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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

well I guess the first questions was quite easy. How about this one? do you still use numbers to solve?

OK. Algebraic approach:

Given: x=8y+12.

(1) 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 --> x=8*12z+12 --> x=12(8z+1) --> so 12 is a factor both x and y.

Is it GCD of x and y? Why can not it be more than 12, for example 13, 16, 24, ... We see that factors of x are 12 and 8z+1: so if 8z+1 has some factor >1 common with z then GCD of x and y will be more than 12 (for example if z and 8z+1 are multiples of 5 then x would be multiple of 12*5=60 and y also would be multiple of 12*5=60, so GCD of x and y would be more than 12). But z and 8z+1 CAN NOT share any common factor >1, as 8z+1 is a multiple of z plus 1, so no factor of z will divide 8z+1 evenly, which means that GCD of x and y can not be more than 12. GCD(x,y)=12. Sufficient.

Re: GCD 2 (Tougher) [#permalink]
25 Oct 2010, 07:55

Expert's post

rafi: Same logic as that given by Bunuel and shrouded1 above, just worded differently in case you have come across this before: "Two consecutive integers do not have any common factors other than 1"

So 8z and 8z + 1 will not share any factors other than 1 and all factors of z will be factors of 8z too. Therefore, z and 8z + 1 will not have any common factors other than 1. _________________

hey guys, A metallurgist but currently working in a NGO and have scheduled my GMAT in December for second round .....u know. I read some but valuable blogs on this...

One thing I did not know when recruiting for the MBA summer internship was the following: just how important prior experience in the function that you're recruiting for...

Many of my classmates and I have been receiving queries from MBA aspirants who are interested in applying to SBS. The questions are usually focussed on the career opportunities after...