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Re: Consider an integer x=251n9 where n represents the tens digit of x, wh
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04 Nov 2016, 11:26
Top Contributor
2
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
Re: Consider an integer x=251n9 where n represents the tens digit of x, wh
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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.
Posted from my mobile device
gmatclubot
Re: Consider an integer x=251n9 where n represents the tens digit of x, wh
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16 Aug 2019, 00:38