Choosing a number similar to a group of numbers on the basis of certain common properties that they possess.
Which number is like the given set of numbers ?
(50, 101 ,170)

Options

A. 80
B. 37
C. 121
D. 120

Explanation

To solve the problem of finding a number similar to the set (50, 101, 170) based on a common property, we can follow these steps:

### Step 1: Identify the common property in the given numbers
We need to analyze the numbers 50, 101, and 170 to find a pattern.

- For 50: If we subtract 1, we get 49, which is \(7^2\) (the square of 7).
- For 101: If we subtract 1, we get 100, which is \(10^2\) (the square of 10).
- For 170: If we subtract 1, we get 169, which is \(13^2\) (the square of 13).

### Step 2: Establish the pattern
The pattern we observe is that when we subtract 1 from each number, the result is a perfect square.

### Step 3: Check the options against the identified pattern
Now we will check each option to see if it follows the same pattern:

1. **Option 1: 80**
- Subtract 1: \(80 - 1 = 79\)
- 79 is not a perfect square.
- **Conclusion:** Not similar.

2. **Option 2: 37**
- Subtract 1: \(37 - 1 = 36\)
- 36 is \(6^2\) (the square of 6).
- **Conclusion:** Similar.

3. **Option 3: 121**
- Subtract 1: \(121 - 1 = 120\)
- 120 is not a perfect square.
- **Conclusion:** Not similar.

4. **Option 4: 120**
- Subtract 1: \(120 - 1 = 119\)
- 119 is not a perfect square.
- **Conclusion:** Not similar.

### Step 4: Conclusion
The only option that follows the same pattern as the given set is **Option 2: 37**.