6 or 3
al;l of which are multiple of 3 then it must be multiple of 3 too .where m i going wrong?
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,994
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,994
If x and y are positive integers such that y is a multiple of 5 and 3x 10 Oct 2019, 22:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
vanam52923
GMATPrepNow
AbdurRakib
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:
Show Spoiler
E




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


and
but my doubut is :
but my doubt is :
x = (20)(10 - k)/3
so this can b integer only if k =1 or 4 or 7 ,so 10-k will be =9 or 6 or 3
al;l of which are multiple of 3 then it must be multiple of 3 too .where m i going wrong?
Show more


y = 5a
3x + 4y = 200
3x + 4*5a = 200

3x + 20a = 200

x = 20(10 + a)/3

x has to be an integer. So (10 + a) must be divisible by 3 and x must be a multiple of 20. This implies that x must be a multiple of 10.

Note that x may not be a multiple of 3. Say a = 2, x = 20*12/3 = 80 (not a multiple of 3)
On the other hand, if a= 8, x = 20*18/3 = 120 (a multiple of 3)

Whether x is a multiple of 3, depends on the value of a. But it definitely is a multiple of 20 because x = 20 * (10 + a)/3 = Integer
So x = 20 * integer = Integer
User avatar
jkolachi
User avatar
Joined: 12 Oct 2015
Last visit: 05 Feb 2025
Posts: 237
Own Kudos:
404
 [1]
Given Kudos: 144
Location: Canada
Concentration: Leadership, Accounting
Schools: Ivey '19 (A) Queen's 19 (A) Schulich Jan 18 Intake (A)
GMAT 1: 700 Q47 V39
GPA: 3
WE:Accounting (Accounting)
Products:
My Reviews
Schools: Ivey '19 (A) Queen's 19 (A) Schulich Jan 18 Intake (A)
GMAT 1: 700 Q47 V39
Posts: 237
Kudos: 404
 [1]
If x and y are positive integers such that y is a multiple of 5 and 3x 17 Feb 2020, 13:20
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,994
 [1]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,994
 [1]
If x and y are positive integers such that y is a multiple of 5 and 3x 23 Mar 2021, 23:43
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Great1stan
okaypompeii
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.

If y = 10, then 3x+4(10)=200
3x+40=200
3x=160
x=53.333333

does this not mean X is not a multiple of 10?
What am I missing here?
Show more


You are given that x and y are positive integers and they satisfy 3x + 4y = 200.
Not all values of x and y will work because they will not satisfy all these constraints.
In your example, x is not an integer.

All examples which do satisfy all constraints will have x as a multiple of 10.
e.g. x = 40, y = 20
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,784
Own Kudos:
12,806
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,784
Kudos: 12,806
 [1]
If x and y are positive integers such that y is a multiple of 5 and 3x 19 Apr 2021, 20:50
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi All,

This prompt gives us lots of information to work with. We’re told:

X and Y are POSITIVE INTEGERS
Y is a multiple of 5
3X + 4Y = 200

We’re then asked what X MUST be a multiple of. This question can be solved with a bit of Arithmetic and TESTing VALUES. There’s also a subtle Number Property Rule built into this question that can save you some time if you recognize it. If you don’t immediately spot the Number Property, then you can still solve this problem with a bit of ‘brute force.’

Let’s start by TESTing the simplest multiple of 5…

IF…. Y = 5…..
3X + 20 = 200
3X = 180
X = 60
60 is a multiple of both 6 and 10, so the correct answer has to be either B or E.

Next, let’s work up through the next few multiples of 5….

IF…. Y = 10
3X + 40 = 200
3X = 160
160 is NOT evenly divisible by 3 though (meaning that X would be a non-integer, which is not allowed)

IF…. Y = 15
3X + 60 = 200
3X = 140
140 is NOT evenly divisible by 3 though (meaning that X would be a non-integer, which is not allowed)

IF…. Y = 20
3X + 80 = 200
3X = 120
X = 40
Between the two remaining answers, 40 is only a multiple of 10.

Final Answer:
Show Spoiler
E

The Number Property in this question is if you add a multiple of 5 to another multiple of 5, then the sum will be a multiple of 5.

Since Y is a MULTIPLE of 5, then 4Y will also be a multiple of 5. The sum of the two terms (200) is ALSO a multiple of 5, so the remaining term (the 3X) must ALSO be a multiple of 5. The answers are written in such a way that there’s only one multiple of 5 among them (re: the correct answer).

GMAT Assassins aren’t born, they’re made,
Rich
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 19 Nov 2025
Posts: 4,844
Own Kudos:
8,945
Given Kudos: 225
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,844
Kudos: 8,945
If x and y are positive integers such that y is a multiple of 5 and 3x Updated on: 14 Dec 2021, 23:57
Originally posted by CrackverbalGMAT on 24 Apr 2021, 03:42.
Last edited by CrackverbalGMAT on 14 Dec 2021, 23:57, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Solution:

Given 3x = 200 -4y

=> 3x = Difference of even numbers = even

=> As 3 is odd x must be even (So A & C eliminated)

Also it is a difference of multiples of 5 => 3x is also a multiple of 5

=> x is a multiple of 5 as 3 is not =>So 10

(option e)

D.S
GMAT SME
 1   2   
Moderators:
Bunuel
Math Expert
105389 posts
Krunaal
Tuck School Moderator
805 posts