Question

\[ (11,13;\,64):(13,17;\,\underline{\hspace{1cm}}) \;::\; (17,19;\,144):(19,23;\,196) \] 

• A. \((13,17;900)\)
• B. \((13,17;100)\)
• C. \((13,17;450)\)
• D. \((13,17;300)\)

Hint:

In analogy questions, always verify a suspected pattern using all given pairs before applying it to the missing term.

Answer 1

The Correct Option is B

Concept: Observe the relationship between the two prime numbers and the third number.

Step 1: Examine the second pair. For \[ (17,19;144), \] difference: \[ 19-17=2. \] Sum: \[ 17+19=36. \] Then \[ \frac{36}{3}=12 \] and \[ 12^2=144. \]

Step 2: Verify with the last pair. \[ 19+23=42 \] \[ \frac{42}{3}=14 \] \[ 14^2=196. \] Rule verified.

Step 3: Apply to the missing pair. \[ 13+17=30 \] \[ \frac{30}{3}=10 \] \[ 10^2=100. \] Hence the missing value is \[ 100. \]