It is currently 23 Jan 2018, 19:57

### 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 June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43380
If x is an integer, is 3x + 7 even? [#permalink]

### Show Tags

15 Nov 2017, 08:44
00:00

Difficulty:

35% (medium)

Question Stats:

85% (00:43) correct 15% (00:46) wrong based on 64 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.
[Reveal] Spoiler: OA

_________________
Senior Manager
Joined: 06 Jul 2016
Posts: 437
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.

_________________

Put in the work, and that dream score is yours!

DS Forum Moderator
Joined: 21 Aug 2013
Posts: 681
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.

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.
Intern
Joined: 20 Feb 2017
Posts: 44
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
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4716
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.

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

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