Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 17 Aug 2009
Posts: 225

If c and d are integers, is c even? [#permalink]
Show Tags
30 Jan 2010, 12:15
5
This post was BOOKMARKED
Question Stats:
63% (01:38) correct 37% (01:10) wrong based on 324 sessions
HideShow timer Statistics
If c and d are integers, is c even? (1) c(d+1) is even (2) (c+2)(d+4) is even
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 43892

Re: GMATprep DS (Number properties) [#permalink]
Show Tags
30 Jan 2010, 14:39
8
This post received KUDOS
Expert's post
6
This post was BOOKMARKED



Manager
Joined: 17 Aug 2009
Posts: 225

Re: GMATprep DS (Number properties) [#permalink]
Show Tags
31 Jan 2010, 09:49
Thanks Bunuel
OA is C
But i got lost in this number property question (was consuming too much time) and hence picked E on the test.
Is there any faster way to solve this?



Math Expert
Joined: 02 Sep 2009
Posts: 43892

Re: GMATprep DS (Number properties) [#permalink]
Show Tags
31 Jan 2010, 10:43



Manager
Joined: 17 Jan 2010
Posts: 147
Concentration: General Management, Strategy
GPA: 3.78
WE: Engineering (Manufacturing)

Re: GMATprep DS (Number properties) [#permalink]
Show Tags
01 Feb 2010, 13:46
7
This post received KUDOS
obviously, 1 or 2 separatly is not sufficient.
Both: start with a second statement:
(c+2)(d+4)=cd +4c+2d+8=even => cd is even
now statement one says :
c(d+1)=cd+c is even. From statement 2, cd is even => for stament 2 to be true c has to be even.
Answer C



Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 403
Location: Milky way
Schools: ISB, Tepper  CMU, Chicago Booth, LSB

Re: GMAT PREP DS [#permalink]
Show Tags
22 Aug 2010, 18:27
uzzy12 wrote: If c and d are integers, is c even?
(1) c(d +1) is even (2) (c+ 2)(d + 4) is even Statement 1 is insufficient since c could be even or odd and (d+1) could also be even or odd and still c * (d+1) could be even. Refer the below table. c ***** d+1 ***** c (d+1) E ***** E ***** E E ***** O ***** E O ***** E ***** E Statement 2 is insufficient. (c+2) (d+4) = cd + 2d + 4c + 8. (Here 2d, 4c and 8 are even). Hence c * d should even, however we cannot say whether c is even. Refer the below table. c ***** d ***** c * d E ***** E ***** E E ***** O ***** E O ***** E ***** E Combining two statements. c(d+1) and cd is even. Also if d is even then (d+1) is odd and vice versa. Now set up a table. c ***** d ***** (d+1) **** cd *********** c(d+1) O ***** E ***** O **** Even *********** Odd  This combination does not work E ***** O ***** E **** Even *********** Even  This works and hence c is even. Hence combining both statements would answer the question. Answer C.
_________________
Support GMAT Club by putting a GMAT Club badge on your blog



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1945

Re: If c and d are integers, is c even? [#permalink]
Show Tags
22 Feb 2011, 00:58
I don't know the best way; but here's how I would solve it; 1. c(d+1) is even c even and d+1 even i.e. d odd OR c odd and d+1 even i.e. d odd OR c even and d+1 odd i.e. d even We can see that c can be even or odd. Not sufficient. 2. (c+2)(d+4) is even c+2 even and d+4 even i.e. c even and d even OR c+2 odd and d+4 even i.e. c odd and d even OR c+2 even and d+4 odd i.e. c even and d odd C can be even or odd. Not sufficient. If you see the odd case for c in both statements; c odd and d+1 even i.e. d odd c+2 odd and d+4 even i.e. c odd and d even You see that for c=odd; 1 statement says d=odd; 2nd statement says d=even; Conflict; D can't be odd and even at the same time. If you consider c=even; c even and d+1 even i.e. d odd c+2 even and d+4 odd i.e. c even and d odd Both statements match. c even and d+1 odd i.e. d even c+2 even and d+4 even i.e. c even and d even Both statements match. Ans: "C"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Director
Status: =Given to Fly=
Joined: 04 Jan 2011
Posts: 826
Location: India
Concentration: Leadership, Strategy
GMAT 1: 650 Q44 V37 GMAT 2: 710 Q48 V40 GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)

Re: If c and d are integers, is c even? [#permalink]
Show Tags
22 Feb 2011, 01:00
I tried this approach: Statement 1: c(d+1) is even Therefore, we have three possibilities. a) c  E & (d+1)  E => c is even and d is odd b) c  E & (d+1)  O => c is even and d is even c) c  O & (d+1)  E => c is odd and d is odd So c and be even or odd! Thus statement is not sufficient. Statment 2: (c+2) (d+4) is even Therefore, there are three possibilities. a) (c+2) is even and (d+4) is even => c is even and d is even b) (c+2) is even and (d+4) is odd => c is even and d is odd c) (c+2) is odd and (d+4) is even => c is odd and d is even So c can be even or odd! Thus statement is not sufficient. Both Statements together: For the cases c even and d odd or even, both the statements will always be true! Thus c is even! Ans: 'C'
_________________
"Wherever you go, go with all your heart"  Confucius
Useful Threads
1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club)
2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog)
My Experience With GMAT
1. From 650 to 710 to 750  My Tryst With GMAT
2. Quest to do my Best  My GMAT Journey Log



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1945

Re: If c and d are integers, is c even? [#permalink]
Show Tags
22 Feb 2011, 01:09
Subtracting 2 from 1; c(d+1)(c+2)(d+4) = eveneven=even cd+ccd4c2d8=even c4c2d8=even 4c;2d;8 are all even c should be even.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 21 Mar 2010
Posts: 305

Re: GMATprep DS (Number properties) [#permalink]
Show Tags
24 Feb 2011, 22:38
zaarathelab wrote: Thanks Bunuel
OA is C
But i got lost in this number property question (was consuming too much time) and hence picked E on the test.
Is there any faster way to solve this? No easy way to do this but you can jump to c quickly ruling out a,d and b. Once you see which statements remain valid while taking into consideration 1 and 2, we can see that c is even.



