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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 largest digit n for which the number 123,45n is tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## What is the largest digit n for which the number 123,45n is ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] What is the largest digit n for which the number 123,45n is divisible by 3? A. 3 B. 5 C. 6 D. 7 E. 9 _________________ 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:
[GMAT math practice question]

What is the largest digit n for which the number 123,45n is divisible by 3?

A. 3
B. 5
C. 6
D. 7
E. 9
RULE: if the SUM of the digits of a number is divisible by 3, then that number is divisible by 3
Take, for example, the number 1,001,226
1 + 0 + 0 + 1 + 2 + 2 + 6 = 12
Since 12 is divisible by 3, we know that 1,001,226 is divisible by 3

If 123,45n is divisible by 3, then 1 + 2 + 3 + 4 + 5 + n must be divisible by 3
Simplify: 15 + n must be divisible by 3
If n = 9, then the sum of the digits of 123,45n = 24, which is divisible by 3

Cheers,
Brent

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Recall that a number is divisible by 3 if and only if the sum of its digits is divisible by 3. The sum of the digits of 123,45n is 1 + 2 + 3 + 4 + 5 + n = n + 15. This is divisible by 3 exactly when n is divisible by 3.
So, n must be a multiple of 3.
Thus, the largest digit, n is 9.

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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 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 Max@Math Revolution wrote: [GMAT math practice question] What is the largest digit n for which the number 123,45n is divisible by 3? A. 3 B. 5 C. 6 D. 7 E. 9 Since the sum of the digits of a number divisible by 3 equal a multiple of 3, we have: 1 + 2 + 3 + 4 + 5 + n = 15 + n Since 15 is a multiple of 3, then n also has to be a multiple of 3. Therefore, the largest digit for n is 9. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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