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

 It is currently 20 Aug 2019, 15:50 ### 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
Your Progress

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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # If x is a positive integer greater than 1, is x! + x + 1 a p

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager  Joined: 21 Oct 2013
Posts: 414
If x is a positive integer greater than 1, is x! + x + 1 a p  [#permalink]

### Show Tags

1
10 00:00

Difficulty:   55% (hard)

Question Stats: 63% (01:50) correct 37% (01:42) wrong based on 480 sessions

### HideShow timer Statistics

If x is a positive integer greater than 1, is x! + x + 1 a prime number?

(1) x < 10

(2) x is odd

OE
(1) INSUFFICIENT
If x = 2: 2! + (2 + 1) = 5, which is prime.
If x = 3: 3! + (3 + 1) = 6 + (3 + 1) = 10, which is not prime.

(2) SUFFICIENT:
If x = 3: 3! + (3 + 1) = 10, which is not prime.
If x = 5: 5! + (5 + 1) = (5 × 4 × 3 × 2 × 1) + 6.
This expression must be divisible by 3, since both of its terms are divisible by 3.
Furthermore it must be even, because both terms are even.
Therefore, it is not a prime number.
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Sep 2009
Posts: 57155
Re: If x is a positive integer greater than 1, is x! + x + 1 a p  [#permalink]

### Show Tags

2
5
goodyear2013 wrote:
If x is a positive integer greater than 1, is x! + x + 1 a prime number?

(1) x < 10

(2) x is odd

OE
(1) INSUFFICIENT
If x = 2: 2! + (2 + 1) = 5, which is prime.
If x = 3: 3! + (3 + 1) = 6 + (3 + 1) = 10, which is not prime.

(2) SUFFICIENT:
If x = 3: 3! + (3 + 1) = 10, which is not prime.
If x = 5: 5! + (5 + 1) = (5 × 4 × 3 × 2 × 1) + 6.
This expression must be divisible by 3, since both of its terms are divisible by 3.
Furthermore it must be even, because both terms are even.
Therefore, it is not a prime number.

If x is a positive integer greater than 1, is x! + x + 1 a prime number?

(1) x < 10.

If x=2, then x! + x + 1 = 5 = prime.
If x=3, then x! + x + 1 = 10, not a prime.

Not sufficient.

(2) x is odd. So, x is an odd integer greater than 1: 3, 5, 7, ... In this case x! + x + 1 = even + odd + odd = even > 2, not a prime. Sufficient.

Answer: B.
_________________
##### General Discussion
Intern  Joined: 07 Jul 2014
Posts: 12
Re: If x is a positive integer greater than 1, is x! + x + 1 a p  [#permalink]

### Show Tags

Let X<10, then
for the x=2
x! + x + 1 = 5 = prime number
& for the x=3
x! + x + 1 = 10, not a prime number
So it is not possible if x is a positive integer greater than 1, is x! + x + 1 a prime number..
Manager  Joined: 20 Jan 2014
Posts: 139
Location: India
Concentration: Technology, Marketing
Re: If x is a positive integer greater than 1, is x! + x + 1 a p  [#permalink]

### Show Tags

Bunuel wrote:
goodyear2013 wrote:
If x is a positive integer greater than 1, is x! + x + 1 a prime number?

(1) x < 10

(2) x is odd

OE
(1) INSUFFICIENT
If x = 2: 2! + (2 + 1) = 5, which is prime.
If x = 3: 3! + (3 + 1) = 6 + (3 + 1) = 10, which is not prime.

(2) SUFFICIENT:
If x = 3: 3! + (3 + 1) = 10, which is not prime.
If x = 5: 5! + (5 + 1) = (5 × 4 × 3 × 2 × 1) + 6.
This expression must be divisible by 3, since both of its terms are divisible by 3.
Furthermore it must be even, because both terms are even.
Therefore, it is not a prime number.

If x is a positive integer greater than 1, is x! + x + 1 a prime number?

(1) x < 10.

If x=2, then x! + x + 1 = 5 = prime.
If x=3, then x! + x + 1 = 10, not a prime.

Not sufficient.

(2) x is odd. So, x is an odd integer greater than 1: 3, 5, 7, ... In this case x! + x + 1 = even + odd + odd = even > 2, not a prime. Sufficient.

Answer: B.

Is there any other way , apart from testing number. I solved it correctly but took more than 2 min.
_________________
Consider +1 Kudos Please Intern  Joined: 30 Nov 2015
Posts: 8
Re: If x is a positive integer greater than 1, is x! + x + 1 a p  [#permalink]

### Show Tags

(1) x < 10.

If x=2, then f(x)= 5 => prime
If x=3, then f(x) = 10 => not prime

Not suff.

