NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 12:37 It is currently 24 Apr 2024, 12:37
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

For positive integer x, if x^2 has 4 digits, which of the following

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
banksy
Manager
Manager
Joined: 10 Feb 2011
Posts: 86
Own Kudos [?]: 1627 [3]
Given Kudos: 10
Send PM
For positive integer x, if x^2 has 4 digits, which of the following [#permalink] New post   17 Feb 2011, 15:06
1
Kudos
2
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

59% (01:57) correct 41% (02:08) wrong based on 135 sessions
Hide Show timer Statistics
For positive integer x, if x^2 has 4 digits, which of the following must be true?

I. x must be a 2-digit integer
II. 2x must be a 3-digit integer
III. 3x must be a 3-digit integer

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
ShowHide Answer
Official Answer
A
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92902
Own Kudos [?]: 618799 [1]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: For positive integer x, if x^2 has 4 digits, which of the following [#permalink] New post   17 Feb 2011, 16:15
1
Kudos
Expert Reply
banksy wrote:
186. For positive integer x, if x^2 has 4 digits, which of the following must be true?
I. x must be a 2-digit integer
II. 2x must be a 3-digit integer
III. 3x must be a 3-digit integer
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only


As \(x\) is an integer and \(x^2\) is a 4-digit perfect square then \(32\leq{x}\leq{99}\) (32^2=1024 is the first 4-digit perfect square and 100^2=10,000 is already a 5-digit perfect square).

Hence only I must be true (if \(x=32\) then \(2x=64\) and \(3x=96\) so not the 3-digit integers).

Answer: A.
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6272 [0]
Given Kudos: 1646
Send PM
Re: For positive integer x, if x^2 has 4 digits, which of the following [#permalink] New post   31 Mar 2017, 12:34
Expert Reply
banksy wrote:
For positive integer x, if x^2 has 4 digits, which of the following must be true?

I. x must be a 2-digit integer
II. 2x must be a 3-digit integer
III. 3x must be a 3-digit integer

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only


Since x is a positive integer and x^2 has 4 digits, the minimum value of x is 32 since 32^2 = 1,024 (and 31^2 = 961) and the maximum value of x is 99 since 99^2 is 9,801 (and 100^2 = 10,000).

Thus, we see that x MUST BE a two-digit integer; however, since 2 x 32 = 64 and 3 x 32 = 96, neither 2x nor 3x has to be a three-digit integer.

Answer: A
User avatar
D
shashankism
Director
Director
Joined: 13 Mar 2017
Affiliations: IIT Dhanbad
Posts: 628
Own Kudos [?]: 589 [0]
Given Kudos: 88
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy and Utilities)
Send PM
Re: For positive integer x, if x^2 has 4 digits, which of the following [#permalink] New post   14 Aug 2017, 02:58
banksy wrote:
For positive integer x, if x^2 has 4 digits, which of the following must be true?

I. x must be a 2-digit integer
II. 2x must be a 3-digit integer
III. 3x must be a 3-digit integer

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only


X^2 has 4 digits. So,1000< x^2 <10000
31< x<100
32<=x<=99 , x must be a 2 digit integer.

64 <=2x<=198, x can be a 2 digit/3digit integer

96 <=3x<=297, x can be a 2 digit/3digit integer

Answer A
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32652
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: For positive integer x, if x^2 has 4 digits, which of the following [#permalink] New post   12 Mar 2019, 11:06
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 Club Bot
gmatclubot
Re: For positive integer x, if x^2 has 4 digits, which of the following [#permalink]
12 Mar 2019, 11:06
Moderators:
Bunuel
Math Expert
92902 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions