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

It is currently 22 Oct 2014, 19:50

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

M04#07 If x is an integer, what is the value of x?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 10 Jan 2014
Posts: 24
Followers: 0

Kudos [?]: 1 [0], given: 6

M04#07 If x is an integer, what is the value of x? [#permalink] New post 26 Feb 2014, 01:45
If x is an integer, what is the value of x?
(1) |23x| is a prime number.

(2) 2√x² is a prime number.








___________________________________________________________




My choice was B although I knew it was probably E (which it turned out it was). Here's my problem with statement 2: if we know what that 2√x²=prime number, then why can't we conclude that x=1? Let's assume that x= -1, then according to the equation we would have 2√x²=positive value. but knowing that x= -1 we know that the equation would become 2*(-1)= -2 # 2 (since we know we would have to use the negative root since x= -1). but from statement 2 we know that it must be positive so x can only be positive 1. I know that technically the definition for √x² is |x| but in this case it does not make sense for me. for statement 1 it's no problem, since |x| dictates to multiply by (-1) if negative, but in the case of statement 2, x should only be positive, since otherwise we would have to take the negative square root and then the result would not be positive anymore. I hope I made it clear why I am confused. Maybe someone could help me :)

cheers,

Max

Last edited by damamikus on 26 Feb 2014, 02:23, edited 1 time in total.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23381
Followers: 3607

Kudos [?]: 28803 [0], given: 2849

Re: M04#07 If x is an integer, what is the value of x? [#permalink] New post 26 Feb 2014, 01:50
Expert's post
damamikus wrote:
If x is an integer, what is the value of x?
(1) |23x| is a prime number.

(2) 2√x² is a prime number.


My choice was B although I knew it was probably E (which it turned out it was). Here's my problem with statement 2: if we know what that 2√x²=prime number, then why can't we conclude that x=1? Let's assume that x= -1, then according to the equation we would have 2√x²=positive value. but knowing that x= -1 we know that the equation would become 2*(-1)= -2 # 2 (since we know we would have to use the negative root since x= -1). but from statement 2 we know that it must be positive so x can only be positive 1. I know that technically the definition for √x² is |x| but in this case it does not make sense for me. for statement 1 it's no problem, since |x| dictates to multiply by (-1) if negative, but in the case of statement 2, x should only be positive, since otherwise we would have to take the negative square root and then the result would not be positive anymore. I hope I made it clear why I am confused. Maybe someone could help me :)

cheers,

Max


If x=-1, then 2\sqrt{x^2}=2\sqrt{(-1)^2}=2\sqrt{1}=2.

Complete solution:

If x is an integer, what is the value of x?

(1) |23x| is a prime number. From this statement it follows that x=1 or x=-1. Not sufficient.

(2) 2\sqrt{x^2} is a prime number. The same here: x=1 or x=-1. Not sufficient.

(1)+(2) x could be 1 or -1. Not sufficient.

Answer: E.

Hope it's clear.
_________________

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

Intern
Intern
avatar
Joined: 10 Jan 2014
Posts: 24
Followers: 0

Kudos [?]: 1 [0], given: 6

Re: M04#07 If x is an integer, what is the value of x? [#permalink] New post 26 Feb 2014, 02:07
I think i get it now: since 2√x² must be positive, i am taking the positive square root out of the square-root expression x². but the value that lead to the positive expression inside the square root could be negative or positive. --> x²=z --> 2√z=positive, hence z=positive. but what lead to z being positive (--> x ) could be either negative or positive, since in both cases z would be positive. hope this reasoning is correct :)

thanks!
Manager
Manager
User avatar
Joined: 09 Nov 2013
Posts: 78
Followers: 1

Kudos [?]: 3 [0], given: 2

Re: M04#07 If x is an integer, what is the value of x? [#permalink] New post 03 Mar 2014, 04:49
Bunuel wrote:
damamikus wrote:
If x is an integer, what is the value of x?
(1) |23x| is a prime number.

(2) 2√x² is a prime number.


