Select the option that is related to the third term in the same way as the second term is related to the first term and the sixth term is related to the fifth term. 8 : 36 :: 6 : ? :: 12 : 76
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Analyzing Number Analogy Patterns
The problem presents a number analogy: 8 : 36 :: 6 : ? :: 12 : 76. The goal is to figure out the mathematical rule connecting the first number to the second number in the known pairs (8:36 and 12:76) and then apply this rule to find the missing number in the pair 6:?. We need to identify the consistent relationship.
Deriving the Rule from 8 : 36
Let's examine the relationship between 8 and 36. Let the first number be represented by $N$.
- We can observe that $8 \times 4.5 = 36$. The multiplier 4.5 can be written as $\frac{9}{2}$. So, $8 \times \frac{9}{2} = 36$.
- Alternatively, we can express this using $N$. Notice that $\frac{9}{2}$ is $\frac{N+1}{2}$ when $N=8$. Let's test this: $N \times \frac{N+1}{2}$.
$8 \times \frac{8+1}{2} = 8 \times \frac{9}{2} = 4 \times 9 = 36$. This rule works for the first pair. - Another way to think about $\frac{N+1}{2}$ is relating it to $N/2$. $\frac{N+1}{2} = \frac{N}{2} + \frac{1}{2}$. So the rule is $N \times (\frac{N}{2} + \frac{1}{2})$.
- Let's try another perspective. Consider the operation $N \times (N/2) + C$. For $N=8$, we get $8 \times (8/2) + C = 8 \times 4 + C = 32 + C$. To get 36, $C$ must be 4. So, the potential rule is $N \times (N/2) + 4$.
Validating the Rule with 12 : 76
Now, let's check if the rule $N \times (N/2) + 4$ works for the pair 12 : 76, where $N=12$.
- Applying the rule: $12 \times (12/2) + 4$.
- Calculation step 1: $12/2 = 6$.
- Calculation step 2: $12 \times 6 = 72$.
- Calculation step 3: $72 + 4 = 76$.
The result 76 matches the second number in the pair. This confirms that the relationship $N \times (N/2) + 4$ is the correct pattern.
Calculating the Missing Term for 6 : ?
We apply the confirmed pattern $N \times (N/2) + 4$ to the pair 6 : ?, where $N=6$.
- Step 1: Find half of $N$.
$N/2 = 6/2 = 3$. - Step 2: Multiply $N$ by the result from Step 1.
$N \times (N/2) = 6 \times 3 = 18$. - Step 3: Add 4 to the result from Step 2.
$18 + 4 = 22$.
The missing number in the analogy is 22.
Matching the Result to the Options
The calculated missing number is 22. Let's compare this with the given options:
- 1. 20
- 2. 27
- 3. 22
- 4. 24
Option 3 correctly matches our calculated result.
Similar Questions
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13- Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(4, 60, 5)
(5, 90, 6)
Select the set in which the number are related in the same way as the numbers of the given sets. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting / multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(9, 7, 189)
(4, 13, 156)
Select the option that is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number.
24 : 15 : : 32 : ? : : 46 : 26
Select the set in which the numbers are related in the same way as the numbers of the given sets. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(12, 9, 4)
(18, 9, 6)
Select the set in which the number are related in the same way as the numbers of the given sets. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting / multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(8, 8, 128)
(11, 7, 162)
Select the set in which the numbers are related in the same way as the numbers of the given sets. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting / multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(20, 16, 8)
(10, 13, 12)
Select the option that is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number.
8 : 49 : : 16 : ? : : 12 : 121
Select the number that is related to the third number in the same way as the second number is related to the first number.
12 : 36 :: 18 : ?
Study the given pattern carefully and find the missing number.
(9, 9, 2) (8, __, 1) (4, 8, 8)
Study the given pattern carefully and select the number that can replace the question mark (?) in it.
(17, 9, 4) (13, ?, 7) (14, 3, 13)
Important Questions from Letter and Number Based
Select the option that is related to the third number in the same way as the second number is related to the first number.
22 : 441 :: 13 : ?Select the option that is related to the third number in the same way as the second number is related to the first number.
31 : 90 :: 43 : ?
Select the option which is related to the third number in the same way as the second number is related to the first number.
7 : 56 :: 13 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number.
77 : 11 :: 259 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number.
15 : 270 :: 13 : ?
