Author
Message
TAGS:
Senior Manager

Joined: 03 Mar 2010

Posts: 446

Schools: Kelley,Tepper,Carlson,Kenan Flager,Broad

Followers: 4

Kudos [? ]:
109
[0 ] , given: 22

If A, B, C, and D are integers such that A - C + B is even [#permalink ]
20 Sep 2011, 02:29

1

This post was BOOKMARKED

Question Stats:

73% (02:21) correct

27% (01:52) wrong

based on 81 sessions
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. A + D

B. B + D

C. C + D

D. A + B

E. A + C

_________________

My dad once said to me: Son, nothing succeeds like success.

Last edited by

Bunuel on 05 Mar 2013, 02:02, edited 1 time in total.

Edited the question

Math Forum Moderator

Joined: 20 Dec 2010

Posts: 2047

Followers: 128

Kudos [? ]:
904
[2 ] , given: 376

2

This post received KUDOS

jamifahad wrote:

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.

Ans: "C"

_________________

~flukeGet the best GMAT Prep Resources with GMAT Club Premium Membership

Last edited by

fluke on 21 Sep 2011, 08:46, edited 1 time in total.

Added the warning after TomB pointed out error

Intern

Joined: 07 Jul 2011

Posts: 2

Followers: 0

Kudos [? ]:
8
[8 ] , given: 0

8

This post received KUDOS

Hi Jamifahad, Even matrix method takes more than two mins in this problem since you have to jot down the even and odd values. Try subtracting the equations (A - C + B) - (D + B - A) = 2A-(C+D) Even - Odd = Odd So 2A-(C+D) is odd 2A is always even , so the subtrahend should always be odd, so C+D is odd. Hope I am clear.

Senior Manager

Joined: 03 Mar 2010

Posts: 446

Schools: Kelley,Tepper,Carlson,Kenan Flager,Broad

Followers: 4

Kudos [? ]:
109
[0 ] , given: 22

@abhi6001

Awesome buddy!

+1. and welcome.

_________________

My dad once said to me: Son, nothing succeeds like success.

Senior Manager

Joined: 18 Sep 2009

Posts: 373

Followers: 3

Kudos [? ]:
62
[1 ] , given: 2

1

This post received KUDOS

Hai fluke How did you get that D,B,A are odd. My reasoning is as follows: D + B- A=odd D=odd and B-A could be even . odd+even =odd. B-A= odd-odd=even;even-even=even. Then D is odd but A,B could be even or odd. another possibility: D + B- A=odd. so D= even and B-A=odd, then eithe B or A could be either even or odd. Therefore D=even, B and A are either even or odd. please correct me if i am wrong

Senior Manager

Joined: 18 Sep 2009

Posts: 373

Followers: 3

Kudos [? ]:
62
[0 ] , given: 2

hai @abhi6001 can you explain 2A-(C+D)=odd. how C+D is odd. Thanks

Math Forum Moderator

Joined: 20 Dec 2010

Posts: 2047

Followers: 128

Kudos [? ]:
904
[0 ] , given: 376

TomB wrote:

Hai fluke How did you get that D,B,A are odd. My reasoning is as follows: D + B- A=odd D=odd and B-A could be even . odd+even =odd. B-A= odd-odd=even;even-even=even. Then D is odd but A,B could be even or odd. another possibility: D + B- A=odd. so D= even and B-A=odd, then eithe B or A could be either even or odd. Therefore D=even, B and A are either even or odd. please correct me if i am wrong

My earlier post is wrong. thanks for pointing out. I'll have to use the matrix after all.

_________________

~flukeGet the best GMAT Prep Resources with GMAT Club Premium Membership

Math Forum Moderator

Joined: 20 Dec 2010

Posts: 2047

Followers: 128

Kudos [? ]:
904
[0 ] , given: 376

jamifahad wrote:

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

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

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

By POE, for each of the rows above:

"C+D=ODD"

Ans: "C"

_________________

~flukeGet the best GMAT Prep Resources with GMAT Club Premium Membership

Intern

Status: Need to read faster and get less distracted by the ticking clock!

Affiliations: Golden Key

Joined: 19 Nov 2010

Posts: 23

Location: Toronto, ON

Schools: INSEAD, ISB, NUS

Followers: 0

Kudos [? ]:
8
[0 ] , given: 4

C. 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 Odd +/1 is ODD.. so D+C is odd!

Manager

Joined: 28 Jul 2011

Posts: 213

Followers: 0

Kudos [? ]:
27
[0 ] , given: 13

We know Even + Odd = Odd So, A - C + B = Even E - E + E = Even - 1 O - O + O = Even - 2 D + B - A = ODD 0 + E - E = ODD - 1 E + O - O = ODD - 2 So considering 1 and 2 If C is Even then D is odd & if C is Odd then D is Even So C + D should always be odd

Current Student

Joined: 08 Jan 2009

Posts: 334

GMAT 1 : 770 Q50 V46

Followers: 22

Kudos [? ]:
81
[0 ] , given: 7

A-C+B = Even

D+B-A = Odd

is equivalent to

A+B+C = Even

A+B+D = Odd

We are only interested in C and D now, and need only to consider two scenarios: A+B is odd or even.

