What is the largest digit n for which the number 123,45n is divisible : Problem Solving (PS)

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

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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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Question Stats:

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22% (00:49) wrong

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[GMAT math practice question]

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

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

Spoiler: OA

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Re: What is the largest digit n for which the number 123,45n is divisible [#permalink]

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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.

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Re: What is the largest digit n for which the number 123,45n is divisible [#permalink]

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20 Feb 2019, 19:33

Solution

Given:

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.

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

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Re: What is the largest digit n for which the number 123,45n is divisible [#permalink]

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20 Feb 2019, 19:54

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

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

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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.

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Re: What is the largest digit n for which the number 123,45n is divisible [#permalink]

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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
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