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

 It is currently 19 Aug 2018, 12:19

### 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

# If x is an integer, is (x^2+1)(x+5) an even number?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 20 Oct 2010
Posts: 7
If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

Updated on: 30 Jan 2016, 02:36
9
14
00:00

Difficulty:

15% (low)

Question Stats:

76% (00:55) correct 24% (00:44) wrong based on 789 sessions

### HideShow timer Statistics

If x is an integer, is (x^2 + 1)(x + 5) an even number?

(1) x is an odd number

(2) Each prime factor of x^2 is greater than 7

Originally posted by mybudgie on 04 Nov 2010, 18:37.
Last edited by Bunuel on 30 Jan 2016, 02:36, edited 2 times in total.
Edited the question
Math Expert
Joined: 02 Sep 2009
Posts: 48037
If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

04 Nov 2010, 19:11
8
12
If x is an integer, is (x^2+1)(x+5) an even number?

The product of 2 integers to be even at least one of them must be even. So if $$x$$ is an odd number then $$(x^2+1)(x+5)=even*even=even$$.

(1) x is an odd number. Sufficient.

(2) Each prime factor of x^2 is greater than 7 --> first of all, prime factors of $$x^2$$ are the same as the prime factors of $$x$$: exponentiation does not "produce" new prime factors. So, each prime of $$x$$ is greater than 7, which means that 2 is not a prime factor of $$x$$, thus $$x$$ is an odd number. Sufficient.

_________________
##### General Discussion
Manager
Joined: 02 Oct 2010
Posts: 109
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

19 Dec 2010, 23:45
I could not understand the reason for the explanation of teh second statement...
Can you plsss please explain in a elaborative way...
Math Expert
Joined: 02 Sep 2009
Posts: 48037
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

20 Dec 2010, 01:04
6
1
jullysabat wrote:
I could not understand the reason for the explanation of teh second statement...
Can you plsss please explain in a elaborative way...

Exponentiation does not "produce" new prime factors means that the prime factors of a positive integer x and the prime factors of x^n (where n is a positive integer) are the same. For example if x=12=2^2*3 then it has two prime factors 2 and 3 and x^2=144=2^4*3^2 also has the same two prime factors 2 and 3.

Now, (2) says: each prime factor of x^2 is greater than 7 --> the prime factors of $$x^2$$, or which is the same the prime factors of $$x$$ can be 11, 13, 17, ... So 2<7 is not a prime factor of $$x$$ which means that $$x$$ must be odd, and as we concluded if $$x$$ is an odd number then $$(x^2+1)(x+5)=even*even=even$$. Sufficient.

Hope it's clear.
_________________
Manager
Joined: 02 Oct 2010
Posts: 109
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

20 Dec 2010, 11:43
Bunuel wrote:
jullysabat wrote:
I could not understand the reason for the explanation of teh second statement...
Can you plsss please explain in a elaborative way...

Exponentiation does not "produce" new prime factors means that the prime factors of a positive integer x and the prime factors of x^n (where n is a positive integer) are the same. For example if x=12=2^2*3 then it has two prime factors 2 and 3 and x^2=144=2^4*3^2 also has the same two prime factors 2 and 3.

Now, (2) says: each prime factor of x^2 is greater than 7 --> the prime factors of $$x^2$$, or which is the same the prime factors of $$x$$ can be 11, 13, 17, ... So 2<7 is not a prime factor of $$x$$ which means that $$x$$ must be odd, and as we concluded if $$x$$ is an odd number then $$(x^2+1)(x+5)=even*even=even$$. Sufficient.

Hope it's clear.

Hey thanks now its clear....
I have also given a kudos to you...
Manager
Joined: 14 Feb 2011
Posts: 179
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

23 Apr 2011, 16:19
2
agdimple333 wrote:
if x is an integer, is (x^2 + 1) (x + 5) an even number?

(1) x is an odd number
(2) each prime factor of x ^ 2 is greater than 7

Statement 1 - if x is odd then x+5 is even and hence the expression is even, sufficient
Statement 2 - if each prime factor of x^2 is greater than 7, then all factors are odd and hence x^2 is odd and hence x^2+1 is even making the expression even, sufficient

Retired Moderator
Joined: 16 Nov 2010
Posts: 1458
Location: United States (IN)
Concentration: Strategy, Technology
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

24 Apr 2011, 22:04
(1)

If x is odd, (X+5) is even. Hence (x^2 + 1) (x + 5) is an even number.

(2)

If X^2 has each prime factor greater than 7, x^2 is odd, and then x is odd too. (x^2 does not have 2 as factor)

By same reasoning as above, (x^2 + 1) (x + 5) is an even number.

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1124
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

24 Apr 2011, 23:43
Straight D it is.
Only thing to be considered here is each of the prime numbers greater than 3 is either 6x+1 or 6x-1. Hence necessarily an odd number.
VP
Joined: 24 Jul 2011
Posts: 1459
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

29 Jul 2011, 02:56

We need to state if we have enough information to conclude whether (x^2 +1) (x+5) is an even number.

From statement (1), if x is odd, then x+5 will be even. Therefore (x^2 +1) (x+5) will be (odd +1)*(odd+5) = even * even = even

From statement (2), we know that each prime factor of x^2 is greater than 7. This rules out 2 as being a factor of x^2. Since 2 is the only prime that is also even, this means that x^2 can therefore be expressed entirely as a product of primes, all of which are odd. Therefore x^2 is odd. Therefore (x^2 + 1) is even. Therefore (x^2 + 1) (x+5) is even.

