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What is the tens' digit of the sum of the first 40 terms of

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LM
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What is the tens' digit of the sum of the first 40 terms of [#permalink] New post   26 Jan 2012, 07:28
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What is the tens' digit of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...?

A. 2
B. 3
C. 4
D. 8
E. 9
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B
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Bunuel
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Re: tens' digit [#permalink] New post   26 Jan 2012, 09:50
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LM wrote:
What is the tens' digit of the sum of the first 40 terms of 1,11,111,1111,11111,111111,.......?

A. 2
B. 3
C. 4
D. 8
E. 9


----1
---11
--111
-1111
11111
......

For the units digit we should add 40 1's --> 40*1=40, so 0 will be units digit and 4 will be carried over;

For the tens digit we should add 39 1's --> 39*1=39+4=43, so 3 will be the tens digit.

Answer: B.

Similar question: infinite-seq-of-97477.html

Hope it helps.
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Re: What is the tens' digit of the sum of the first 40 terms of [#permalink] New post   21 Sep 2020, 07:10
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1 + 11 + 111 + .........

Unit digit: Sum of [1's] till 40: 40 * 1 = 40 [carried over '4' to ten's digit]

Ten's digit: We have 39 [1's]. Therefore, sum: 39 * 1 = 39 + 4[carry over] = 43.

Ten's digit is 3.

Answer B
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Re: tens' digit [#permalink] New post   26 Jan 2012, 09:19
LM wrote:
What is the tens' digit of the sum of the first 40 terms of 1,11,111,1111,11111,111111,.......?

A)2
B)3
C)4
D)8
E)9


All of the first 40 terms have 1 at the units place.
Except the first term, the tens digit of all the remaining 39 terms is 1.

So now if you do the addition

1 1
1 1
. . .
. . .
. . .
1 1
0 1
3 0

Answer is B
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Re: What is the tens' digit of the sum of the first 40 terms of [#permalink] New post   21 Dec 2012, 07:53
LM wrote:
What is the tens' digit of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...?

A. 2
B. 3
C. 4
D. 8
E. 9


40*1 (units digits) = 40, carry over 4
39*1 + 4 = 43, carry over 4

Answer: B
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Re: What is the tens' digit of the sum of the first 40 terms of [#permalink] New post   18 Aug 2014, 23:02
LM wrote:
What is the tens' digit of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...?

A. 2
B. 3
C. 4
D. 8
E. 9


:( I misunderstood when reading the problem. Tens's digit = tenth digit :( OMG
Anyways, the answer should be B
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Re: What is the tens' digit of the sum of the first 40 terms of [#permalink] New post   21 Sep 2020, 08:38
What is the tens' digit of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...?

A. 2
B. 3
C. 4
D. 8
E. 9
______________________________

1
+ 11
+111
.
.
40 terms
That means for unit digit there are 40 1s hence unit digit will be 0 and carry over is 4

Now while adding the second term there are only 39 terms ( as we have used up 1st term which was "1"
Now 39 + 4 = 43

Hence tens' digit is 3

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Re: What is the tens' digit of the sum of the first 40 terms of [#permalink] New post   17 Feb 2024, 12:30
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Re: What is the tens' digit of the sum of the first 40 terms of [#permalink]
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