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Consider an integer x=251n9 where n represents the tens digit of x, wh

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Consider an integer x=251n9 where n represents the tens digit of x, wh  [#permalink]

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New post 04 Nov 2016, 09:35
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Consider an integer x=251n9 where n represents the tens digit of x, what is the value of x?

(1) x is a multiple of 3
(2) x is a multiple of 9

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Re: Consider an integer x=251n9 where n represents the tens digit of x, wh  [#permalink]

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New post 04 Nov 2016, 11:26
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stonecold wrote:
Consider an integer x=251n9 where n represents the tens digit of x, what is the value of x?

(1) x is a multiple of 3
(2) x is a multiple of 9


Nice question, stonecold

This question tests two divisibility rules:
1) If an integer is divisible by 3 (i.e., a multiple of 3), the sum of its digits must be divisible by 3.
2) If an integer is divisible by 9 (i.e., a multiple of 9), the sum of its digits must be divisible by 9.


Target question: What is the value of x?

Given: x = 251n9 where n represents the tens digit of x

Statement 1: x is a multiple of 3
This means the sum of the digits of x must be divisible by 3
In other words, the sum 2+5+1+n+9 must be divisible by 3
Simplify: 17+n must be divisible by 3
This means there are several possible cases:
Case a: n = 1, so that 17+n = 17+1 = 18, which is divisible by 3. In this case, x = 25119
Case b: n = 4, so that 17+n = 17+4 = 21, which is divisible by 3. In this case, x = 25149
Case c: n = 7, so that 17+n = 17+7 = 24, which is divisible by 3. In this case, x = 25179
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is a multiple of 9
This means the sum of the digits of x must be divisible by 9
In other words, the sum 2+5+1+n+9 must be divisible by 9
Simplify: 17+n must be divisible by 9
This means there is only one possible case: n = 1, so that 17+n = 17+1 = 18, which is divisible by 9.
Since no other single-digit value of n will be such that 17+n is divisible by 9, we can conclude that x = 25119
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

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Re: Consider an integer x=251n9 where n represents the tens digit of x, wh  [#permalink]

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New post 16 Aug 2019, 00:38
In ref to the solution posted by Brent.

It just says that x is a multiple of 3 or 9. It doesn’t say that the entire number should be divisible by 3 or 9. Please correct me if I am wrong. Would be awesome if someone could help me with this query.

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Re: Consider an integer x=251n9 where n represents the tens digit of x, wh   [#permalink] 16 Aug 2019, 00:38
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Consider an integer x=251n9 where n represents the tens digit of x, wh

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