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# Which of the following is a perfect square?

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Math Expert
Joined: 02 Sep 2009
Posts: 51285
Which of the following is a perfect square?  [#permalink]

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09 Sep 2017, 07:00
1
4
00:00

Difficulty:

25% (medium)

Question Stats:

81% (00:45) correct 19% (01:31) wrong based on 138 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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Joined: 02 Nov 2015
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Re: Which of the following is a perfect square?  [#permalink]

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09 Sep 2017, 07:22
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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Re: Which of the following is a perfect square?  [#permalink]

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09 Sep 2017, 07:22
1
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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Which of the following is a perfect square?  [#permalink]

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09 Sep 2017, 07:42
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 $$55,225$$

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

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09 Sep 2017, 09:34
A. 55,225 as only 225 is perfect square among the last three digits of the options.
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Re: Which of the following is a perfect square?  [#permalink]

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01 Dec 2018, 08:07
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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01 Dec 2018, 18:51
1
stne FYI

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

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

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02 Dec 2018, 00:06
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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Re: Which of the following is a perfect square?  [#permalink]

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02 Dec 2018, 11:14
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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02 Dec 2018, 18:10
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
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Re: Which of the following is a perfect square? &nbs [#permalink] 02 Dec 2018, 18:10
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