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Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Consider an integer x=251n9 where n represents the tens digit of x, wh  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 69% (01:32) correct 31% (01:37) wrong based on 208 sessions

### HideShow timer Statistics 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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Joined: 12 Sep 2015
Posts: 3853
Re: Consider an integer x=251n9 where n represents the tens digit of x, wh  [#permalink]

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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

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

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_________________ Re: Consider an integer x=251n9 where n represents the tens digit of x, wh   [#permalink] 01 Sep 2018, 08:20
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# Consider an integer x=251n9 where n represents the tens digit of x, wh  