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

 It is currently 12 Dec 2018, 07:05

CMU Tepper in Calling R1 Admits   |  Kellogg Calls are Expected Shortly

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
• ### GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

# If x and y are positive integers such that x = 8y + 12, what is the

Author Message
TAGS:

### Hide Tags

Intern
Joined: 23 Dec 2014
Posts: 9
If x and y are positive integers such that x = 8y + 12, what is the  [#permalink]

### Show Tags

21 Aug 2017, 08:00
Hello All,

My take on this question:

As given , x = 8y+12 and x and y are positive integers.

Statement 1: x = 12u, u is integer

It means x is multiple of 12. But x is also 8y+12 then it means 8y should also be multiple of x, which in turn means y can take values 3 , 6, 9 ...etc i.e. multiple of 3.
Case 1: say y = 3 then x = 8*3 + 12 = 36 , GCD(x,y) = 3
Case 2: say y = 6 then x = 8*6 +12 = 60, GCD(x,y) = 6

Clearly 1 insufficient.

Statement 2: y = 12u, u is integer

It means y is multiple of 12 , which in turn means x = 8(multiple of 12) + 12 i.e. x is nothing but the next multiple of 12 than y or y and x are consecutive multiples of 12.
So GCD of two consecutive multiples of 12 should be 12 ,hence sufficient. Answer B.

Hope it helps.

Thanks
Manoj Parashar
Intern
Joined: 14 May 2016
Posts: 23
Re: If x and y are positive integers such that x = 8y + 12, what is the  [#permalink]

### Show Tags

07 Apr 2018, 06:19
Bunuel wrote:
If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

Given: $$x=8y+12$$.

(1) x = 12u, where u is an integer --> $$x=12u$$ --> $$12u=8y+12$$ --> $$3(u-1)=2y$$ --> the only thing we know from this is that 3 is a factor of $$y$$. Is it GCD of $$x$$ and $$y$$? Not clear: if $$x=36$$, then $$y=3$$ and $$GCD(x,y)=3$$ but if $$x=60$$, then $$y=6$$ and $$GCD(x,y)=6$$ --> two different answers. Not sufficient.

(2) y = 12z, where z is an integer --> $$y=12z$$ --> $$x=8*12z+12$$ --> $$x=12(8z+1)$$. So, we have $$y=12z$$ and $$x=12(8z+1)$$. Now, as $$z$$ and $$8z+1$$ do not share any common factor but 1 (8z and 8z+1 are consecutive integers and consecutive integers do not share any common factor 1. As 8z has all factors of z then z and 8z+1 also do not share any common factor but 1). Thus, 12 must be GCD of $$x$$ and $$y$$. Sufficient.

Hope it's clear.

Hello Bunuel,

is it possible to take the approach for Statement 1 when dividing by 4 both sides ----> 3u = 2y + 3 can I say that this is insufficient since we have one equation with two variables?
Intern
Joined: 30 Nov 2017
Posts: 41
If x and y are positive integers such that x = 8y + 12, what is the  [#permalink]

### Show Tags

Updated on: 17 May 2018, 03:58
Bunuel wrote:
If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

Given: $$x=8y+12$$.

(1) x = 12u, where u is an integer --> $$x=12u$$ --> $$12u=8y+12$$ --> $$3(u-1)=2y$$ --> the only thing we know from this is that 3 is a factor of $$y$$. I

Can you please explain this Bunuel?

3(u-1)=2y

So, we know that 3 is a factor of 2y, but how can we conclude that 3 is a factor of y? Is it because 2 and 3 don't have any factor in common, except 1?

Originally posted by Nived on 17 May 2018, 03:48.
Last edited by Nived on 17 May 2018, 03:58, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 51121
Re: If x and y are positive integers such that x = 8y + 12, what is the  [#permalink]

### Show Tags

17 May 2018, 03:54
1
Nived wrote:
Bunuel wrote:
If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

Given: $$x=8y+12$$.

(1) x = 12u, where u is an integer --> $$x=12u$$ --> $$12u=8y+12$$ --> $$3(u-1)=2y$$ --> the only thing we know from this is that 3 is a factor of $$y$$. I

Can you please explain the Bunuel?

