Number Analogy: Solving the Pattern $3:17::6:?:: 9:47$

This question is a type of number analogy problem. We need to find the relationship between the first number and the second number in the given pairs and apply that same relationship to find the missing number.

The question presents the analogy in the format: $A:B::C:D::E:F$. Here, we have:

• First pair: $A=3$, $B=17$
• Second pair: $C=6$, $D=?$
• Third pair: $E=9$, $F=47$

We need to determine the relationship between A and B, and between E and F, and then use that relationship to find D.

Analyzing the Relationship Between Pairs

Let's look at the first pair, $3:17$. We need to find a mathematical operation that transforms 3 into 17.

• Possibility 1: Multiplication and Addition. Let's try multiplying the first number by a factor and adding a constant. If we multiply 3 by 5, we get $3 \times 5 = 15$. Adding 2 gives $15 + 2 = 17$. So, the pattern could be (Number $\times 5) + 2$.
• Possibility 2: Squaring. $3^2 = 9$. To get 17, we need to add 8: $3^2 + 8 = 9 + 8 = 17$. The pattern could be (Number$^2$) + 8.

Testing the Pattern with the Third Pair

Now, let's test these potential patterns using the third pair, $9:47$.

• Testing Possibility 1: (Number $\times 5) + 2$

  Applying this to 9: $(9 \times 5) + 2 = 45 + 2 = 47$. This matches the second number in the third pair!

• Testing Possibility 2: (Number$^2$) + 8

  Applying this to 9: $(9^2) + 8 = 81 + 8 = 89$. This does not match 47.

Since the pattern (Number $\times 5) + 2$ works for both the first ($3:17$) and the third ($9:47$) pairs, we can confidently use this pattern to find the missing number.

Calculating the Missing Number

We use the confirmed pattern (Number $\times 5) + 2$ for the second pair, $6:?$.

• The first number in the pair is 6.
• Applying the pattern: $(6 \times 5) + 2$
• Calculation: $30 + 2 = 32$.

Therefore, the missing number is 32.

Conclusion

The relationship established is that the second number is obtained by multiplying the first number by 5 and then adding 2. This relationship holds true for the pairs $3:17$ and $9:47$. Applying this pattern to the pair $6:?$, we find the missing number to be 32.

The sequence is $3:17::6:32:: 9:47$.

The correct option is the one containing the number 32.