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

 It is currently 15 Nov 2019, 07:52 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x and y are positive integers such that y is a multiple of 5 and 3x

Author Message
TAGS:

### Hide Tags

Intern  S
Joined: 29 Jan 2017
Posts: 42
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

Can someone pls verify if this method will work for all similar question types? This is the way I approached as well

wvu wrote:
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.
Director  P
Joined: 31 Jul 2017
Posts: 510
Location: Malaysia
GMAT 1: 700 Q50 V33 GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

mrdlee23 wrote:
Can someone pls verify if this method will work for all similar question types? This is the way I approached as well

wvu wrote:
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.

We know that -
$$3x + 4y = 200, y = 5m$$
$$3x + 20m = 200$$
$$x = \frac{10(20 - m)}{3}$$

So, x has to be multiple of 10.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9784
Location: Pune, India
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

mrdlee23 wrote:
Can someone pls verify if this method will work for all similar question types? This is the way I approached as well

wvu wrote:
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.

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.
_________________
Karishma
Veritas Prep GMAT Instructor

Intern  B
Joined: 25 Dec 2017
Posts: 7
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

Abhishek009 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

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)

Hey, Abhishek009! 40 is also a multiple of 8, option D. So we still have D and E remaining.
Board of Directors V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3568
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

1
Hey, Abhishek009! 40 is also a multiple of 8, option D. So we still have D and E remaining.

As Abhishek009 has explained, we have already rejected option D when we substituted y = 5 in the equation.

Remember for a "MUST" be true question, it should work for all the scenarios but we are not getting x a multiple of 8 whenever we have y = 5.

Hence, D cannot be the answer.

Does that make sense?
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Intern  B
Joined: 25 Dec 2017
Posts: 7
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

abhimahna wrote:
Hey, Abhishek009! 40 is also a multiple of 8, option D. So we still have D and E remaining.

As Abhishek009 has explained, we have already rejected option D when we substituted y = 5 in the equation.

Remember for a "MUST" be true question, it should work for all the scenarios but we are not getting x a multiple of 8 whenever we have y = 5.

Hence, D cannot be the answer.

Does that make sense?

Hey abhimahna! Thank you for bringing this to my notice.
Manager  S
Joined: 02 Aug 2017
Posts: 51
Concentration: Strategy, Nonprofit
Schools: ISB '20
GPA: 3.71
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

X,Y >0 i.e.X,Y both positive
Y=mul(5) i.e. Y is multiple of 5

3X+4Y=200
Because Y=mul(5),4Y will be multiple of 20
200 is also multiple of 20.
Hence 200-4Y will also be multiple of 20
I.e. 3X= multiple of 20
Hence, X will be multiple of 20, 10×2, and hence of 10.

Posted from my mobile device
_________________

Everything is in flux, nothing stays still

MGMAT1 :590 Q42 V30 (07/07/18)
VERITAS :660 Q48 V33 (16/07/18)
GMATPREP1 :690 Q46 V36 (22/07/18)
GMATPREP2 :740 Q51 V39 (06/08/18)
ECONOMIST :740 Q49 V44 (11/08/18)
KAPLAN :690 Q49 V36 (17/08/18)
PRINCETON :690 Q48 V38 (26/08/18)
MGMAT2 :720 Q43 V45 (02/09/18)
IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1370
Location: India
WE: Engineering (Other)
If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

niks18 chetan2u pushpitkc KarishmaB gmatbusters

Quote:
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?

Given: y is a multiple of 5, so unit digits of product with y must end with 0 or 5.

4*y = (Unit digit will always end with 0, since 4*5 = 20 and 4*0 =0 )

Now look RHS, I need unit digit as 0, __ + 0 = 0
Hence 3 must be some multiple an integer ending with 0.
Ans: 10
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1271
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

This is the perfect approach. niks18 chetan2u pushpitkc KarishmaB gmatbusters

Quote:
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?

Given: y is a multiple of 5, so unit digits of product with y must end with 0 or 5.

