Understanding Number Analogy Problems

Number analogy questions test your ability to find the relationship between a pair of numbers and apply that same relationship to another number to find a missing value. These relationships can involve various mathematical operations like addition, subtraction, multiplication, division, percentages, squares, cubes, or a combination of these.

Analyzing the Given Number Pairs

We are given two pairs of numbers with a specific relationship, and we need to find the number related to the fifth number using the same pattern.

The pairs are:

• 175 and 210
• 310 and 372

We need to find the number related to 295.

Discovering the Relationship Pattern

Let's examine the relationship between the numbers in the first pair (175 and 210).

• Difference: $210 - 175 = 35$. Is the second number obtained by adding 35? Let's check the second pair: $310 + 35 = 345$. This is not 372, so simple addition is not the rule.
• Ratio: Let's check the ratio of the second number to the first number: $\frac{210}{175}$.

Simplifying the ratio:

$\frac{210}{175} = \frac{210 \div 5}{175 \div 5} = \frac{42}{35} = \frac{42 \div 7}{35 \div 7} = \frac{6}{5}$

So, $210 = 175 \times \frac{6}{5}$.

Let's check if this multiplication rule applies to the second pair (310 and 372).

Is $372 = 310 \times \frac{6}{5}$?

$310 \times \frac{6}{5} = \frac{310}{5} \times 6 = 62 \times 6 = 372$.

Yes, the relationship holds true for the second pair as well.

Identifying the Consistent Rule

The rule is that the second number is obtained by multiplying the first number by $\frac{6}{5}$. This is equivalent to multiplying by 1.2, or adding 20% of the first number ($1 + \frac{1}{5} = 1.2$ or $100\% + 20\% = 120\%$).

Applying the Rule to Find the Missing Number

Now we apply the same rule to the fifth number, 295, to find the missing number.

Missing Number $= 295 \times \frac{6}{5}$

Let's calculate this value:

$295 \times \frac{6}{5} = \frac{295}{5} \times 6 = 59 \times 6$

$59 \times 6 = 354$

So, the missing number is 354.

Matching with the Options

Let's compare our calculated value with the given options:

• Option 1: 362
• Option 2: 354
• Option 3: 348
• Option 4: 340

Our calculated value, 354, matches Option 2.

Conclusion

The pattern in the number analogy is multiplying the first number by $\frac{6}{5}$ (or 1.2) to get the second number. Applying this rule to 295 gives 354.

Revision Table: Number Analogy Pattern

Additional Information: Solving Analogy Questions

To excel at number analogy questions, practice identifying various patterns. Common patterns include:

• Arithmetic progression (adding/subtracting a constant)
• Geometric progression (multiplying/dividing by a constant ratio)
• Square or cube relationships ($n \to n^2$, $n \to n^2+1$, $n \to n^3$, etc.)
• Digit operations (sum of digits, product of digits)
• Combination of operations (e.g., multiply by a number and then add/subtract a constant)
• Ratio and proportion

Always test your hypothesized rule with all given pairs before applying it to find the missing number. If a rule works for one pair but not another, it is not the correct rule for the analogy.