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 500,000 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 \(A\) , \(B\) , \(C\) , and \(D\) are integers such that \(A - C + B\) is even and \(D + B - A\) is odd, which of the following expressions is always odd?

\(A + D\) \(B + D\) \(C + D\) \(A + B\) \(A + C\)

I am wondering if there is any matrix method to do these sort of Even/Odd question. If anybody knows about any such method, kindly post.

***THIS SOLUTION HAS FLAWS AS POINTED OUT BY TomB***

Sorry, didn't use the matrix for this one.

A-C+B=even; means Either one of these Or two of these Or All three of them ARE EVEN.

But, NOT all of them are ODD.

D + B - A=odd Means, ALL of them are ODD

That confirms; A, B, D are ODD; and from before, C must be EVEN.

If \(A\) , \(B\) , \(C\) , and \(D\) are integers such that \(A - C + B\) is even and \(D + B - A\) is odd, which of the following expressions is always odd?

\(A + D\) \(B + D\) \(C + D\) \(A + B\) \(A + C\)

Start with all possible combinations for A and B:

ODD: O EVEN: E

C

A

B

D

O

E

E

O

O

O

E

E

Now fill in the column 1, i.e. C's type with either odd or even; based on statement 1

C

A

B

D

O

O

E

O

E

O

E

O

O

E

E

E

Now fill in the column 4, i.e. D's type with either odd or even; based on statement 2

Even - Odd = Odd Therefore: A-C+B - (D+B-A) = ODD .. 2A-D-C = ODD ( now we know anything multiplied by 2 makes it Even.. so 2A cannot be the factor to cause this to be odd.. ) so we can simplfy it : -(D+C) = ODD

If \(A\) , \(B\) , \(C\) , and \(D\) are integers such that \(A - C + B\) is even and \(D + B - A\) is odd, which of the following expressions is always odd?

\(A + D\) \(B + D\) \(C + D\) \(A + B\) \(A + C\)

I am wondering if there is any matrix method to do these sort of Even/Odd question. If anybody knows about any such method, kindly post.

Looks good question....

We always need simple, easy and quick/fast approach:

A-C+B = EVEN ............I D+B-A = ODD..............II

Add I and II:

A-C+B+D+B-A = EVEN+ODD 2B-C+D = ODD

No matter whether B is even or odd, 2B has to be an even number. If so, then remaining number, (D-C), has to be odd.

If \(A\) , \(B\) , \(C\) , and \(D\) are integers such that \(A - C + B\) is even and \(D + B - A\) is odd, which of the following expressions is always odd?

\(A + D\) \(B + D\) \(C + D\) \(A + B\) \(A + C\)

I am wondering if there is any matrix method to do these sort of Even/Odd question. If anybody knows about any such method, kindly post.

Make it plain and simple:

A - C + B = even D + B - A = odd

Add both: A - C + B + D + B - A = Even +odd 2B - C + D = odd 2B + (D - C) = odd

Since 2B is even, (D-C) must be odd. Alternatively, C could be odd or even and same is D but if C is odd, D must be even and vice versa. However it is not necessary to find out whether C is odd or even.

If so, either (C+D) or (C-D) is odd. So its C that \(C + D\) is always odd.

Re: If A, B, C, and D are integers such that A - C + B is even [#permalink]

Show Tags

23 Jul 2014, 21:09

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If A, B, C, and D are integers such that A - C + B is even [#permalink]

Show Tags

27 Aug 2015, 18:29

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...