GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 23:42

### 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

# Which of the following is a perfect square?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58403
Which of the following is a perfect square?  [#permalink]

### Show Tags

28 Feb 2016, 08:16
13
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:25) correct 41% (01:24) wrong based on 207 sessions

### HideShow timer Statistics

Which of the following is a perfect square?

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

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7960
Which of the following is a perfect square?  [#permalink]

### Show Tags

28 Feb 2016, 09:43
6
5
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
_________________
##### General Discussion
Intern
Joined: 06 Oct 2013
Posts: 45
Re: Which of the following is a perfect square?  [#permalink]

### Show Tags

07 Mar 2016, 13:53
2
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
VP
Joined: 14 Feb 2017
Posts: 1194
Location: Australia
Concentration: Technology, Strategy
Schools: LBS '22
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
WE: Management Consulting (Consulting)
Which of the following is a perfect square?  [#permalink]

### Show Tags

18 Jun 2019, 17:03
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
_________________
Goal: Q49, V41

+1 Kudos if I have helped you
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8085
Location: United States (CA)
Re: Which of the following is a perfect square?  [#permalink]

### Show Tags

21 Jun 2019, 11:37
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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: Which of the following is a perfect square?   [#permalink] 21 Jun 2019, 11:37
Display posts from previous: Sort by