Which of the following numbers is a perfect square? : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 25 Feb 2017, 11:58

### 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

# Which of the following numbers is a perfect square?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 120
Followers: 1

Kudos [?]: 878 [2] , given: 17

Which of the following numbers is a perfect square? [#permalink]

### Show Tags

22 Mar 2013, 00:04
2
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:16) correct 33% (01:21) wrong based on 224 sessions

### HideShow timer Statistics

Which of the following numbers is a perfect square?

A. 1266
B. 1444
C. 2022
D. 4034
E. 8122
[Reveal] Spoiler: OA

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

Last edited by Bunuel on 22 Mar 2013, 02:21, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 17 Oct 2012
Posts: 74
Location: India
Concentration: Strategy, Finance
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 99 [1] , given: 52

Re: Which of the following numbers is a perfect square? 1266 [#permalink]

### Show Tags

22 Mar 2013, 00:20
1
KUDOS
perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022.
38*38 = 1444
hence B.
Math Expert
Joined: 02 Sep 2009
Posts: 37113
Followers: 7255

Kudos [?]: 96619 [10] , given: 10770

Re: Which of the following numbers is a perfect square? [#permalink]

### Show Tags

22 Mar 2013, 02:40
10
KUDOS
Expert's post
3
This post was
BOOKMARKED
emmak wrote:
Which of the following numbers is a perfect square?

A. 1266
B. 1444
C. 2022
D. 4034
E. 8122

A perfect square, is an integer that is the square of an integer. For example 16=4^2, is a perfect square.

From above we can deduce that the units digit of a perfect square cannot be 2, 3, or 7. Discard C and E.

Another property: perfect square always has even powers of its prime factors. The reverse is also true: if a number has even powers of its prime factors then it's a perfect square. For example: $$36=2^2*3^2$$, powers of prime factors 2 and 3 are even.

Make prime factorization of the options:

A. 1266 = 2*3*211. Discard. We could discard 1266 after we got that 1266 = 2*633 = 2*odd, so 2 in 1266 has an odd power, which means that 1266 is NOT a prefect square.

B. 1444 = 2^2*19^2 --> so, 1444 IS a perfect square.

D. 4034 = 2*2017. Discard. We could discard 4034 after we got that 4034 = 2*2017 = 2*odd, so 2 in 4034 has an odd power, which means that 4034 is NOT a prefect square.

Hope it's clear.
_________________
Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 64

Kudos [?]: 605 [4] , given: 355

Re: Which of the following numbers is a perfect square? [#permalink]

### Show Tags

05 Feb 2014, 13:27
4
KUDOS
emmak wrote:
Which of the following numbers is a perfect square?

A. 1266
B. 1444
C. 2022
D. 4034
E. 8122

Let's begin by eliminating answer choices C and E since a perfect square cannot end in 2,3,7 or 8

Now between A,B and D

Well we can see that all numbers are even for starters. This means that they also must be divisible by 4

Only B fits the bill

Hence B is the correct answer

Hope its clear
Cheers
J
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 49

Kudos [?]: 1989 [1] , given: 193

Re: Which of the following numbers is a perfect square? [#permalink]

### Show Tags

04 Mar 2014, 01:45
1
KUDOS
Perfect squares cannot end with 2,3,7 or 8, so options C & E are eliminated

A. 1266
B. 1444
E. 8122

Look at the above 3 options. All are divisible by 2, but only 1444 is divisible by 4.
Hence Answer = B

NB - Consider last two digits of any number. If Last two digits of any number are divisible by 4, then the complete number is divisible by 4
Also, If Last digit of any number is divisible by 2, then the complete number is divisible by 3
If Last three digits of any number are divisible by 8, then the complete number is divisible by 8

_________________

Kindly press "+1 Kudos" to appreciate

Intern
Status: Into the last good fight
Joined: 22 Feb 2012
Posts: 19
GMAT 1: 550 Q42 V24
GMAT 2: 550 Q44 V23
GMAT 3: 540 Q41 V24
Followers: 0

