lexis wrote:

Each of the 25 balls in a certain box is either red, blue or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?

(1) The probability that the ball will both be white and have an even number painted on it is 0

(2) The probability that the ball will be white minus the probability that the ball will have an even number painted on it is 0.2

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.

...........| White | Not White

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.....Even.| a | b

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

Not Even.| c | d

=> Q: ( a + b + c ) / 25 ?

a + b + c + d = 25

Since we have 4 variables and 1 equation, E could be the answer most likely.

1) & 2)

From the condition 1), we have a = 0.

From the condition 2), ( a + c ) / 25 - ( a + b ) / 25 = ( c - b ) / 25 = 0.2

c - b = 5

Since we have only 2 equations a = 0 and c - b = 5, we can't figure out b + c and solve this question.

Therefore, the answer is E as expected.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.

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.

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