Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Oct 2014, 11:11

Going on right now!

Interview Invites from Chicago - Booth | Join the chat room for Live Updates.


Close

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x > 1, what is the value of integer x?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 16 Mar 2011
Posts: 179
Followers: 1

Kudos [?]: 25 [0], given: 13

If x > 1, what is the value of integer x? [#permalink] New post 18 Mar 2011, 13:07
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

32% (02:16) correct 68% (00:54) wrong based on 36 sessions
If x > 1, what is the value of integer x?

(1) There are x unique factors of x.
(2) The sum of x and any prime number larger than x is odd.

[Reveal] Spoiler:
This is the answer in the book but I just don't get it..

Statement (1) tells us that there are x unique factors of x. In order for this to be true,
EVERY integer between 1 and x, inclusive, must be a factor of x. Testing numbers, we can
see that this property holds for 1 and for 2, but not for 3 or for 4. In fact, this property does
not hold for any higher integer, because no integer x above 2 is divisible by x-I. Therefore,
x = 1 or 2. However, the original problem stem told us that x > 1, so x must equal 2.
SUFFICIENT.
Statement (2) tells us that x plus any prime number larger than x is odd. Since x > 1, x must
equal at least 2, so this includes only prime numbers larger than 2. Therefore, the prime
number is odd, and x is even. However, this does not tell us which even number x could be.
INSUFFICIENT. The correct answer is (A): Statement (1) is sufficient to answer the ques-
tion, but Statement (2) is insufficient.


OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-1-what-is-the-value-of-integer-x-110661.html
[Reveal] Spoiler: OA
Kaplan Promo CodeKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
Manager
Manager
avatar
Joined: 05 Jul 2010
Posts: 205
Followers: 1

Kudos [?]: 11 [0], given: 18

Re: If x > 1, what is the value ofinteger x? [#permalink] New post 18 Mar 2011, 13:39
even i was confuse for the first time. But I think the answer explainations tells, if say x = 5, then it needs 5 unique factor, but for 5 it is only 1 and 5. For 4 it is 1,2, and 4. So for any number greater than 2 there is no way you can have as many factor as the number itself. hence it should be 2. I hope I interpreted right, but as I said it is a confusing question.
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 768
Followers: 14

Kudos [?]: 58 [0], given: 42

CAT Tests
Re: If x > 1, what is the value ofinteger x? [#permalink] New post 18 Mar 2011, 14:24
You seemed to have solved the problem by yourself /posted the solution, then what are you confused about?

Please be clear in what you need help with..Then we might be able to assist you better.
1 KUDOS received
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 768
Followers: 14

Kudos [?]: 58 [1] , given: 42

CAT Tests
Re: If x > 1, what is the value ofinteger x? [#permalink] New post 18 Mar 2011, 14:34
1
This post received
KUDOS
Well here is how i would do it.

1. x has x factors

meaning if you take any integer , that should have that many factors

1 has 1 factor (i.e 1 , meets the criteria)
2 has 2 factors (i.e 1 and 2)
3 has 2 factors (i.e 1 and 3, doesnt meet the criteria, to satisfy this should have had 3 factors)

take any other number lets say 17 , to meet this criteria this should have 17 factors. not satisfied.

so only 1 and 2 satisfies the condition, then again in the question it says x has to be greater than 1 . so that rules out 1 . Hence x =2 .

So sufficient.
2. x + ( prime >x )has to be odd

primes (2,3,5,7,11....)

2+ (prime >2)
= 2 +3 = odd (x could be 3)
2+5 = odd (x could be 5)

Not sufficient as there are more possible values for x.

Answer is A.
Expert Post
3 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4877
Location: Pune, India
Followers: 1154

Kudos [?]: 5369 [3] , given: 165

Re: If x > 1, what is the value ofinteger x? [#permalink] New post 18 Mar 2011, 18:13
3
This post received
KUDOS
Expert's post
l0rrie wrote:

If x > 1, what is the value of integer x?