3(u-1)=2y

So, we know that 3 is a factor of 2y, but how can we conclude that 3 is a factor of y? Is it because 2 and 3 don't have any factor in common, except 1?

Exactly. 2y/3 = integer (because u-1 is an integer). This to be true, y must be a multiple of 3.
_________________
Manager
Joined: 10 Sep 2014
Posts: 84
GPA: 3.5
WE: Project Management (Manufacturing)
Re: If x and y are positive integers such that x = 8y + 12, what is the  [#permalink]

### Show Tags

10 Sep 2018, 06:16
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8665
Location: Pune, India
Re: If x and y are positive integers such that x = 8y + 12, what is the  [#permalink]

### Show Tags

11 Sep 2018, 22:45
enigma123 wrote:
If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

(1) x = 12u, where u is an integer.
(2) y = 12z, where z is an integer.

x = 8y + 12

(1) x = 12u, where u is an integer.

If x is a multiple of 12, it means 8y is a multiple of 12. Since 8 already has three 2s, we NEED y to have a 3 but it COULD have 2s and/or other factors too.
So we cannot say what the GCD of x and y is.
Not sufficient.

(2) y = 12z, where z is an integer.
If y is a multiple of 12, x is a multiple of 12 too. So they certainly have 12 common. Let's see what else they could have common.
x is 12 more than a multiple of y so the only common factors they could have are the factors of 12. We already know that they both have 12 in them. So GCD must be 12.
(This concept has been discussed in detail here: https://www.veritasprep.com/blog/2015/0 ... -the-gmat/)
Sufficient.

_________________

Karishma
Veritas Prep GMAT Instructor

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 536
Re: If x and y are positive integers such that x = 8y + 12, what is the  [#permalink]

### Show Tags

11 Nov 2018, 06:57
enigma123 wrote:
If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

(1) x = 12u, where u is an integer.
(2) y = 12z, where z is an integer.

$$\left\{ \begin{gathered} x,y\,\, \geqslant \,\,1\,\,{\text{ints}} \hfill \\ x - 8y = 12\,\,\,\,\,\left( * \right) \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = \,\,GCD\left( {x,y} \right)$$

$$\left( 1 \right)\,\,\,x = 12u\,\,,\,\,\,u\,\,\operatorname{int} \,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,8y = 12\left( {u - 1} \right)$$

$$\,\left\{ \begin{gathered} \,{\text{Take}}\,\,u = 3\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,\,y = 3\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {x,y} \right) = \left( {12 \cdot 3\,,\,3} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 3 \hfill \\ \,{\text{Take}}\,\,u = 5\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,\,y = 6\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {x,y} \right) = \left( {12 \cdot 5\,,\,6} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 6\,\, \hfill \\ \end{gathered} \right.$$

$$\left( 2 \right)\,\,\,y = 12z\,\,,\,\,\,z\,\,\operatorname{int} \,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,x = 12 + 8 \cdot 12 \cdot z = 12\left( {8z + 1} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\,? = 12$$

$$\left( {**} \right)\,\,\,GCD\,\,\left( {z\,,\,8z + 1} \right) = \,\,k \geqslant 1\,\,\,{\text{int}}\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \begin{gathered} \,\frac{z}{k} = {\text{in}}{{\text{t}}_{\text{1}}} \hfill \\ \,\frac{{8z + 1}}{k} = {\operatorname{int} _2}\,\,\,\,\, \hfill \\ \end{gathered} \right. \Rightarrow \,\,\,\,\,\,\,\,\frac{1}{k} = {\operatorname{int} _2} - 8\left( {\frac{z}{k}} \right) = {\operatorname{int} _2} - 8 \cdot {\operatorname{int} _1} = \operatorname{int} \,\,\,\,\,\,\,\mathop \Rightarrow \limits^{k\, \geqslant \,1\,\,\,{\text{int}}} \,\,\,\,\,k = 1$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

Re: If x and y are positive integers such that x = 8y + 12, what is the &nbs [#permalink] 11 Nov 2018, 06:57

Go to page   Previous    1   2   [ 27 posts ]

Display posts from previous: Sort by