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28 Feb 2016, 08:16
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (01:35) correct
34%
(01:47)
wrong
based on 828
sessions
History
Date
Time
Result
Not Attempted Yet
Which of the following is a perfect square?
A. 649
B. 961
C. 1664
D. 2509
E. 100000
A. 649
B. 961
C. 1664
D. 2509
E. 100000
28 Feb 2016, 09:43
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Bunuel
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
07 Mar 2016, 13:53
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Bunuel
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
