saswata4s wrote:

Out of the 60 employees of a startup, only 10 are non-engineers. How many employees of the startup are engineers with a MBA degree?

(1) Only 1 out of every 12 employees with a MBA degree is a non-engineer

(2) More than 55 percent of all employees have a MBA degree

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.

This question is a 2x2 type question.

........ | Engr | Non-Engr

-------------------------

.... MBA | a | b

-------------------------

non MBA | c | d

a+b+c+d = 60

b+d = 10

The question asks for the value of a.

Since we have 4 variables and 2 equations, we need 2 more equations to solve.

However we have only one equation from the conditions, because the condition 1) has an equation b =5 and the condition 2) has an inequality. Thus E is most likely.

Condition 1) & 2):

1) b = 5

2) a + b > 33

a = 30, b = 5, c = 20, d = 5

a = 31, b = 5, c = 19, d = 5

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

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