Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
46% (02:02) correct
54%
(02:10)
wrong
based on 1015
sessions
History
Date
Time
Result
Not Attempted Yet
If x is a positive integer, is x! + (x + 1) a prime number?
(1) x < 10
(2) x is even
(1) x < 10
(2) x is even
Updated on: 08 May 2015, 04:36
Originally posted by EgmatQuantExpert on 08 May 2015, 02:17.
Last edited by EgmatQuantExpert on 08 May 2015, 04:36, edited 1 time in total.
Last edited by EgmatQuantExpert on 08 May 2015, 04:36, edited 1 time in total.
Kudos
Bookmarks
Radhika11
Dear Radhika11
Here's an alternate solution.
We'll first analyze the question statement and only then go to St. 1 and 2.
Given: x is a positive integer. So, possible values of x: 1, 2, 3, 4 . . .
To find: If x! + x + 1 is Prime
Analysis:
For x = 1, x! = 1
And, x! + x +1 = 1 + 1 + 1 = 3, which is a Prime number
For x > 1,
x! will always be an even number (Because, x! contains the product of consecutive integers. So, this product will have Even AND odd terms. We know that when an even number is multiplied with anything, the product is always even)
So, the sum (x! + x + 1) = (An even number + x + Odd number) = (Odd number + X)
Even for the lowest possible value of x (x = 1), the value of the sum (x! + x + 1) was equal to 3.
So, for x > 1, the value of this sum is definitely going to be greater than 3.
And, we know that all Prime numbers greater than 2 are odd.
So, the sum (Odd number +X) can be prime only if first, this sum is an odd number.
That is, if, X is an even number.
So, for x > 1, x being an even number is a NECESSARY condition for the sum (x! + x + 1) to be prime.
But is it a SUFFICIENT condition? That is, can you say that if x is even, that must mean that the sum (x! + x + 1) will be prime?
Let's see:
x x! + x + 1
2 2! + 2 + 1 = 7 (Prime)
4 4! + 4 + 1 = 29 (Prime)
6 6! + 6 + 1 = 727 (Prime)
8 8! + 9 (both terms in this sum are divisible by 3) (NOT Prime)
Thus, we see that for some even values of x, the sum (x! + x + 1) will be Prime and for others, it will not be.
With this understanding, let's now look at the two statements:
Statement 1: x < 10
As per this statement, x can be even (=> some possibility of the sum (x! + x + 1) to be prime)
or x can be odd (=> NO possibility of the sum (x! + x + 1) to be prime)
Clearly not sufficient.
Statement 2: x is even
As illustrated in our analysis of the question statement, x being Even is not a sufficient condition for the sum to be prime.
Not Sufficient.
Statement 1 + 2
=> x is an even number < 10
As we saw in our analysis above, for x = 8, the sum is not prime. For all other possible values of x, the sum is prime.
Not Sufficient.
Therefore, correct answer: Option E
(Note: Had Statement 1 been: x < 8, then the correct answer would have been Option C)
I hope this helped!
Japinder
17 Jul 2007, 02:34
Kudos
Bookmarks
Consider 8! + 8 + 1. As both 8! and 8+1 are multiples of 3, so is 8! + 8 + 1. Thus (2) is not sufficient