So (D).
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Retired Moderator
Joined: 20 Dec 2010
Posts: 1877
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

29 Jul 2011, 04:01
1
siddhans wrote:
If x is an integer, is (x^2 +1) (x+5) an even number?
(1) x is an odd number
(2) Each prime factor of x^2 is greater than 7

Is $$x$$ even?
OR
Is $$x$$ odd?

(1) $$x$$ is odd. Sufficient.
(2) All prime factors of $$x^2$$ is greater than 7.
Rule: If a number doesn't have at least one 2 as its prime factor, the number will be odd.
Statement 2 is a convoluted way to say that there is NO 2 as a prime factor of $$x$$
OR
$$x$$ is odd. Same as statement 1.
Sufficient.

Ans: "D"
_________________
Current Student
Joined: 08 Jan 2009
Posts: 309
GMAT 1: 770 Q50 V46
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

29 Jul 2011, 04:29
is (x^2 +1) (x+5) an even

To be even, we need one of the brackets to be even. In both brackets, we are adding odd numbers (1 and 5), hence, if x or x^2 is odd, result will be even.

Restate: is x odd?

1) Sufficient. Plug in a couple numbers as well, looks good.
2) x^2 does not have a two as a factor, as 2 < 7. x is odd.

D
Intern
Joined: 15 Mar 2010
Posts: 9
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

29 Jul 2011, 06:11
If x is an integer, is (x^2 +1) (x+5) an even number?
(1) x is an odd number
(2) Each prime factor of x^2 is greater than 7

Ans: 1. Stmt 1 suff as an odd number squared will also be an odd number and sum of two odd numbers will give an even number. Without checking further, the product will also be even. Suff

Stmt 2: Prime factor greater than 7, then only odd factors, therefore, an odd integer. Following the same logic as derived in stmt1, product will always give an even number. Suff

D
Manager
Joined: 13 Jul 2011
Posts: 99
Concentration: Operations, Strategy
GMAT 1: 680 Q46 V37
WE: Engineering (Telecommunications)
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

12 Dec 2011, 10:40
I have one question here,
what if x = -5? in that case (-5+5) = 0 and hence the equation's value ll be 0 right ? is 0 too considered as even ?
VP
Joined: 24 Jul 2011
Posts: 1459
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

12 Dec 2011, 20:02
Yes,0 is also an even integer
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Intern
Joined: 16 Dec 2011
Posts: 42
GMAT Date: 04-23-2012
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

Updated on: 23 May 2013, 04:53
2
If x is an integer, is (x^2+1)(x+5) an even number?

(1) x is an odd number

(2) Each prime factor of x^2 is greater than 7

Originally posted by pbull78 on 28 Jan 2012, 05:56.
Last edited by Bunuel on 23 May 2013, 04:53, edited 2 times in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 48037
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

28 Jan 2012, 06:02
2
3
pbull78 wrote:
If x is an integer, is (x2+1)(x+5) an even number?
1). x is an odd number. 2). each prime factor of x2 is greater than 7

although discussed but still need explanation of this not able to understand .......... 2) each prime factor of x2 is greater than 7

If x is an integer, is (x^2+1)(x+5) an even number?

(1) x is an odd number --> (x^2+1)(x+5)=(odd+odd)(odd+odd)=even*even=even. Sufficient.

(2) Each prime factor of x^2 is greater than 7 --> 2 is not a prime factor of x^2, so not a prime factor of x as well --> x=odd --> the same as above. Sufficient.

_________________
Intern
Joined: 16 Dec 2011
Posts: 42
GMAT Date: 04-23-2012
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

28 Jan 2012, 06:20
i copied this question from source as it is

but still i am not able to understand this point

2) Each prime factor of x^2 is greater than 7 --> 2 is not a prime factor of x^2, so not a prime factor of x as well --> x=odd --> the same as above.
Can u expalin with example ?
Math Expert
Joined: 02 Sep 2009
Posts: 48037
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

28 Jan 2012, 06:33
2
1
pbull78 wrote:
i copied this question from source as it is

but still i am not able to understand this point

2) Each prime factor of x^2 is greater than 7 --> 2 is not a prime factor of x^2, so not a prime factor of x as well --> x=odd --> the same as above.
Can u expalin with example ?

Each prime factor of x^2 is greater than 7 --> as 2 is less than 7, then 2 is not a prime factor of x^2, which means that 2 is not a prime of x as well, because if it is a prime of x then x^2 would also have it.

Or:
Each prime factor of x^2 is greater than 7 --> as 2 is less than 7, then 2 is not a prime factor of x^2, which means that x^2 is an odd number --> x^2=odd --> x^2=x*x=odd --> x=odd.

Or:
Each prime factor of x^2 is greater than 7 --> primes more than 7 are odd (in fact the only even prime is 2) --> x is a product of some odd primes more than 7 --> x^2 is an odd number --> x=odd.

Hope it's clear.
_________________
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2649
GRE 1: Q169 V154
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

01 Jan 2017, 17:07
Here We really need to find the even / odd nature of x here
Here both the statements are sufficient
if x is odd=> sufficient
x^2 has all prime factors >7 => x^2 will be odd => x will be odd to
hence D

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Senior Manager
Joined: 25 Mar 2013
Posts: 263
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: If x is an integer, is (x^2+1)(x+5) an even number?  [#permalink]

### Show Tags

23 Jan 2017, 11:36
(x^2+1)(x+5) an even number
1, x = odd number
oddxodd = odd
odd + 1 = even
odd + odd = even
even x even = even number always
2, x^2 > 7
All x values are ODD other than 2
D
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Re: If x is an integer, is (x^2+1)(x+5) an even number? &nbs [#permalink] 23 Jan 2017, 11:36

Go to page    1   2    Next  [ 25 posts ]

Display posts from previous: Sort by

# Events & Promotions

 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®.