(1) There are x unique factors of x.
(2) The sum of x and any prime number larger than x is odd.



First of all, it is not a very straight forward question. Definitely needs some thinking so relax...

Ques: What is the value of x?
So we are looking for a single value of x.

First consider statement 2 since it is easier.
x + prime number greater than x = odd
There will be many many prime numbers greater than x. All prime numbers are odd except 2. So if you can add any prime number greater than x to x and get an odd number, it means x must be even. (because Even + Odd = Odd)
So all statement 2 tells you is that x is even. It could be 2 or 4 or 6 etc

Now look at statement 1.
There are x unique factors of x. Think of the first number greater than 1.
2 has 2 unique factors: 1 and 2 ( 2 is a prime number)
What about 3? It has 2 unique factors: 1 and 3 (a prime number)
4 has 3 unique factors: 1, 2 , 4
Is it possible that any greater number x has x unique factors? No. Why?
For x to have x unique factors, each number from 1 to x must be a factor of x. Say if 10 had 10 unique factors, each number 1, 2, 3, 4, 5..., 9,10 would have to be a factor of 10 (because factors are always positive integers)
But can 9 be a factor of 10 i.e. can (x-1) be a factor of x? No. 2 consecutive positive integers share only one common factor i.e. 1. Why? Check out the post given below for the answer:
question-from-practice-exam-78880.html#p847817

So statement 1 is enough to tell us that x is 2.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
avatar
Joined: 16 Mar 2011
Posts: 179
Followers: 1

Kudos [?]: 25 [0], given: 13

Re: If x > 1, what is the value ofinteger x? [#permalink] New post 19 Mar 2011, 02:34
Thanks everyone!! Really much appreciated, I get it now.. This has been extremely helpful.. I need to do a GMAT but it's been 6 years since I've studied maths.. And even in high school I was horrible so i'm really stressed about this.. Hopefully I'll get better haha.. Again, thanks!
CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2834
Followers: 207

Kudos [?]: 42 [0], given: 0

Premium Member
Re: If x > 1, what is the value ofinteger x? [#permalink] New post 19 Sep 2013, 13:37
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23398
Followers: 3610

Kudos [?]: 28837 [0], given: 2854

Re: If x > 1, what is the value of integer x? [#permalink] New post 19 Sep 2013, 23:34
Expert's post
If x>1, what is the value of integer x?

(1) There are x unique factors of x --> x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x, inclusive but x can not be divisible by x-1 unless x=2, for example 3 is not divisible by 2, 4 is not divisible by 3, etc, but 2 is divisible by 1 (other value of x which has x distinct positive factors (1) is excluded by the stem as x>1). So this statement implies that x=2. Sufficient.

(2) The sum of x and any prime number larger than x is odd --> x+prime=odd, now as x itself is more than 1 then prime more than x cannot be 2 thus it's odd and we have x+odd prime=odd --> x=even, so x could be ANY even number. Not sufficient.

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-1-what-is-the-value-of-integer-x-110661.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: If x > 1, what is the value of integer x?   [#permalink] 19 Sep 2013, 23:34
    Similar topics Author Replies Last post
Similar
Topics:
3 If x>1, what is the value of integer x? 1) There are x jgonza8 5 10 Aug 2011, 17:45
2 If x > 1, what is the value of integer x? (1) There are x Silver89 6 01 Jul 2011, 11:39
3 Experts publish their posts in the topic If x>1, what is the value of integer x? GMATD11 15 10 Mar 2011, 05:50
2 Experts publish their posts in the topic If 8x > 4 + 6x, what is the value of the integer x? (1) 6 heyholetsgo 14 18 Aug 2010, 09:06
If 8x > 4 + 6x, what is the value of the integer x? (1) 6 beckee529 5 14 Oct 2007, 13:41
Display posts from previous: Sort by

If x > 1, what is the value of integer x?

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.