Three of the following four triads are alike in a certain way as they are formed by performing the same mathematical operations among themselves and thus form a group. Which triad does NOT belong to that group?

Question

Accepted Answer

**Solution:**

1. Analyze the relationship between the first and third numbers in each triad:
   - For all triads, the third number is the square of the first number.
     - $11 : 21 : 121 \Rightarrow 121 = 11^2$
     - $7 : 15 : 49 \Rightarrow 49 = 7^2$
     - $2 : 3 : 4 \Rightarrow 4 = 2^2$
     - $9 : 17 : 81 \Rightarrow 81 = 9^2$

2. Analyze the relationship between the first and second numbers:
   - Triad 1: $21 = 2 	imes 11 - 1$
   - Triad 2: $15 = 2 	imes 7 + 1$
   - Triad 3: $3 = 2 	imes 2 - 1$
   - Triad 4: $17 = 2 	imes 9 - 1$

3. Observation:
   - Triads 1, 3, and 4 follow the rule $b = 2a - 1$.
   - Triad 2 follows a different rule $b = 2a + 1$.

**Answer:** The triad that does NOT belong to the group is **7 : 15 : 49**.

Answer

Answer

Answer