Data Sufficiency

[GMAT math practice question]

What is the remainder when a positive integer n is divided by 36?

1) The remainder when n is divided by 12 is 5.
2) The remainder when n is divided by 18 is 11.

The remainder when n is divided by 12=5
Given that n= 12p +5
12p will be divisible by 36 only for values of p which are multiple of 3
Example:
n = (12*3)+5
n= $$\frac{41}{36}=\ 1.5$$
Probable values for student 1 include 17, 29, 41, 53, 65, 77 e.t.c.
for statement 1 we are not sure .
statement 2 : the remainder when n is divided by 8 is 11
Given that n = 18q +11 ; 18q will be divisible by 36 only for values of q which are multiples of 2. Example : n=(18*2) +11
= $$\frac{47}{36}=1.11$$
Probable values of n for statement 2 includes 29,47,65,83,101,119....
For statement 2 we are also not SURE.
Looking at statement 1 and 2 only 29 qualifies so n= 29 when divided by 36 leaves 29 as remainder.
The answer is = C as we need both statement.

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1)
Since the divisor (12) of condition 1) is not a multiple of the divisor (36) of the question, condition 1) is not sufficient.
For example, if n = 5, the remainder when n is divided by 36 is 5.
If n = 17, the remainder when n is divided by 36 is 17.
Since we don't have a unique solution, condition 1) is not sufficient.
Condition 2)
Since the divisor (18) of condition 2) is not a multiple of the divisor (36) of the question, condition 2) is not sufficient.
For example, if n = 11, the remainder when n is divided by 36 is 11.
If n = 29, the remainder when n is divided by 36 is 29.
Since we don't have a unique solution, condition 2) is not sufficient.
Conditions 1) & 2)
The first integer satisfying both conditions is 29, and the lcm of 12 and 18 is 36. Therefore, the integers satisfying both conditions are 29, 65, 101, ....
Each of these integers has a remainder of 29 when it is divided by 36.
Both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.