A+B C D Odd Odd Even Even Even Odd

C+D is always odd.

c)

_________________

My Debrief

Director

Joined: 03 May 2007

Posts: 899

Schools: University of Chicago, Wharton School

Followers: 6

Kudos [? ]:
44
[0 ] , given: 6

jamifahad wrote:

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 (D-C) is odd, (D+C) has also to be always odd.

Therefore C.

VP

Status: There is always something new !!

Affiliations: PMI,QAI Global,eXampleCG

Joined: 08 May 2009

Posts: 1365

Followers: 11

Kudos [? ]:
136
[0 ] , given: 10

subtracting and adding the two terms

2A- (C+D) = odd meaning C+D = odd

2B - C+D = odd meaning (C-D) = odd. not provided in the options.

hence C it is.

_________________

Visit -- http://www.sustainable-sphere.com/ Promote Green Business,Sustainable Living and Green Earth !!

Director

Joined: 03 May 2007

Posts: 899

Schools: University of Chicago, Wharton School

Followers: 6

Kudos [? ]:
44
[1 ] , given: 6

1

This post received KUDOS

jamifahad wrote:

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.

Director

Status: Gonna rock this time!!!

Joined: 22 Jul 2012

Posts: 550

Location: India

GMAT 1 : 640 Q43 V34GMAT 2 : 630 Q47 V29

WE: Information Technology (Computer Software)

Followers: 2

Kudos [? ]:
28
[1 ] , given: 562

Re: If A, B, C, and D are integers such that A - C + B is even [#permalink ]
05 Mar 2013, 01:47
1

This post received KUDOS

Bunuel /Karishma/ Experts,

This is how I solved:

A−C+B is even and D+B−A is odd

Add them

2B + D-C must be odd

since 2B is even , D-C must be odd.

So C+D must be ODD :D

Kudos if this helps anybody _________________

hope is a good thing, maybe the best of things. And no good thing ever dies. Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595 My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

Math Expert

Joined: 02 Sep 2009

Posts: 25206

Followers: 3418

Kudos [? ]:
25043
[0 ] , given: 2702

Re: If A, B, C, and D are integers such that A - C + B is even [#permalink ]
05 Mar 2013, 02:06

Manager

Joined: 02 Jan 2013

Posts: 53

GMAT 1 : 750 Q51 V40

WE: Consulting (Consulting)

Followers: 0

Kudos [? ]:
34
[1 ] , given: 1

Re: If A, B, C, and D are integers such that A - C + B is even [#permalink ]
05 Mar 2013, 05:08
1

This post received KUDOS

Alternatively, you could also subtract both equations:

A- C + B = EVEN

D + B - A = ODD

Subtracting the 1st from the 2nd:

D +C - 2A = EVEN + ODD

Or,

D + C = EVEN + EVEN + ODD = ODD

_________________

Please press "kudo" if this helped you!

Director

Status: Gonna rock this time!!!

Joined: 22 Jul 2012

Posts: 550

Location: India

GMAT 1 : 640 Q43 V34GMAT 2 : 630 Q47 V29

WE: Information Technology (Computer Software)

Followers: 2

Kudos [? ]:
28
[0 ] , given: 562

Re: If A, B, C, and D are integers such that A - C + B is even [#permalink ]
05 Mar 2013, 05:14

caioguima wrote:

Alternatively, you could also subtract both equations: A- C + B = EVEN D + B - A = ODD Subtracting the 1st from the 2nd: D +C - 2A = EVEN + ODD Or, D + C = EVEN + EVEN + ODD = ODD

yeah you can do that since these are equations.

but know that u shud never subtract in case of inequalities.. .

Kudos if this helps.

_________________

hope is a good thing, maybe the best of things. And no good thing ever dies. Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595 My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

SVP

Joined: 09 Sep 2013

Posts: 2215

Followers: 185

Kudos [? ]:
36
[0 ] , given: 0

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

_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If A, B, C, and D are integers such that A - C + B is even
[#permalink ]
23 Jul 2014, 21:09

Similar topics
Author
Replies
Last post
Similar Topics:

2
If for integers a, b, c, and d, a + b + c + d = 4
yogirb8801
2
16 May 2013, 07:19

The four integers a , b , c , and d are such that a < b
kannn
2
14 Jul 2011, 10:06

4
If a,b,c, d are distinct even integers and a is prime, is
enigma123
7
06 Jul 2011, 05:22

If c and d are integers, is c even? a. c(d+1) is even b.
redbeanaddict
7
11 Oct 2008, 00:28

A, B, C, and D are integers such that A - C + B is even and
bmwhype2
2
20 Nov 2007, 06:13