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On the number line shown, is zero between 'a' and 'c'?

(1) The distance of 'a' from zero is greater than the distance of 'c' from zero.

(2) The distance between 'c' and 'a' is the same as the distance between 'c' and '-b'.

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ExpertsGlobalIf we can establish that 'a' and 'c' are of opposite signs, the answer is Yes. Alternatively, if we can establish that 'a' and 'c' are of the same sign, the answer is No. In either case, the data is sufficient. If we cannot establish either, the data is not sufficient. The question stem has drawn the number line. So, a < b < c.

Statement 1: The distance of 'a' from zero is greater than the distance of 'c' from zero.

Example: a = -4, c = -1. The distance of 'a' from zero is greater than the distance of 'c' from zero. Zero is not in between 'a' and 'c'.

Counter example: a = -2, c = 1. The distance of 'a' from zero is greater than the distance of 'c' from zero. Zero is in between 'a' and 'c'.

Statement 1 alone is not sufficient.

Statement 2: The distance between 'c' and 'a' is the same as the distance between 'c' and '-b'.

Example: a = -5, c = -1 and b = -3. a < b < c. |a - c| = 4. |(-b) - c| = 4. Zero does not lie between 'a' and 'c'. (In all such cases, c will be the arithmetic mean of 'a' and '-b')

Counter example: a = -1, b = 1, c = 2. a < b < c. |a - c| = 3. |(-b) - c| = 3. Zero lies between 'a' and 'c'. (In all such cases, a = -b.)

Statement 2 alone is not sufficient.

Statements together: The distance of 'a' from zero is greater than the distance of 'c' from zero and The distance between 'c' and 'a' is the same as the distance between 'c' and '-b'

Example: a = -5, c = -1 and b = -3. a < b < c. Satisfies condition in both statements. Zero does not lie between 'a' and 'c'.

Counter example: 'a' has to be negative. 'c' has to be positive.

If a is negative and c is positive and if |a - c| = |(-b) - c| then it is possible only when a = -b.

That is 'a' and 'b' have the same magnitude but are of opposite signs. So, |a - 0| = |b - 0|. And if b < c as given in the number line, |a - 0| will not be greater than |c - 0|. It is not possible to find a counter example.

a = -1, b = 1, c = 2 clearly shows that distance between -1 and 0 is not greater than 2 and 0.

The counter example is not possible when we combine the two statements.

We can conclude that zero does not lie between 'a' and 'c'.

Choice C is the answer.

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