If [x] is the greatest integer less than or equal to x, what is the value of [-1.6] + [3.4] + [2.7]?

Options

A. a. 1
B. b. 2
C. c. 3
D. d. 4

Answer

To solve the problem, we need to evaluate the greatest integer function (GIF), denoted as [x], for the given values: -1.6, 3.4, and 2.7. The greatest integer function returns the largest integer that is less than or equal to x.

Let's break down the solution step by step:

### Step 1: Evaluate [-1.6]
- The value -1.6 lies between -2 and -1.
- The greatest integer less than or equal to -1.6 is -2.

So, \([-1.6] = -2\).

### Step 2: Evaluate [3.4]
- The value 3.4 lies between 3 and 4.
- The greatest integer less than or equal to 3.4 is 3.

So, \([3.4] = 3\).

### Step 3: Evaluate [2.7]
- The value 2.7 lies between 2 and 3.
- The greatest integer less than or equal to 2.7 is 2.

So, \([2.7] = 2\).

### Step 4: Add the results
Now we add the results from the three evaluations:
\[ [-1.6] + [3.4] + [2.7] = -2 + 3 + 2 \]

Calculating this:
- First, add -2 and 3:
\(-2 + 3 = 1\)
- Then, add 2 to the result:
\(1 + 2 = 3\)

### Final Answer
Thus, the value of \([-1.6] + [3.4] + [2.7]\) is \(3\).

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