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# What is the largest digit n for which the number 123,45n is divisible

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42
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What is the largest digit n for which the number 123,45n is divisible  [#permalink]

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20 Feb 2019, 18:37
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15% (low)

Question Stats:

78% (00:45) correct 22% (00:49) wrong based on 46 sessions

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[GMAT math practice question]

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

$$A. 3$$
$$B. 5$$
$$C. 6$$
$$D. 7$$
$$E. 9$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 19 Jan 2019 Posts: 93 Re: What is the largest digit n for which the number 123,45n is divisible [#permalink] ### Show Tags 20 Feb 2019, 19:08 A number is divisible by 3 if the sum of its digits is divisible by 3. In the above question. 1+2+3+4+5+n should be a number that is divisible by 3... And looking into the answer choices, the largest number that can take the value of n is 9, Because 1+2+3+4+5+9= 24 which is divisible by 3. Option E is the right answer. Posted from my mobile device e-GMAT Representative Joined: 04 Jan 2015 Posts: 3092 Re: What is the largest digit n for which the number 123,45n is divisible [#permalink] ### Show Tags 20 Feb 2019, 19:33 Solution Given: • The number 123,45n is divisible by 3 • Also, n is representing a digit To find: • The largest possible value of n Approach and Working: We know that if a number is divisible by 3, then the sum of all the digits of the number should also be a multiple of 3. For the number 123,45n • Sum of the digits = (1 + 2 + 3 + 4 + 5 + n) = 15 + n We know that (15 + n) is a multiple of 3. • 15 itself is a multiple of 3. • Hence, n should also be a multiple of 3. Also, n is a single-digit integer. • Therefore, highest possible value of n = highest single-digit multiple of 3 = 9 Hence, the correct answer is option E. Answer: E _________________ Manager Joined: 13 Oct 2018 Posts: 85 Location: India GPA: 3.1 WE: Information Technology (Computer Software) Re: What is the largest digit n for which the number 123,45n is divisible [#permalink] ### Show Tags 20 Feb 2019, 19:54 1 for a number to be divisible by 3 . the sum of digita should be divisible by 3 here sum of digits = 15 so find the next biggest digit which can be added to 15 and the sum.is still divisible by 3 so the options are 3,6,9 9 is the biggest. Option E Posted from my mobile device _________________ Ankit GMAT is tough so I am ... Giving Kudos is the best way to encourage and appreciate people Intern Joined: 07 Feb 2019 Posts: 14 What is the largest digit n for which the number 123,45n is divisible [#permalink] ### Show Tags 21 Feb 2019, 09:28 We know that if sum of the digits are divisible by 3, the number is also divisible by 3.here, 4+5+9(largest one) = 18 which is divisible by 3. So answer is E. Posted from my mobile device Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8033 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the largest digit n for which the number 123,45n is divisible [#permalink] ### Show Tags 22 Feb 2019, 00:17 => 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 $$9$$. Therefore, the answer is E. Answer: E _________________ MathRevolution: 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$79 for 1 month Online Course"
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Re: What is the largest digit n for which the number 123,45n is divisible   [#permalink] 22 Feb 2019, 00:17
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# What is the largest digit n for which the number 123,45n is divisible

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