Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 120

Which of the following numbers is a perfect square? [#permalink]
Show Tags
22 Mar 2013, 00:04
1
This post received KUDOS
9
This post was BOOKMARKED
Question Stats:
64% (01:21) correct 36% (01:35) wrong based on 274 sessions
HideShow timer Statistics
Which of the following numbers is a perfect square? A. 1266 B. 1444 C. 2022 D. 4034 E. 8122
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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: 70
Location: India
Concentration: Strategy, Finance
WE: Information Technology (Computer Software)

Re: Which of the following numbers is a perfect square? 1266 [#permalink]
Show Tags
22 Mar 2013, 00:20
1
This post received KUDOS
1
This post was BOOKMARKED
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: 43867

Re: Which of the following numbers is a perfect square? [#permalink]
Show Tags
22 Mar 2013, 02:40
13
This post received KUDOS
Expert's post
8
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. Answer: B. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 06 Sep 2013
Posts: 1954
Concentration: Finance

Re: Which of the following numbers is a perfect square? [#permalink]
Show Tags
05 Feb 2014, 13:27
4
This post received 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: 1839
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Which of the following numbers is a perfect square? [#permalink]
Show Tags
04 Mar 2014, 01:45
2
This post received 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: 17
Location: Bangladesh
GMAT 1: 550 Q42 V24 GMAT 2: 550 Q44 V23 GMAT 3: 540 Q41 V24

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: 43867

Re: Which of the following numbers is a perfect square? [#permalink]
Show Tags
25 Jun 2014, 01:47



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7951
Location: Pune, India

Re: Which of the following numbers is a perfect square? [#permalink]
Show Tags
25 Jun 2014, 01:49
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 ... lynumber/http://www.veritasprep.com/blog/2010/12 ... tsquares/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: 93

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



NonHuman User
Joined: 09 Sep 2013
Posts: 13804

Re: Which of the following numbers is a perfect square? [#permalink]
Show Tags
14 Oct 2017, 08:11
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




Re: Which of the following numbers is a perfect square?
[#permalink]
14 Oct 2017, 08:11






