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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the 777th decimal digit of 0.345634563456â€¦â€¦..? tagged by: Max@Math Revolution ##### This topic has 4 expert replies and 0 member replies ### GMAT/MBA Expert ## What is the 777th decimal digit of 0.345634563456â€¦â€¦..? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] What is the 777th decimal digit of 0.345634563456â€¦â€¦..? A. 3 B. 4 C. 5 D. 6 E. 7 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

What is the 777th decimal digit of 0.345634563456â€¦â€¦..?

A. 3
B. 4
C. 5
D. 6
E. 7
Determine the number of times the four-digit pattern "3456" is repeated.
777 Ã· 4 = 194 R1, so the four-digit pattern occurs 194 times. The remainder of 1 indicates that the 777th digit is the first digit in the next repetition of the pattern.
The correct answer is choice A.

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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

What is the 777th decimal digit of 0.345634563456â€¦â€¦..?

A. 3
B. 4
C. 5
D. 6
E. 7
Look for a pattern...
1st decimal digit: 3
2nd decimal digit: 4
3rd decimal digit: 5
4th decimal digit: 6
5th decimal digit: 3
6th decimal digit: 4
7th decimal digit: 5
8th decimal digit: 6
9th decimal digit: 3
...etc

This pattern repeats itself every 4 digits
In other words, the pattern has a cycle of 4

So, we can see that the 4th digit is 6, the 8th digit is 6, the 12th digit is 6, etc
In other words, for every term that is a multiple of 4, the digit will be 6

Now let's find the multiple of 4 that's closest to 777
Well, 776 is a multiple of 4, so the 776th digit must be 6
This means the next digit, the 777th digit, must be 3

Cheers,
Brent

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The digits of 0.345634563456â€¦. repeat with period 4.
Since the 1st, 5th, 9th, â€¦ decimal digits are 3, the n-th decimal digit is 3 if n has a remainder of 1 when it is divided by 4.
Since the 2nd, 6th, 10th, â€¦ decimal digits are 4, the n-th decimal digit is 4 if n has a remainder of 2 when it is divided by 4.
Since the 3rd, 7th, 11th, â€¦ decimal digits are 5, the n-th decimal digit is 5 if n has a remainder of 3 when it is divided by 4.
Since the 4th, 8th, 12th, â€¦ decimal digits are 6, the n-th decimal digit is 6 if n is a multiple of 4.
Since 777 has a remainder of 1 when it is divided by 4, the 777th decimal digit is 3.

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Only $149 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1465 messages Followed by: 18 members Upvotes: 39 Max@Math Revolution wrote: [Math Revolution GMAT math practice question] What is the 777th decimal digit of 0.345634563456â€¦â€¦..? A. 3 B. 4 C. 5 D. 6 E. 7 The pattern is 3, 4, 5, 6. The decimal repeats every 4 digits. We see that the digit 6 is the 4th, the 8th, the 16th, etc. digit in the pattern. Thus, the digit 6 always occupies the position of a digit that is a multiple of 4 . Since 776 is a multiple of 4, then the 776th digit will be a 6 and the 777th digit will be a 3. Answer: A _________________ Jeffrey Miller Head of GMAT Instruction jeff@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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