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# What is the sum of the digits of the square of 111,111,111?

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Math Expert
Joined: 02 Sep 2009
Posts: 58454
What is the sum of the digits of the square of 111,111,111?  [#permalink]

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28 Mar 2019, 00:37
1
1
00:00

Difficulty:

65% (hard)

Question Stats:

47% (01:47) correct 53% (01:41) wrong based on 38 sessions

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What is the sum of the digits of the square of 111,111,111?

(A) 18
(B) 27
(C) 45
(D) 63
(E) 81

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Manager
Joined: 31 Dec 2018
Posts: 114
Location: India
Re: What is the sum of the digits of the square of 111,111,111?  [#permalink]

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28 Mar 2019, 01:18
111111111 X 111111111= 12345678987654321
Sum =81

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 58454
Re: What is the sum of the digits of the square of 111,111,111?  [#permalink]

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28 Mar 2019, 01:27
1
mohitranjan05 wrote:
111111111 X 111111111= 12345678987654321
Sum =81

Posted from my mobile device

The point of this question is to find other way of solving and not just multiply.
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Intern
Joined: 30 Mar 2018
Posts: 27
Location: India
Concentration: Marketing, Nonprofit
GMAT 1: 650 Q44 V35
WE: Research (Non-Profit and Government)
Re: What is the sum of the digits of the square of 111,111,111?  [#permalink]

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28 Mar 2019, 01:36
1
1
If you were to lay out the number and multiply the number by itself, it would take a very long time to arrive at the answer.

Look at this neat little pattern here

Sum of digits of 11 = 2.
Sum of digits of its square, 121 = 4.

Similarly.

Sum of digits of 111=3
Sum of digits of its square, 12321 =9.

Using the pattern above:

Count up the number of 1s in the number, you will get 9. Square this. You will get 81.

E.
Senior Manager
Joined: 13 Feb 2018
Posts: 450
GMAT 1: 640 Q48 V28
Re: What is the sum of the digits of the square of 111,111,111?  [#permalink]

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28 Mar 2019, 01:52
swatato best approach so far, at least better than mine
Here is mine

11*11=121
111*111=12321

Note that the answer consists of ascending and descending digits and ascending stops at the value how many 1s have the initial number

111 111 111 has nine 1s so the result after quadratic will be = 12345678987654321

Sum from 1 to 8 = 36
36*2+9=81
Re: What is the sum of the digits of the square of 111,111,111?   [#permalink] 28 Mar 2019, 01:52
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