NEW HERE? LEARN MORE
closeclose
Last visit was: 14 May 2024, 14:40 It is currently 14 May 2024, 14:40
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

Which of the following is a perfect square?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93260
Own Kudos [?]: 623773 [37]
Given Kudos: 81863
Send PM
CAT Tests Forum Quiz Mode
Which of the following is a perfect square? [#permalink] New post   28 Feb 2016, 08:16
3
Kudos
34
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

62% (01:28) correct 38% (01:47) wrong based on 512 sessions
Hide Show timer Statistics
Which of the following is a perfect square?

A. 649
B. 961
C. 1664
D. 2509
E. 100000
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11251
Own Kudos [?]: 32512 [16]
Given Kudos: 305
Send PM
Reviews Badge Forum Quiz Mode
Which of the following is a perfect square? [#permalink] New post   28 Feb 2016, 09:43
10
Kudos
6
Bookmarks
Expert Reply
Bunuel wrote:
Which of the following is a perfect square?

A. 649
B. 961
C. 1664
D. 2509
E. 100000


Hi,
Normally you will start checking by division method..
But the choices should stand out, as they seem to be combination of perfect square..
649--64 and 9 are perfect square
1664---16 and 64 are perfect square
2509--- 25 and 09 are perfect square

The best way would be to see the range in tens and solve after looking at the units digit
lets see all choices--
A. 649
\(20^2=400\) and \(30^2=900\)..
since only 3 and 7 have the perfect square ending in 9, we require to try only for 27 as it is more than 25^2, 625
it is not \(27^2\), as next square of 26 itself after 625 will be \(>625+2*25\) or \(>675\)
actually \(26^2\) will be \(25^2+25+26\)

B. 961
between 30^2 and 40^2...
only 1 and 9 have squares ending with onw..
since it is very close to 30^2, 900.. it can be 31^2
CORRECT

C. 1664
between 40^2 and 50^2..
closer is 42, but that should be atleast 1600+41+42.. NO

D. 2509
between 50^2 and 60^2..
very close to 50^2 so next square of 51 will be atleast 2500+51.. no

E. 100000
odd number of 0s, not possible

ans B
User avatar
B
AdlaT
Intern
Intern
Joined: 06 Oct 2013
Posts: 40
Own Kudos [?]: 142 [7]
Given Kudos: 34
Send PM
Re: Which of the following is a perfect square? [#permalink] New post   07 Mar 2016, 13:53
5
Kudos
1
Bookmarks
Bunuel wrote:
Which of the following is a perfect square?

A. 649
B. 961
C. 1664
D. 2509
E. 100000


Solution.

Two important things before solving the problem to make easy.

--> First, look at the units digit in every option, For example. 1) 649--> you can get 9 as a unit digit by squaring the digit 3 or 7.

2) 961---> you can get 1 as a unit digit by squaring the digit 1 or 9.


-->Second, we know squares of 10,20,30,40,50 ,60... and Formula \((a+b)^2=a^2+2ab+b^2\)

Now for Option A).649--> We know (20)^2=400, and (30)^2=900. So the digit should be between 20 and 30. try (20+3)^2 or (20+7)^2.


\((20+3)^2=400+120+9=529--No\)
\((20+7)^2=400+280+49=729--No\)

Option B).961--> we know that (30)^2=900, \((30+1)^2=900+60+1=961--->YES\)

try all remaining--\((30+9)^2=900+540+81=1521--->NO\)

Option C).1664--> we know that (40)^2=1600, \((40+2)^2=1600+160+4=1764-->NO\)

\((40+8)^2=1600+640+64=2304---> NO.\)

Option D) 2509-->. We know that (50)^2=2500, \((50+3)^2=2500+300+9=2809--> NO\)

\((50+7)^2=2500+700+49=3249--> NO\)

E) No need to check as it has odd number of 0'-->no.

Ans.B
General Discussion
User avatar
L
dcummins
VP
VP
Joined: 14 Feb 2017
Posts: 1114
Own Kudos [?]: 2168 [2]
Given Kudos: 368
Location: Australia
Concentration: Technology, Strategy
Schools: INSEAD Sept'21 Intake (WA$) Melbourne (A$) AGSM (A$) Kellogg '23 (WL) Said '22 (A$) CBS '23 (D) Booth '23 (D) Anderson '23 (WL) Cambridge '22 (WL) LBS '23 (D) Stern '24 (WA)
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 600 Q38 V35
GMAT 6: 710 Q47 V41
WE:Management Consulting (Consulting)
Send PM
Reviews Badge
Which of the following is a perfect square? [#permalink] New post   18 Jun 2019, 17:03
1
Kudos
1
Bookmarks
The solutions above seem way complicated to follow, so I went with this method: Identifying the nearest perfect square

(a) 649
nearest perfect square is 625 = 25^2
26^2 is obviously the next perfect square and that's significantly larger --> eliminate

(b) 961
30^2 = 900
so try 31^2 = 961
Perfect. Can stop here, but will work through the others

(c) 1664
It's fairly easy to divide this number down to its prime factors and then examine to prime factors to realise they aren't in even powers
1664 = 16*14
=2^4 * (7*2)
= 2^5 * 7^1
Does not contain even powers --> eliminate

(d) 2509
Closest perfect square is 2500 = 50^2
51^2 is the next perfect square and that's obviously significantly larger

(e) 100000
100000 = 10^5
same reason as (c), --> eliminate
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18851
Own Kudos [?]: 22218 [1]
Given Kudos: 285
Location: United States (CA)
Send PM
Re: Which of the following is a perfect square? [#permalink] New post   21 Jun 2019, 11:37
1
Bookmarks
Expert Reply
Bunuel wrote:
Which of the following is a perfect square?

A. 649
B. 961
C. 1664
D. 2509
E. 100000


Let’s look at each answer choice.

A) 649

Since 25^2 = 625, and since 26^2 = 676, 649 is not a perfect square.

B) 961

Since 30^2 = 900 and since 31^2 = 961, 961 is a perfect square.

Answer: B
User avatar
G
Basshead
Director
Director
Joined: 09 Jan 2020
Posts: 963
Own Kudos [?]: 225 [0]
Given Kudos: 434
Location: United States
Send PM
Re: Which of the following is a perfect square? [#permalink] New post   22 Nov 2020, 14:59
Bunuel wrote:
Which of the following is a perfect square?

A. 649
B. 961
C. 1664
D. 2509
E. 100000


Find the closest perfect square for each answer choice:

A. 25*25 = 625; 649 is not a perfect square

B. 30*30 = 900; 31 * 31 = 961 CORRECT

C. 40*40 = 1600; 1,664 is not a perfect square

D. 50 * 50 = 2,500; 2,590 is not a perfect square

E. 100,000 = odd number of zeros; not a perfect square.

Answer is B.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 33011
Own Kudos [?]: 828 [0]
Given Kudos: 0
Send PM
Re: Which of the following is a perfect square? [#permalink] New post   01 Sep 2023, 03:14
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: Which of the following is a perfect square? [#permalink]
01 Sep 2023, 03:14
Moderators:
Bunuel
Math Expert
93260 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3136 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