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

 It is currently 13 Nov 2018, 08:36

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Essential GMAT Time-Management Hacks

November 14, 2018

November 14, 2018

07:00 PM PST

08:00 PM PST

Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST
• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # If x is an integer, is 3x + 7 even?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 50570 If x is an integer, is 3x + 7 even? [#permalink] ### Show Tags 15 Nov 2017, 08:44 00:00 Difficulty: 25% (medium) Question Stats: 86% (01:16) correct 14% (01:48) wrong based on 75 sessions ### HideShow timer Statistics If x is an integer, is 3x + 7 even? (1) (x – 5)(x + 1) = 0 (2) x is a factor of 105. _________________ Senior Manager Joined: 06 Jul 2016 Posts: 372 Location: Singapore Concentration: Strategy, Finance Re: If x is an integer, is 3x + 7 even? [#permalink] ### Show Tags 15 Nov 2017, 08:50 Bunuel wrote: If x is an integer, is 3x + 7 even? Question is essentially asking if x is odd? Quote: (1) (x – 5)(x + 1) = 0 x = -1,5 in both cases x is odd => 3x + 7 is even. Sufficient. Quote: (2) x is a factor of 105. x = 1,3,5,7,21,105 in all these cases x is odd => 3x + 7 is even. Sufficient. D is the answer. _________________ Put in the work, and that dream score is yours! DS Forum Moderator Joined: 21 Aug 2013 Posts: 1365 Location: India Re: If x is an integer, is 3x + 7 even? [#permalink] ### Show Tags 15 Nov 2017, 10:06 We are given that x is an integer. So if x is odd, 3x will be odd and hence 3x+7 will be even. And if x is even, 3x will be even and hence 3x+7 will be odd. So we just need to know whether x is odd or even. (1) (x-5)(x+1) = 0 this tells us that either x=5 or x=-1. Both these values are odd. So 3x+7 will be even in either case. Sufficient. (2) x is a factor of 105. Since 105 is an odd number, ALL its factors have to be odd. So no matter which of its factors x is, x will be odd. So 3x+7 will be even in either case. Sufficient. Hence D answer Intern Joined: 26 Sep 2017 Posts: 3 Re: If x is an integer, is 3x + 7 even? [#permalink] ### Show Tags 15 Nov 2017, 19:14 I would say D. If we know that x= odd integer, then we are good to go. Manager Joined: 20 Feb 2017 Posts: 166 Location: India Concentration: Operations, Strategy WE: Engineering (Other) Re: If x is an integer, is 3x + 7 even? [#permalink] ### Show Tags 15 Nov 2017, 20:06 Basic Properties : odd X odd = odd odd + odd = even Number of factors : if N = a^p X b^q X c^ r (where a,b and c are prime factors) then no. of factors = (p+1)(q+1)(r+1) From statement 1 : (x – 5)(x + 1) = 0 => x can be either 5 or -1 either case are odd (-1 is an odd number)( All negative integers can either be odd or even) Thus substituting these values will give 3x+7 as even. hence Sufficient From statement 2 : X is a factor of 105. the factors of 105 are : 1,3,5,7,15,21,35,105 (there are 8 factors of 105.) since all these factors are odd, the expression 3x+7 will be even. Hence sufficient. As both the options are sufficient the answer should be D _________________ If you feel the post helped you then do send me the kudos (damn theya re more valuable than$)

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6499
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x is an integer, is 3x + 7 even?  [#permalink]

### Show Tags

16 Nov 2017, 22:18
Bunuel wrote:
If x is an integer, is 3x + 7 even?

(1) (x – 5)(x + 1) = 0

(2) x is a factor of 105.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the numbers of variables and equations.

The question that $$3x + 7$$ is even is equivalent to the statement that $$x$$ is odd, because if $$x$$ is odd, $$3x + 7$$ is even and if $$x$$ is even, $$3x + 7$$ is odd.

Condition 1)
$$(x-5)(x+1)=0$$ is equivalent to $$x = 5$$ or $$x = -1$$.
Both of them are odd.
Thus this is sufficient.

Condition 2)
The condition 2) that $$x$$ is a factor of $$105$$ means all factors are odd since $$105$$ doesn't have a factor $$2$$.
Thus $$x$$ must be odd.
Thus this is sufficient, too.

Therefore, the answer is D.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59 % chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: If x is an integer, is 3x + 7 even? &nbs [#permalink] 16 Nov 2017, 22:18
Display posts from previous: Sort by

# If x is an integer, is 3x + 7 even?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.