What is the remainder when the two-digit, positive integer x is divided by 3?
(1) The sum of the digits of x is 5
(2) The remainder when x is divided by 9 is 5
The OA is D.
I got confused. I could not determine the statements alone are sufficient. Can any expert help me here?
What is the remainder when the two-digit, positive integer.
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Statement 1: The sum of the digits of x is 5.Vincen wrote:What is the remainder when the two-digit, positive integer x is divided by 3?
(1) The sum of the digits of x is 5
(2) The remainder when x is divided by 9 is 5
The OA is D.
I got confused. I could not determine the statements alone are sufficient. Can any expert help me here?
Divisibility rule of 3:
If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
However, if the sum of the digits of a number is NOT divisible by 3, then the remainder is the same when the number is divided by 3.
Thus, the remainder when the two-digit, positive integer x is divided by 3 = Remainder when 5 is divided by 3 = 2. Sufficient.
Statement 2: The remainder when x is divided by 9 is 5.
The rule for divisibility of 9 is same as that for 3.
The remainder when the two-digit, positive integer x is divided by 3 = Remainder when 5 is divided by 3 = 2. Sufficient.
Alternatively,
Say X = 9q + 5, where q is quotient
Thus, X/3 = (9/3)*q + 5/3
X/3 = 3q + 1 + 2/3
=> Remainder = 2. Sufficient.
The correct answer: D
Hope this helps!
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