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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, 07:16
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A
B
C
D
E

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  45% (medium)

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

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New post 28 Feb 2016, 08:43
5
4
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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

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New post 07 Mar 2016, 12:53
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
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Re: Which of the following is a perfect square?  [#permalink]

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Re: Which of the following is a perfect square?   [#permalink] 10 Oct 2018, 04:35
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