What is the remainder when x is divided by 3?

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the remainder when x is divided by 3?

(1) The sum of the digits of x is 5
(2) When x is divided by 9, the remainder is 2


In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation for 2) 1 equation, which is likely to make D the answer.
In case of 1), the remainder derived by dividing some number by 3 is as same as the remainder derived by dividing sum of all digits by 3. In 5=3*1+2, the remainder is 2, which is unique and sufficient.
For 2), in x=9p+2=3(3q)+2, the remainder derived by dividing with 3 is 2, which is unique and sufficient.
Therefore, the answer is D.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

st 1:
sum of digits is 5 ...remainder will always be 2
Sufficient

St2: remainder will always be 2

Ans: D

statement 1
sum of digits is 5 therefore possible combination 41,14,23,32 which yields remainder 2
statement 2
x/9 remainder 2 which means x= 11,20,29 etc
check above with 3 it gives 2 every time

therefore D

To get the remainder when a number is divided b 3 we need the remainder when sum of the digits divided by 3 so statement 1 i sufficient
now statement 2=> x=9n+2 => 3P+2=> remainder =2
hence D is sufficient

statement 1
As sum of digits is 5 remainder will always be 2.

Statement 2
also sufficient

Answer D

Can someone explain the parts in bold? Is this a rule?

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.