Bunuel wrote:

Are there more than five red chips on the table?

(1) The probability of drawing a non-red chip from the pile of 100 chips is 24/25.

(2) The probability of drawing a red chip is 1/25

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.

The last step of the VA method is to make the number of variables and the equations equal (from the whole question including the original condition, conditions 1) and 2) )

Assume r is the number of re chips and n is the number of non-red chips.

Since we have 2 variables and 0 equation, we need 2 equations.

Condition 1)

r + n = 100, r / ( r + n ) = 24/25

Since we have 2 equations in the condition 1), we can get n = 96.

Thus r = 4.

The answer is No.

This is sufficient by CMT (Common Mistake Type) 1.

Condition 2)

r / ( r + n ) = 1/25

r = 1, n = 24 / r = 10, n = 240.

This is not sufficient.

Therefore, the answer is A.

Normally, in problems which require 2 or more additional 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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