Which set of numbers is like the given set?
2, 14, 16

Question

Which set of numbers is like the given set? 
2, 14, 16

Accepted Answer

To determine which set of numbers is like the given set (2, 14, 16), we need to identify a pattern or relationship within the given set and find a similar pattern in the options provided.

### Explanation for Option 3 (3, 21, 24):

1. **Pattern in the Given Set (2, 14, 16):**
   - The first number is 2.
   - The second number is 14, which is 7 times the first number (2 x 7 = 14).
   - The third number is 16, which is 8 times the first number (2 x 8 = 16).

2. **Pattern in Option 3 (3, 21, 24):**
   - The first number is 3.
   - The second number is 21, which is 7 times the first number (3 x 7 = 21).
   - The third number is 24, which is 8 times the first number (3 x 8 = 24).

The pattern of multiplying the first number by 7 to get the second number and by 8 to get the third number is consistent in both the given set and Option 3. Therefore, Option 3 is like the given set.

### Explanation for Why Other Options are Incorrect:

1. **Option 1 (2, 7, 8):**
   - The first number is 2.
   - The second number is 7, which is not 7 times the first number (2 x 7 = 14, not 7).
   - The third number is 8, which is not 8 times the first number (2 x 8 = 16, not 8).
   - The pattern does not match the given set.

2. **Option 2 (2, 9, 16):**
   - The first number is 2.
   - The second number is 9, which is not 7 times the first number (2 x 7 = 14, not 9).
   - The third number is 16, which matches the pattern of being 8 times the first number (2 x 8 = 16), but the second number does not fit the pattern.
   - The pattern is incomplete and does not fully match the given set.

3. **Option 4 (4, 16, 18):**
   - The first number is 4.
   - The second number is 16, which is 4 times the first number (4 x 4 = 16), not 7 times.
   - The third number is 18, which is not 8 times the first number (4 x 8 = 32, not 18).
   - The pattern does not match the given set.

In conclusion, Option 3 is the only set that follows the same pattern as the given set, making it the correct answer.