4*y = (Unit digit will always end with 0, since 4*5 = 20 and 4*0 =0 )

Now look RHS, I need unit digit as 0, __ + 0 = 0
Hence 3 must be some multiple an integer ending with 0.
Ans: 10

_________________
Director  S
Joined: 17 Dec 2012
Posts: 623
Location: India
If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

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.
_________________
Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Intern  B
Joined: 30 May 2017
Posts: 18
Location: India
Concentration: Finance, Strategy
Schools: Wharton, IESE, ISB, NUS
GPA: 4
WE: Engineering (Consulting)
If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

Clearly we can assume y = 5k since y is a multiple of 5. Now the equation becomes
3x + 4(5k) = 200
So 3x + 20k = 200
Now for any integer value of k , we will have unit digit ending with 0 (e.g 20*1 = 20 , 20*2 = 40 etc)

Applying the unit digit concept, we know that
sum of both terms of LHS is 200 and since 20k has unit digit 0 , therefore 3x must have unit digit 0.
So 3x can end with unit digit 0 only when x is a multiple of 10

Hope i could clarify in a simpler way.
_________________
You say this is a problem , I say this must be an opportunity
Manager  B
Joined: 10 Sep 2014
Posts: 76
GPA: 3.5
WE: Project Management (Manufacturing)
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

Bunuel, VeritasKarishma anyway to do it using number testing ? Thanks.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9784
Location: Pune, India
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

Bunuel, VeritasKarishma anyway to do it using number testing ? Thanks.

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.

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. For more, check: https://www.veritasprep.com/blog/2011/0 ... -of-thumb/
_________________
Karishma
Veritas Prep GMAT Instructor

Intern  Joined: 12 Feb 2019
Posts: 1
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

thanks this will help me
Manager  S
Joined: 28 Jun 2015
Posts: 78
Location: Australia
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

Hi Bunuel

Any chance you post few similar questions?

Regards
Manager  B
Joined: 25 Sep 2018
Posts: 65
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

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
=>x=200-4y/3
y is a multiple of 5. So we'll test:
When 5,

200-20/3=6*10
When20,
200-80/3=4*10

x must be a multiple of 10

Posted from my mobile device
Manager  B
Joined: 15 Aug 2017
Posts: 74
Location: India
Schools: HBS '22
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

Abhishek009 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

the same doesn't work when you substitute the equation by 10.
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)

The same doesn't work if you substitute it by 10.
_________________
"You don't want to to look back and know you could've done better".
Intern  B
Joined: 14 May 2019
Posts: 13
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

well the Prime factors of 200 are : 2x2x2x5x5.
4y = 4(5i) = 2x2x5xi = which hogs 2-2's and 1-5 leaving another 2 and 5 which must be provided by the 3x part.

so, 3x must have a 3x2x5xk or 3x10xk.

hence, x must be multiple of 10 for 3x+4y =200 to be true.

_________________
"The cure to boredom is curiosity. There is no cure to curiosity"
Manager  B
Joined: 24 Sep 2018
Posts: 99
Location: India
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

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

Y is multiple of 5 .

3x+4y =200

So 4y must be multiple of 5. So

3x+ (multiple of 5) 4y = 200 (multiple of 5)
3x= 200 (multiple of 5) - 4x (multiple of 5)

So 3x must be multiple of 5

HOW: 35(multiple of 5)-15(multiple of 5)= 20(multiple of 5)

25(multiple of 5)- 10 (multiple of 5) =15 (multiple of 5)

Ok if 3x is multiple of 5

So 3* x should be multiple of 5.

So x should be multiple of 5. In answer opt

3 * which opt of answer is multiple of 5

3*1 (NO)
3*6 (NO)
3*7(NO)
3.8 (NO)
3.10(YES) 10 is multiple of 5 and 30 is also multiple of 5. So E is the answer
_________________
Thanks,
Bijaya

If this post is helpful for you please press the kudos button
Manager  G
Joined: 31 Jan 2019
Posts: 184
Location: Switzerland
Concentration: General Management
GPA: 3.9
Re: If x and y are positive integers such that y is a multiple of 5 and 3x  [#permalink]

### Show Tags

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?

Since we know that y is a multiple of 5 we can rewrite this equation i the following way: 3x+4*(5k)=200
Upon simplification: 3x=200-20k and 3x=20*(10-k)
Now since 3 is not a factor of 20 it must be a factor of (10-k).
Hence x is a multiple of 20 and of all 20's factors, including 10.

A) 3

B) 6

C) 7

D) 8

E) 10 Correct Re: If x and y are positive integers such that y is a multiple of 5 and 3x   [#permalink] 12 Aug 2019, 11:34

Go to page   Previous    1   2   3    Next  [ 44 posts ]

Display posts from previous: Sort by

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