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Which of the following is a perfect square?

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

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New post 28 Feb 2016, 08:16
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A
B
C
D
E

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Question Stats:

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

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New post 28 Feb 2016, 09:43
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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
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Re: Which of the following is a perfect square?  [#permalink]

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New post 07 Mar 2016, 13:53
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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
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Which of the following is a perfect square?  [#permalink]

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

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New post 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.

Answer: B
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Re: Which of the following is a perfect square?   [#permalink] 21 Jun 2019, 11:37
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