(2) x is odd.

x! + x + 1 = x(x-1)(x-2)(x-3)...(x-n) + x + 1 (with n always is even)

=> x[1 + (x-1)(x-2)(x-3)...(x-n)] + 1

We have (x-1) always even, (x-2) odd, (x-3) even, ... (x-n)odd => (x-1)(x-2)(x-3)...(x-n) = even

=> [1 + (x-1)(x-2)(x-3)...(x-n)] = odd (1+ even)
=> x[1 + (x-1)(x-2)(x-3)...(x-n)] = odd (odd * odd)
=> x[1 + (x-1)(x-2)(x-3)...(x-n)] + 1 = even (odd + 1)

=> suff.

I just write in detail, it would be very quick to infer that.
Board of Directors P
Joined: 17 Jul 2014
Posts: 2531
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: If x is a positive integer greater than 1, is x! + x + 1 a p  [#permalink]

### Show Tags

1
goodyear2013 wrote:
If x is a positive integer greater than 1, is x! + x + 1 a prime number?

(1) x < 10

(2) x is odd

I got to B in ~1 minute..
1. x<10 -> 1<x<10
suppose x=2.
2+2+1 = 5
suppose x=3
3! = 6.
6+3+1 = 10 - not prime.

2 outcomes - insufficient.

2. x is odd.
since x can't be 1, x! of any odd number will always be even.
since x is odd, x+1 will always be even
now..x!(even) + x+1(even) = even.
even number can't be a prime number.
_________________
Intern  B
Joined: 24 Feb 2017
Posts: 32
Re: If x is a positive integer greater than 1, is x! + x + 1 a p  [#permalink]

### Show Tags

definitely no. this is why option b ?

please help anyone   Math Expert V
Joined: 02 Sep 2009
Posts: 57155
If x is a positive integer greater than 1, is x! + x + 1 a p  [#permalink]

### Show Tags

mkumar26 wrote:
definitely no. this is why option b ?

please help anyone   This is an YES/NO data sufficiency question. A statement is sufficient if you can get a definite YES or definite NO answer to the question asked.

So, (2) is sufficient because it gives a definite NO answer to the question: x! + x + 1 is NOT a prime.
_________________
Intern  B
Joined: 24 Feb 2017
Posts: 32
Re: If x is a positive integer greater than 1, is x! + x + 1 a p  [#permalink]

### Show Tags

thank bunuel sir !    Manager  G
Joined: 26 Dec 2015
Posts: 242
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
Re: If x is a positive integer greater than 1, is x! + x + 1 a p  [#permalink]

### Show Tags

him1985 wrote:
Bunuel wrote:
goodyear2013 wrote:
If x is a positive integer greater than 1, is x! + x + 1 a prime number?

(1) x < 10

(2) x is odd

OE
(1) INSUFFICIENT
If x = 2: 2! + (2 + 1) = 5, which is prime.
If x = 3: 3! + (3 + 1) = 6 + (3 + 1) = 10, which is not prime.

(2) SUFFICIENT:
If x = 3: 3! + (3 + 1) = 10, which is not prime.
If x = 5: 5! + (5 + 1) = (5 × 4 × 3 × 2 × 1) + 6.
This expression must be divisible by 3, since both of its terms are divisible by 3.
Furthermore it must be even, because both terms are even.
Therefore, it is not a prime number.

If x is a positive integer greater than 1, is x! + x + 1 a prime number?

(1) x < 10.

If x=2, then x! + x + 1 = 5 = prime.
If x=3, then x! + x + 1 = 10, not a prime.

Not sufficient.

(2) x is odd. So, x is an odd integer greater than 1: 3, 5, 7, ... In this case x! + x + 1 = even + odd + odd = even > 2, not a prime. Sufficient.

Answer: B.

Is there any other way , apart from testing number. I solved it correctly but took more than 2 min.

The main takeaways from this question is this: 2 is the ONLY number (apart from 1) that, when expressed as a factorial, will give you a prime # (when you add "x" and "1"). Why, you ask? B/c any number > 2 will include "2" in its prime factorization. Meaning, if you have 3! = 3x2; or 5! = 5x4x3x2.

ALSO, any number multiplied by an even will be EVEN. and the ONLY EVEN PRIME = 2.

Therefore, (1) = insufficient b/c x<10 includes 2 (prime) as well as 3, 4, 5, 6, 7, 8, 9 (which are all NOT prime).
(2) is sufficient b/c we know "1" cannot be included here, so the only numbers to play with are: 3, 5, 7, 9 -- which are all NOT prime. This is sufficient b/c we can safely say "x! + x + 1 is NOT PRIME" under these conditions
Non-Human User Joined: 09 Sep 2013
Posts: 12053
Re: If x is a positive integer greater than 1, is x! + x + 1 a p  [#permalink]

### Show Tags

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.
_________________ Re: If x is a positive integer greater than 1, is x! + x + 1 a p   [#permalink] 23 Dec 2018, 10:34
Display posts from previous: Sort by

# If x is a positive integer greater than 1, is x! + x + 1 a p

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  