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

 It is currently 29 May 2016, 01:13

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 24 Jan 2013
Posts: 6
Concentration: Marketing, General Management
GMAT 1: 710 Q48 V40
GPA: 3
Followers: 0

Kudos [?]: 0 [0], given: 12

If x is an integer, what is the value of x? [#permalink]

### Show Tags

01 Jul 2013, 19:54
00:00

Difficulty:

45% (medium)

Question Stats:

48% (01:35) correct 52% (00:30) wrong based on 29 sessions

### HideShow timer Statistics

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

(1) |23x| is a prime number
(2) $$2*\sqrt{x^2}$$ is a prime number

M04-07

[Reveal] Spoiler:
Now, I get why statement 1 is not sufficient (x could be 1 or -1). But the OA says that in statement 2, x could still be 1 or -1. Is it not the rule that the square root of a number only yields a positive number. Shouldn't x be here. Help.
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Jul 2013, 22:09, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Status: Looking to improve
Joined: 15 Jan 2013
Posts: 177
GMAT 1: 530 Q43 V20
GMAT 2: 560 Q42 V25
GMAT 3: 650 Q48 V31
Followers: 1

Kudos [?]: 55 [0], given: 65

### Show Tags

01 Jul 2013, 20:55

Stmt 1) Not sufficient since x can be only -1 or 1 because |23x| = 23x when x > 0 and -23x when x < 0

Stmt 2) Not sufficient since x can be only -1 or 1 because sqrt(x*2) = |x|

Considering Stmt 1) and Stmt 2) x can be -1 or 1
_________________

KUDOS is a way to say Thank You

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 72

Kudos [?]: 933 [0], given: 136

### Show Tags

01 Jul 2013, 21:42
Expert's post
srujani wrote:
If x is an integer, what is the value of x?

(1) |23x| is a prime number
(2) $$2*\sqrt{x^2}$$ is a prime number

What you are saying is exactly correct : Square root of a number will always be a non-negative entity. The question doesn't wrestle that point.
$$\sqrt{x^2} = |x| \geq{0}.$$. However, as you can see, both x = 1 and x = -1 are valid as because |1| = |-1| = 1.

So basically, $$(-1)^2 = (1)^2 = 1$$, but $$\sqrt{1}$$ = 1.

From F. S 1, we know that |23x| is a prime number for both x =1 and x=-1. Thus,no unique value of x is present. Insufficient

From F.S 2, $$2*\sqrt{x^2}$$ can be a prime no only if $$x^2 = 1$$. Again, $$x^2 = 1$$ $$\to$$ $$x = \pm1$$. Just as above, we get 2 values of x, hence Insufficient.

Even after combining both the fact statements, no unique value of x can be found.

E.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 33055
Followers: 5771

Kudos [?]: 70749 [0], given: 9856

Re: If x is an integer, what is the value of x? [#permalink]

### Show Tags

01 Jul 2013, 22:12
Expert's post
srujani wrote:
If x is an integer, what is the value of x?

(1) |23x| is a prime number
(2) $$2*\sqrt{x^2}$$ is a prime number

M04-07

[Reveal] Spoiler:
Now, I get why statement 1 is not sufficient (x could be 1 or -1). But the OA says that in statement 2, x could still be 1 or -1. Is it not the rule that the square root of a number only yields a positive number. Shouldn't x be here. Help.

1. 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.

Discussed here: new-set-number-properties-149775-40.html#p1205341

_________________
Manager
Joined: 22 Sep 2012
Posts: 143
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 63 [0], given: 49

Re: If x is an integer, what is the value of x? [#permalink]

### Show Tags

02 Jul 2013, 22:12
Bunuel,

As per the explanation for the option 2) , x can be either +1 or -1. But since 2 sqrt(x^2) is a prime number, can we not assume that x can't be -1 because a prime number is "an integer that has no integral factors but itself and 1" which will not be the case if x is -1.
Math Expert
Joined: 02 Sep 2009
Posts: 33055
Followers: 5771

Kudos [?]: 70749 [0], given: 9856

Re: If x is an integer, what is the value of x? [#permalink]

### Show Tags

02 Jul 2013, 22:20
Expert's post
kinghyts wrote:
Bunuel,

As per the explanation for the option 2) , x can be either +1 or -1. But since 2 sqrt(x^2) is a prime number, can we not assume that x can't be -1 because a prime number is "an integer that has no integral factors but itself and 1" which will not be the case if x is -1.

If you plug $$x=-1$$ into $$2\sqrt{x^2}$$ you'll still get a prime number:

$$2\sqrt{x^2}=2\sqrt{(-1)^2}=2\sqrt{1}=2=prime$$.
_________________
Re: If x is an integer, what is the value of x?   [#permalink] 02 Jul 2013, 22:20
Similar topics Replies Last post
Similar
Topics:
7 What is the value of integer x? 10 28 Feb 2015, 07:08
3 What is the value of integer x? 8 29 Jan 2015, 08:36
12 What is the value of integer x? 9 21 Jan 2014, 15:48
4 What is the value of integer x? 3 27 Jun 2011, 21:31
25 What is the value of integer x ? 11 20 Apr 2010, 07:04
Display posts from previous: Sort by