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655-705 Level|   Sequences|      
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pablovaldesvega
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The string of digits 3691215...300 is formed by merging together the 17 Dec 2023, 22:33
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67% (02:08) correct 33% (02:33) wrong based on 610 sessions

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The string of digits 3691215...300 is formed by merging together the decimal representations of the first 100 positive integer multiples of 3. Counting from the left, what is the 72nd digit of this string of digits?

A. 0
B. 1
C. 6
D. 8
E. 9
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The string of digits 3691215...300 is formed by merging together the 18 Dec 2023, 08:25
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pablovaldesvega
The string of digits 3691215...300 is formed by merging together the decimal representations of the first 100 positive integer multiples of 3. Counting from the left, what is the 72nd digit of this string of digits?

A. 0
B. 1
C. 6
D. 8
E. 9

1-digit multiples of 3: 3, 6, 9 (there are 3 numbers for a total of 3 digits)

2-digit multiples of 3: 12, 15, 18, . . . 99 (there are 30 numbers for a total of 60 digits)

At this point, we have dealt with the first 3 + 60 = 63 digits in the number.

Now we can add the 3-digit multiples of 3 to the end of our 63-digit number: [63-digit number]102105108

We see that 8 is the 72nd digit
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The string of digits 3691215...300 is formed by merging together the 07 Apr 2024, 09:26
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curiousPope
­Bunuel can you please shae similar questions, to practice?
­
Similar questions to practice:
Hope it helps.
 ­
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Raging
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The string of digits 3691215...300 is formed by merging together the 17 Dec 2023, 23:07
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Thinking about it logically, you can see that there are 33 multiples under 100 with the last multiple being 99. If 33 total multiples are there, then they will have 3 + 30*2 number of digits till 100. That is 63 digits are done. Now you need the 72nd digit which means that you need 3 - 3digit numbers after 99. Which will be 102, 105, 108. Here "8" will be your 72nd digit.
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The string of digits 3691215...300 is formed by merging together the 13 Jan 2024, 10:49
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Is there a different approach to this question?
I struggled since the beggining with the "decimal representation" claim... Why does the string of digits end in 300? shouldn´t it end in 99?
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Bunuel
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The string of digits 3691215...300 is formed by merging together the 13 Jan 2024, 14:03
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ruis
The string of digits 3691215...300 is formed by merging together the decimal representations of the first 100 positive integer multiples of 3. Counting from the left, what is the 72nd digit of this string of digits?

A. 0
B. 1
C. 6
D. 8
E. 9

Is there a different approach to this question?
I struggled since the beggining with the "decimal representation" claim... Why does the string of digits end in 300? shouldn´t it end in 99?

No, the string of digits correctly ends with 300. This is because the sequence consists of the first 100 positive integer multiples of 3. Since 100 times 3 equals 300, the string ends with 300, not 99. The string of digits starts like this:

3 (the first positive integer multiple of 3), 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ..., 297 (the ninety-ninth positive integer multiple of 3), 300 (the hundredth positive integer multiple of 3).

When combined into a continuous string, it looks like:

369121518212427303336...297300.
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The string of digits 3691215...300 is formed by merging together the 07 Apr 2024, 09:09
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­Bunuel can you please shae similar questions, to practice?
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The string of digits 3691215...300 is formed by merging together the 07 Apr 2024, 09:50
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ruis
Is there a different approach to this question?
I struggled since the beggining with the "decimal representation" claim... Why does the string of digits end in 300? shouldn´t it end in 99?
­You can also think of cyclicity of 3 and its multiples here i.e. 3,6,9,12,15,18,21,24,27,30...
have digits 3,6,9...0 repeat for first 10 multiples.
A little thinking tells you that upto multiples of 3 with 2 digit numbers the total digits in the representation are 3 + 60 = 63(as can be seen from posts from members). Now, we are left with next 9 digits(72 - 63).
Therefore, the next there multiples of 3 give the 72nd digit since each of the three multiples are 3 digit number(102,105,108). 

Know that the question makes solving it easier as well as difficult if you get the logic. Had it been 71st digit it would have troubled many.

Hence 8.

Answer C.
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The string of digits 3691215...300 is formed by merging together the 15 Apr 2025, 14:59
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