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 = 25119Case b: n = 4, so that 17+n = 17+4 = 21, which is divisible by 3. In this case,
x = 25149Case c: n = 7, so that 17+n = 17+7 = 24, which is divisible by 3. In this case,
x = 25179Since 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 = 25119Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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