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.

On the number line, are the points x and y on the same side of zero?

(1) x and y are equidistant from zero

(2) The sum of the distances from x to 1 and from y to 1 is less then 1.

2) -------------------|-------------|---------|-----|------------------yes

0 1/2 x(=y) 1

-------------------|-------------|-------------|-|-|------------- yes

0 1/2 x 1 y

There are 2 variables (x,y) and 2 equations are given by the conditions, so there is high chance (C) will be the answer.

Looking at the conditions together,

x=y and both are numbers close to 1.

For example, x=y=0.7, and the answer seems like (C), but this is a commonly made mistake.

Looking at them separately,

For condition 1, the answer is 'yes' for x=y=1, but 'no' for x=-1, y=1. So this is insufficient.

For condition 2, x=y=0.9 or x=0.9 and y=1.1. This is always 'yes' and is sufficient.

therefore the answer is B

the original question is

On the number line, are 0 between the points x and y?

(1) The distnace between x and 0 is equal to the distance between y and 1

(2) The sum of the distances from x to 0 and from y to 1 is less then 1.

There are 2 variables (x,y) and 2 equations are given by the conditions, so there is high chance (C) will be our answer.

Looking at them together, the answer is 'yes' for (x,y)=(1/4,3/4),

but 'no' for (x,y)=(-1/4,3/4) .

This is insufficient, so the answer becomes (E).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

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