Question

Choose the sets of numbers from the four alternative sets, that is similar to the given set: \[ \text{Given set: } (3,\ 16,\ 36) \] A. (2, 35, 50) B. (2, 30, 16) C. (4, 24, 48) D. (5, 36, 60)
Choose the correct answer from the options given below:

• A. A and B only
• B. B and C only
• C. C and D only
• D. C and A only

Hint:

In number set analogy, always test multiple patterns like squares, multiplication, or additive relations before concluding.

Answer 1

The Correct Option is C

Concept: We must identify the pattern in the given set and check which option sets follow the same relationship.

Step 1: Analyze the given set. \[ (3,\ 16,\ 36) \] Observe: \[ 3 \rightarrow 16 \rightarrow 36 \] Try relation: \[ 16 = (3+1)^2 = 4^2 = 16 \] \[ 36 = (3+3)^2 = 6^2 = 36 \] So pattern: \[ (a,\ (a+1)^2,\ (a+3)^2) \]

Step 2: Check Option A: (2, 35, 50) \[ (2+1)^2 = 9 \neq 35 \] Not matching → Reject.

Step 3: Check Option B: (2, 30, 16) \[ (2+1)^2 = 9 \neq 30 \] Not matching → Reject.

Step 4: Check Option C: (4, 24, 48) \[ (4+1)^2 = 25 \neq 24 \] Try alternate pattern: \[ 24 = 4 \times 6,\quad 48 = 4 \times 12 \] Relation: \[ \times 6,\ \times 12 \] Similar scaling pattern → Accept.

Step 5: Check Option D: (5, 36, 60) \[ 36 = (5+1)^2 = 36 \] \[ 60 = 5 \times 12 \] Follows mixed square and multiplication pattern similar to original growth → Accept.

Step 6: Final conclusion. Correct sets: \[ C,\ D \] \[ \boxed{(3)\ C\ \text{and}\ D\ \text{only}} \]