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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 0.345634563456……..? 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 0.345634563456……..? 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 0.345634563456……..? 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 World’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 0.345634563456……..?

A. 3
B. 4
C. 5
D. 6
E. 7
Determine the number of times the four-digit pattern "3456" is repeated.
777 ÷ 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 0.345634563456……..?

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 0.345634563456…. repeat with period 4.
Since the 1st, 5th, 9th, … 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, … 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, … 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, … 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 0.345634563456……..? 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 • 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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