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# If n^2 = 123,456,787,654,321, what is n?

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Math Expert
Joined: 02 Sep 2009
Posts: 64184
If n^2 = 123,456,787,654,321, what is n?  [#permalink]

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02 Apr 2020, 08:09
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Difficulty:

45% (medium)

Question Stats:

50% (01:15) correct 50% (01:15) wrong based on 34 sessions

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If $$n^2 = 123,456,787,654,321$$, what is n?

A. 12,344,321
B. 11,111,111
C. 1,235,789
D. 1,111,111
E. 111,111

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If n^2 = 123,456,787,654,321, what is n?  [#permalink]

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02 Apr 2020, 08:12
2
n2=123,456,787,654,321
n= 111,111,11
[ 1^2 =1 ; 11^2 = 121 ; 111^2 = 12321; 1111^2 = 1234321 ; .... ]
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Joined: 11 Sep 2015
Posts: 4876
GMAT 1: 770 Q49 V46
Re: If n^2 = 123,456,787,654,321, what is n?  [#permalink]

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02 Apr 2020, 08:34
1
Top Contributor
1
Bunuel wrote:
If $$n^2 = 123,456,787,654,321$$, what is n?

A. 12,344,321
B. 11,111,111
C. 1,235,789
D. 1,111,111
E. 111,111

We can also solve this question by testing some the values that are easy to square

Try 10,000,000² = (10,000,000)(10,000,000) = 100,000,000,000,000
This value is less than 123,456,787,654,321
So, n must be greater than 10,000,000
ELIMINATE C, D and E
Aside: To find the product (10,000,000)(10,000,000), we just add the zeros

Try 12,000,000² = (12,000,000)(12,000,000) = 144,000,000,000,000
This value is greater than 123,456,787,654,321
So, n must be less than 12,000,000
ELIMINATE A

By the process of elimination, the correct answer must be B

Cheers,
Brent
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Re: If n^2 = 123,456,787,654,321, what is n?   [#permalink] 02 Apr 2020, 08:34