# Given that an integer lies between -2.7 and -3 2/5, which of the following are true. The integer is: (A) -2, (B) -3, (C) -3.5, (D) -4 ?

Apr 10, 2017

B $\left(- 3\right)$

#### Explanation:

Let $n$ be the integer, We are told that $n \in \mathbb{Z}$

We are also told that: $- 2.7 > n > - 3 \frac{2}{5}$

i.e. $- 2.7 > n > - 3.4$

Testing each option in turn:

A: $- 2 > - 2.7$ Hence $n \ne - 2$

B: $- 3 < - 2.7$ and $- 3 > - 3.4$ Hence $n = - 3$ is a valid option

C: $- 3.5 < - 3.4$ also $- 3.5 \notin \mathbb{Z}$ Hence $n \ne - 3.5$

D: $- 4 < - 3.4$ Hence $n \ne - 4$

Therefore answer B $\left(- 3\right)$ is the only valid option.