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

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Difficulty:   15% (low)

Question Stats: 77% (01:16) correct 23% (01:44) wrong based on 151 sessions

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Which of the following is a perfect square?

A. 55,225
B. 55,235
C. 55,245
D. 55,255
E. 55,295

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Manager  B
Joined: 02 Nov 2015
Posts: 163
GMAT 1: 640 Q49 V29 Re: Which of the following is a perfect square?  [#permalink]

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The initial two digits are same for all. The last three are different. So 225 is a perfect square.
Hence A.

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Senior PS Moderator V
Joined: 26 Feb 2016
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Re: Which of the following is a perfect square?  [#permalink]

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Bunuel wrote:
Which of the following is a perfect square?

A. 55,225
B. 55,235
C. 55,245
D. 55,255
E. 55,295

$$5$$ is a prime number which will divide the answer option
A perfect square will have to be have a power of 2 for every prime factor,
so $$5^2(25)$$ divides this number.

Of the options available, Only Option A(55225) is a number which 25 divides!
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Director  V
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Concentration: Technology, Strategy
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Which of the following is a perfect square?  [#permalink]

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Bunuel wrote:
Which of the following is a perfect square?

A. 55,225
B. 55,235
C. 55,245
D. 55,255
E. 55,295

Last digit of options are ending in $$5$$. Hence all numbers are divisible by $$5$$

Square of $$5$$ ends in $$25$$

Only option is $$55,225$$

Intern  B
Joined: 05 Dec 2015
Posts: 25
Re: Which of the following is a perfect square?  [#permalink]

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A. 55,225 as only 225 is perfect square among the last three digits of the options.
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Director  V
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Re: Which of the following is a perfect square?  [#permalink]

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Bunuel wrote:
Which of the following is a perfect square?

A. 55,225
B. 55,235
C. 55,245
D. 55,255
E. 55,295

Just for learning sake . Can anybody, please provide me the prime factorization of option A. Thank you.
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Re: Which of the following is a perfect square?  [#permalink]

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stne FYI

Prime Factorization of 55225 =( 5^2 ) * (47^2)

Hope it helps _________________
Manager  S
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GMAT 1: 560 Q44 V23 Re: Which of the following is a perfect square?  [#permalink]

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stne wrote:
Bunuel wrote:
Which of the following is a perfect square?

A. 55,225
B. 55,235
C. 55,245
D. 55,255
E. 55,295

Just for learning sake . Can anybody, please provide me the prime factorization of option A. Thank you.

$$5^2$$*$$47^2$$
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Director  V
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Re: Which of the following is a perfect square?  [#permalink]

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soapbolt wrote:
stne FYI

Prime Factorization of 55225 =( 5^2 ) * (47^2)

Hope it helps Thank you , but how did you calculate that? Without the OA , how would you know that 47^2 will yield 2209?
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Re: Which of the following is a perfect square?  [#permalink]

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Hi stne
As you know--> First of all we start with smallest prime no. and start factorizing . Here in our case its 5

After doing so we come up with the number 2209
Now to know which prime number could be the factor(s) of 2209 we have to check all the prime numbers which are less than $$\sqrt{2209}$$

i.e. approx prime no < 50 ( since $$50^2 = 2500$$)

Also Unit digit of 2209 is 9 hence Prime number should have either 7 or 3 as its unit digit.

On quickly checking, 2209 is not divisible by 3 , 7 , 13 , 17
So i move to back of our list i.e. Prime number <50

I picked Number 47 and hence on checking i got my solution

Hope it helps _________________ Re: Which of the following is a perfect square?   [#permalink] 02 Dec 2018, 19:10
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