Question: What is the value of 1/a + 1/b?

(1) a−b=10
(2) a+b=14

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are not sufficient.

Answer: C

Solution and Explanation:

Approach Solution 1:
It is asked in the question to find out the value of 1/a + 1/b.
Statement 1:
A - b = 10
This is an equation with two variables.
So it requires two equations to solve, but we have only one.
Hence, this is insufficient to find the answer.
Statement 2:
A + b = 14
This is an equation with two variables.
So it requires two equations to solve, but we have only one.
Hence, this is insufficient to find the answer.
But from both statements,
Adding both equations we get,
2a = 24
A = 12
also,
A - b = 10
B = a -10
   = 12 - 10 = 2
Now we can calculate,
1/a+ 1/b = 1/12 + ½
Correct Answer: C

Approach Solution 2:
Forget about using traditional methods to solve arithmetic problems. The simplest and quickest method for finding the solution in DS without really solving the problem is the variable approach. Keep in mind that independent equations with an equal number of variables always have a solution.
What does 1/a + 1/b equal?
(1) a−b=10
(2) a+b=14
There are two variables (a, b) in the initial condition, hence there should be an equal amount of equations. Hence, you require two equations. For 1) 1 equation, for 2) 1 equation, the answer is probably going to be C.
When 1) & 2) are combined, a=12, b=2, which is distinct & adequate, results.
C is the solution, so.
Correct Answer: C

Approach Solution 3:
For situations where we require two more equations, such as initial conditions with "2 variables," "3 variables and 1 equation," or "4 variables and 2 equations," we have one equation in each of cases 1) and 2).
As a result, C has a 70% chance of being the correct response, while E has a 25% chance. The vast majority are these two. There is a 5% probability that the answer will be from A, B, or D in the case of common error type 3, 4, though.
Using 1) and 2) individually and the DS definition, C is the response that is most likely to be the case (It saves us time). Of course, there may be circumstances in which the response is A, B, D, or E.
So we can see that two variable requires two equations and we need both the conditions to form those two equations.
As a result, 
Correct Answer: C

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