Current Student
Joined: 06 Sep 2013
Posts: 1954
Concentration: Finance

Re: If c and d are integers, is c even? [#permalink]
Show Tags
05 Jan 2014, 17:25
zaarathelab wrote: If c and d are integers, is c even?
(1) c(d+1) is even (2) (c+2)(d+4) is even Here I go, catch me Statement 1 Not sufficient obviously Statement 2 Same here Both Statements together Well, lets see of 'c' is not even then d+1 must be even that means that 'd' must be odd Now if d is odd. d+4 will be odd as well that means that c+2 must be even, and thus 'c' must be even So C is sufficient here Gimme some Kudos ok? Cheers! J



Intern
Joined: 10 May 2010
Posts: 5

Re: If c and d are integers, is c even? [#permalink]
Show Tags
06 Jan 2014, 08:43
If c and d are integers, is c even?
(1) c(d+1) is even (2) (c+2)(d+4) is even
Here we have a number properties question. We will be dealing with evens/odds and multiplication/addition. A couple of things to keep in mind before we look at the statements: 1. If c is even it will have at least one factor of 2 2. The rules for addition for evens/odds: E+E = E; O+O = E; E+0 = O; O+E = O 3. The rules for multiplication for evens/odds: We will arrive at an even product EXCEPT when we have O*O which will produce an O result
1. Statement 1 is true if : a. C is Even and D is Even E(E+1) = E*O = E b. C is Even and D is odd E(O+1) = E*E = E c. C is Odd and D is Odd O(O+1) = O*E = E a and b give us an answer of yes; c gives us an answer of no  INSUFFICIENT
2. Statement 2 is true if: a. C is Even and D is Even (E+2)(E+4) = E*E = E b. C is Even and D is Odd (E+2)(O+4) = E*O= E c. C is Odd and D is Even (O+2)(E+4) = O*E=E a and b give us an answer of yes; c gives us an answer of no  INSUFFICIENT
When we take the statements together we notice that the two possible scenarios they have in common are a and b (C is Even and D is Even OR C is Even and D is Odd). In both scenarios C is Even, so we have one definitive answer to the question. SUFFICIENT the answer is C
This may seem like a lengthy explanation; I provided every step for clarity. Make sure to memorize rules for number properties, and you can solve a question similar to this one in two minutes or less.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11068
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If c and d are integers, is c even? [#permalink]
Show Tags
08 Mar 2015, 11:22
Hi All, It appears that all of the posters used Number Property rules to answer this question. You can also TEST VALUES; in that way, you can physically "see" how those same Number Property rules "work" in real life. We're told that C and D are integers. We're asked if C is even. This is a YES/NO question. Fact 1: (C)(D+1) is even This means that one or the other (or both) of the "terms" must be even.... IF.... C = 2 D = 1 (2)(2) = 4 The answer to the question is YES IF.... C = 1 D = 1 (1)(2) = 2 The answer to the question is NO Fact 1 is INSUFFICIENT Fact 2: (C+2)(D+4) = even Just as in Fact 1, this means that one or the other (or both) of the "terms" must be even.... IF.... C = 2 D = 1 (4)(5) = 20 The answer to the question is YES IF... C = 1 D = 2 (3)(6) = 18 The answer to the question is NO Fact 2 is INSUFFICIENT Combined, we know.... (C)(D+1) is even (C+2)(D+4) is even Since D is an integer, ONLY ONE of the two terms  (D+1) and (D+4)  will be even; the other will be odd. As such, the other term in each of the products (the one with the C in it) MUST be even.... eg... C = 2 D = 1 Combined, SUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Director
Joined: 26 Oct 2016
Posts: 682
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: If c and d are integers, is c even? [#permalink]
Show Tags
06 Feb 2017, 11:20
1
This post received KUDOS
Combining both Statements, we get: 1. cd+c=Even 2. cd+4c+2d+8=Even By analyzing statement 2 we can see that, 4c and 2d have to be even in nature( since they are being multiplied by an even number). Furthermore, 8 is also even and we also know that even +even+even=EVEN Therefore, Statement 2 can be rephrased as cd+Even=Even. This means that cd has to be even(Even+Even=Even). Substituting this information in Statement 1, we get, Even+c=Even. This shows that c has to be even under any circumstance. Hence the answer is C
_________________
Thanks & Regards, Anaira Mitch



NonHuman User
Joined: 09 Sep 2013
Posts: 13786

Re: If c and d are integers, is c even? [#permalink]
Show Tags
10 Feb 2018, 00:42
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 c and d are integers, is c even?
[#permalink]
10 Feb 2018, 00:42