Kudos [?]: 7 [0], given: 264

Re: Which of the following numbers is a perfect square? [#permalink]

### Show Tags

25 Jun 2014, 00:48
Well we can see that all numbers are even for starters. This means that they also must be divisible by 4

Only B fits the bill

Hence B is the correct answer

Dear J,

Can you please explain the underlined portion ? It'd be really helpful
Math Expert
Joined: 02 Sep 2009
Posts: 37113
Followers: 7255

Kudos [?]: 96619 [1] , given: 10770

Re: Which of the following numbers is a perfect square? [#permalink]

### Show Tags

25 Jun 2014, 01:47
1
KUDOS
Expert's post
Tanvr wrote:
Well we can see that all numbers are even for starters. This means that they also must be divisible by 4

Only B fits the bill

Hence B is the correct answer

Dear J,

Can you please explain the underlined portion ? It'd be really helpful

For an even number to be a prefect square it must be a multiple of 4. That's because we know that a prefect square must have an even powers of its primes, so 2 in even number must have even power to be a prefect square: 2, 4, 6, ... so in any case it must be a multiple of 4.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7187
Location: Pune, India
Followers: 2170

Kudos [?]: 14037 [2] , given: 222

Re: Which of the following numbers is a perfect square? [#permalink]

### Show Tags

25 Jun 2014, 01:49
2
KUDOS
Expert's post
Tanvr wrote:
Well we can see that all numbers are even for starters. This means that they also must be divisible by 4

Only B fits the bill

Hence B is the correct answer

Dear J,

Can you please explain the underlined portion ? It'd be really helpful

Perfect squares have even powers of prime factors. What this means is that if a number is a perfect square, and it has 2 as a prime factor, the power of 2 in the number will be even i.e. it will have two 2s or four 2s or six 2s etc. Similarly, if it has 3 as a factor, it will have two 3s or four 3s or six 3s etc.
The reason for this is explained here:
http://www.veritasprep.com/blog/2010/12 ... ly-number/
http://www.veritasprep.com/blog/2010/12 ... t-squares/

Now when you see that 2 is a factor of all leftover options, you know that you will have at least two 2s i.e. the number must be divisible by 4 if the number is to be a perfect square. Check the last two digits of the numbers. If the last two digits are divisible by 4, the number will be divisible by 4. Only option (B) is divisible by 4 (because 44 is divisible by 4). Hence (B) is the correct answer.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Manager
Joined: 01 Oct 2013
Posts: 95
Schools: Haas '16, AGSM '16
Followers: 1

Kudos [?]: 21 [0], given: 13

Re: Which of the following numbers is a perfect square? [#permalink]

### Show Tags

23 Jul 2014, 07:25
Quick solution: B

the perfect square of whatever a integer number has the following possible digit 1 ; 4 ; 5 ; 6; 9
=> eliminate: C and E
A and D is divisible by 2, but not by 4 => A and D is not a perfect square

B is correct
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13966
Followers: 591

Kudos [?]: 167 [0], given: 0

Re: Which of the following numbers is a perfect square? [#permalink]

### Show Tags

22 Aug 2015, 21:06
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 Legend
Joined: 09 Sep 2013
Posts: 13966
Followers: 591

Kudos [?]: 167 [0], given: 0

Re: Which of the following numbers is a perfect square? [#permalink]

### Show Tags

04 Sep 2016, 04:40
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.
_________________
Re: Which of the following numbers is a perfect square?   [#permalink] 04 Sep 2016, 04:40
Similar topics Replies Last post
Similar
Topics:
4 Which of the following is a perfect square? 2 28 Feb 2016, 07:16
5 If 945s is a perfect square then s can be which of the following numbe 6 22 Sep 2015, 02:08
If x and y are perfect squares, then which one of the 7 05 Jun 2012, 02:48
2 If x and y are perfect squares, which of the following is 4 03 Oct 2011, 09:49
39 If the positive integer N is a perfect square, which of the following 30 25 Sep 2010, 10:37
Display posts from previous: Sort by

# Which of the following numbers is a perfect square?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.