Solving the Number Analogy Pattern

This question asks us to find a hidden relationship or pattern between pairs of numbers. We are given three pairs, where the relationship between the first and second number in the first pair is the same as the relationship between the first and second number in the third pair. We need to use this consistent relationship to find the missing number in the second pair. The pairs are:

• 24 : 15
• 32 : ?
• 46 : 26

Analyzing the First and Third Number Pairs

Let's look at the first pair, 24 and 15. How can we get from 24 to 15?

• Subtraction: $24 - 15 = 9$. The difference is 9.
• Division: $24 / x = 15$ or $24 = 15 \times x$. This gives $x = 24/15 = 8/5 = 1.6$. This doesn't seem like a simple pattern.

Let's examine the third pair, 46 and 26. How can we get from 46 to 26?

• Subtraction: $46 - 26 = 20$. The difference is 20. Since the differences (9 and 20) are not the same, a simple subtraction rule is not the answer.
• Division: $46 / x = 26$ or $46 = 26 \times x$. This gives $x = 46/26 = 23/13 \approx 1.77$. This also doesn't reveal a simple pattern.

Discovering the Consistent Number Relationship

Since simple arithmetic operations on the numbers themselves didn't reveal a consistent pattern, let's consider operations involving division and potentially addition or subtraction.

Consider the first pair: 24 and 15. What if we divide the first number by 2? $24 / 2 = 12$. How can we get to 15 from 12? We can add 3. $12 + 3 = 15$.

So, a possible rule is: Divide the first number by 2 and then add 3. Let's test this rule on the third pair, 46 and 26.

Apply the rule to the first number of the third pair (46): $46 / 2 + 3 = 23 + 3 = 26$.

This matches the second number in the third pair (26). This suggests that the rule "Divide the first number by 2 and add 3" is the correct relationship for this number analogy.

Applying the Pattern to Find the Missing Number

Now that we have identified the pattern, we can apply it to the second pair: 32 : ?.

Using the rule "Divide the first number by 2 and add 3" with the first number of the second pair (32): Missing Number $= 32 / 2 + 3$ Missing Number $= 16 + 3$ Missing Number $= 19$

The missing number is 19. Let's check this against the given options.

• Option 1: 23
• Option 2: 19
• Option 3: 21
• Option 4: 17

Our calculated missing number, 19, matches Option 2.

Summary of the Number Analogy Solution

The pattern in this number analogy is that the second number is obtained by dividing the first number by 2 and adding 3.

• For 24 : 15: $24 / 2 + 3 = 12 + 3 = 15$ (Correct)
• For 46 : 26: $46 / 2 + 3 = 23 + 3 = 26$ (Correct)
• For 32 : ?: $32 / 2 + 3 = 16 + 3 = 19$

The missing number in the analogy 32 : ? is 19.

Revision Table for Number Analogy Patterns

Additional Information on Solving Number Analogy Problems

Number analogy questions test your ability to identify numerical relationships. These relationships can be simple or complex. Here are some tips for approaching them:

• Look for simple arithmetic: First, check for basic addition, subtraction, multiplication, or division.
• Consider squares, cubes, and roots: See if the second number is a square or cube of the first number, or if it's related to the root.
• Analyze the digits: If simple operations on the whole number don't work, try looking at the individual digits of the first number. Sum of digits, product of digits, squaring/cubing digits are common patterns.
• Look for mixed operations: The pattern might involve a combination of operations, like dividing and then adding, or squaring and then subtracting.
• Check across pairs: Remember the rule must apply consistently to all given pairs. If a rule works for one pair but not another, it's not the correct rule.
• Test options: Once you think you've found a pattern, quickly test it with the first number of the pair with the missing number and see which option it matches.

Solving number analogy problems requires practice to recognize common patterns quickly.