My choice was B although I knew it was probably E (which it turned out it was). Here's my problem with statement 2: if we know what that 2√x²=prime number, then why can't we conclude that x=1? Let's assume that x= -1, then according to the equation we would have 2√x²=positive value. but knowing that x= -1 we know that the equation would become 2*(-1)= -2 # 2 (since we know we would have to use the negative root since x= -1). but from statement 2 we know that it must be positive so x can only be positive 1. I know that technically the definition for √x² is |x| but in this case it does not make sense for me. for statement 1 it's no problem, since |x| dictates to multiply by (-1) if negative, but in the case of statement 2, x should only be positive, since otherwise we would have to take the negative square root and then the result would not be positive anymore. I hope I made it clear why I am confused. Maybe someone could help me :)

cheers,

Max


If x=-1, then 2\sqrt{x^2}=2\sqrt{(-1)^2}=2\sqrt{1}=2.

Complete solution:

If x is an integer, what is the value of x?

(1) |23x| is a prime number. From this statement it follows that x=1 or x=-1. Not sufficient.

(2) 2\sqrt{x^2} is a prime number. The same here: x=1 or x=-1. Not sufficient.

(1)+(2) x could be 1 or -1. Not sufficient.

Answer: E.

Hope it's clear.


Dear Bunuel

If x = -1 or x=1 then it will give -23 or 23. Can negative numbers be prime numbers?

Thanks
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23381
Followers: 3607

Kudos [?]: 28803 [0], given: 2849

Re: M04#07 If x is an integer, what is the value of x? [#permalink] New post 03 Mar 2014, 04:52
Expert's post
sidpopy wrote:
Bunuel wrote:
damamikus wrote:
If x is an integer, what is the value of x?
(1) |23x| is a prime number.

(2) 2√x² is a prime number.


My choice was B although I knew it was probably E (which it turned out it was). Here's my problem with statement 2: if we know what that 2√x²=prime number, then why can't we conclude that x=1? Let's assume that x= -1, then according to the equation we would have 2√x²=positive value. but knowing that x= -1 we know that the equation would become 2*(-1)= -2 # 2 (since we know we would have to use the negative root since x= -1). but from statement 2 we know that it must be positive so x can only be positive 1. I know that technically the definition for √x² is |x| but in this case it does not make sense for me. for statement 1 it's no problem, since |x| dictates to multiply by (-1) if negative, but in the case of statement 2, x should only be positive, since otherwise we would have to take the negative square root and then the result would not be positive anymore. I hope I made it clear why I am confused. Maybe someone could help me :)

cheers,

Max


If x=-1, then 2\sqrt{x^2}=2\sqrt{(-1)^2}=2\sqrt{1}=2.

Complete solution:

If x is an integer, what is the value of x?

(1) |23x| is a prime number. From this statement it follows that x=1 or x=-1. Not sufficient.

(2) 2\sqrt{x^2} is a prime number. The same here: x=1 or x=-1. Not sufficient.

(1)+(2) x could be 1 or -1. Not sufficient.

Answer: E.

Hope it's clear.


Dear Bunuel

If x = -1 or x=1 then it will give -23 or 23. Can negative numbers be prime numbers?

Thanks


No, only positive integers can be primes (the smallest prime is 2).

Now, if x=-1, then |23x|=|23*(-1)|=|-23|=23. I think you missed modulus sign there |23x|.

Hope it helps.
_________________

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: M04#07 If x is an integer, what is the value of x?   [#permalink] 03 Mar 2014, 04:52
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic What is the value of integer x? 3111987 6 21 Jan 2014, 14:48
Experts publish their posts in the topic If x is an integer, what is the value of x? srujani 5 01 Jul 2013, 18:54
16 Experts publish their posts in the topic If x is an integer, what is the value of x? rohitgoel15 20 01 Feb 2012, 21:58
2 Experts publish their posts in the topic If x is an integer, what is the value of x? ajitsah 6 02 Jun 2010, 08:48
12 Experts publish their posts in the topic What is the value of integer x ? MBAUncle 9 20 Apr 2010, 06:04
Display posts from previous: Sort by

M04#07 If x is an integer, what is the value of x?

  Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: WoundedTiger, Bunuel



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®.