Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Aug 2211:00 AM EDT
-11:59 PM EDT
More and more TTP students are earning impressive scores on the GMAT. Now is the perfect time to join the many GMAT students who made the switch to TTP and surpassed their wildest expectations on test day.
Aug 2910:00 PM IST
-11:30 PM IST
With brand new features like:AI-driven Planner tool, 850+ data Insights practice questions and GMAT Focus Edition Adaptive mock tests with ESR+ analysis and personal mentor support, our course is the most comprehensive course for GMAT Focus Edition.
Aug 3112:00 PM EDT
-03:00 PM EDT
Save 20% on Target Test Prep and Score in the 100th Percentile in GMAT Verbal! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
Aug 3103:00 PM EDT
-11:59 PM EDT
For a limited time use code FALL20 to save on prep. Valid on Complete Course, Advanced Course, Bootcamp Course, Tutoring, and the Executive Assessment Course. This discount ends September 16th.
Sep 0212:01 AM PDT
-11:59 PM PDT
On Monday the 2nd, GMAT Club Tests will be Absolutely Free! Including all the Quizzes, Questions, and Tests. 12 AM - 11:59 PM PST- Sep 07
11:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.
The string of digits 135791113...999 is formed by
[#permalink]
28 Jun 2023, 07:33
28 Jun 2023, 07:33
9
Kudos
113
Bookmarks
Show timer
00:00
A
B
C
D
E
Difficulty:
55%
(hard)
Question Stats:
70% (02:09) correct
30%
(02:27)
wrong
based on 627
sessions
The string of digits 135791113...999 is formed by merging together the decimal representations of the odd integers from 1 through 999. Counting from left, what is the 110th digit of this string of digits?
A) 0
B) 3
C) 5
D) 7
E) 9
A) 0
B) 3
C) 5
D) 7
E) 9
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3128
Given Kudos: 1859
Location: India
Concentration: Strategy, Leadership
The string of digits 135791113...999 is formed by
[#permalink]
28 Jun 2023, 08:04
28 Jun 2023, 08:04
18
Kudos
11
Bookmarks
rakman123 wrote:
The string of digits 135791113...999 is formed by merging together the decimal representations of the odd integers from 1 through 999. Counting from left, what is the 110th digit of this string of digits?
A) 0
B) 3
C) 5
D) 7
E) 9
A) 0
B) 3
C) 5
D) 7
E) 9
A good one!
Let's visualize this
\(\quad1 \quad3 \quad5 \quad7 \quad9 \quad11 \quad13 \quad....\quad 997 \quad 999\)
This is an arithmetic sequence with a common difference = 2
We want to find the 110th digit of this string (counting from the left)
Length of the string contributed by the 1 digit number = 5 (i.e. 13579)
Each of the two-digit numbers will contribute a length of two to the string
Total length contributed by the two-digit numbers = Number of two-digit numbers * 2
Number of two-digit numbers =\(\frac{ (99 - 11) }{ 2 }+ 1 = 45 \)
length contributed by the two-digit numbers = 45 * 2 = 90
Total Length obtained so far = 90 + 5 = 95
Remaining length = 110 - 95 = 15
Each three-digit number will contribute a length of 3 to the string. Hence, we need \(\frac{15}{3} = 5\) three digit numbers.
101 103 105 107 109
110th digit = 9
Option E
Re: The string of digits 135791113...999 is formed by
[#permalink]
04 Jul 2023, 06:33
04 Jul 2023, 06:33
7
Kudos
1
Bookmarks
Expert Reply
rakman123 wrote:
The string of digits 135791113...999 is formed by merging together the decimal representations of the odd integers from 1 through 999. Counting from left, what is the 110th digit of this string of digits?
A) 0
B) 3
C) 5
D) 7
E) 9
A) 0
B) 3
C) 5
D) 7
E) 9
Talking about positive integers, first we have 9 one digit integers (from 1 to 9), then 90 two digit integers (from 10 to 99) and then 900 three digit integers.
If you are not sure how to calculate, say how many two digit integers we have, you know that we have 10 to 99 two digit integers. Number of integers in this case is 99 - 10 + 1 = 90
(We take + 1 because 10 is also a two digit integer)
Of the 9 one digit integers, 5 are odd because we start with 1 and end with 9 (both odd).
Of the 90 two digit integers, 45 are odd because we start with 10 and end with 99 (one even one odd so equal split)
This accounts for total 5 + 2 * 45 = 95 digits.
We still have another 15 digits to go. Now all numbers will be three digit numbers. I simply need the next 5 three digit numbers.
101, 103, 105, 107, 109
So the 110th digit is 9.
Answer (E)
