Which of the following numbers, if rational, is not between and ?

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\frac{- 3}{10}

\frac{3}{10}

\frac{- 1}{4}

\frac{- 7}{20}

answer is B.

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Detailed Solution

Concept- A The definition of a rational number is one that has the form

, where I is a set of integers. Finally, we must establish that the supplied number does not fall inside the realm of reason.
The rational numbers given are

and

.
We must determine the rational number that does not fall between

and

.
First, we are already familiar with what constitutes a rational number.
The definition of a rational number is one that has the form

, where I is a set of integers.
Since

and

are both irrational negative numbers,
Therefore, we are free to select any rational number that is not between the stated range.
Since there can never be a positive number in between two negative integers, this is known.
In this case, the positive number will not appear in the range

.
Therefore, we have a wide range of numbers to pick from that do not fall within the aforesaid range, but only one is necessary in this case. We must therefore just find that.
Therefore, we can pick at random a positive rational number that does not fall inside the aforementioned range.
Any positive rational number, such as

, can be chosen.
Hence, option 4 is correct.

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