Select the set in which the numbers are related in the same way as are the numbers of the following set. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.) (4, 3, 16) (6, 4, 28)
(8, 2, 20)
This problem requires identifying a numerical pattern common to two given sets and then applying that pattern to find the correct option among the choices provided. The constraint is that operations must be performed on the whole numbers.
Analyzing the Number Sets for a Pattern
Let's denote the numbers in each set as $(a, b, c)$. We need to find a relationship between $a$, $b$, and $c$ that holds true for the given examples.
Given Set 1: (4, 3, 16)
- Here, $a=4$, $b=3$, and $c=16$.
Given Set 2: (6, 4, 28)
- Here, $a=6$, $b=4$, and $c=28$.
We look for a consistent mathematical operation linking $a$ and $b$ to produce $c$. Let's explore possible operations:
- Consider multiplication of the first two numbers: $a \times b$.
- For Set 1: $4 \times 3 = 12$.
- For Set 2: $6 \times 4 = 24$.
- Now, let's see how $c$ relates to $a \times b$.
- For Set 1: $c = 16$. The difference is $16 - 12 = 4$.
- For Set 2: $c = 28$. The difference is $28 - 24 = 4$.
In both cases, the difference between $c$ and the product $a \times b$ is 4. This suggests the relationship might be $c = (a \times b) + 4$.
Verifying the Identified Pattern
Let's verify if the relationship $c = a \times b + 4$ holds true for both given sets:
- Set 1: $(4, 3, 16)$
- Using the formula: $4 \times 3 + 4 = 12 + 4 = 16$. This matches the third number ($c=16$).
- Set 2: $(6, 4, 28)$
- Using the formula: $6 \times 4 + 4 = 24 + 4 = 28$. This matches the third number ($c=28$).
The relationship $c = a \times b + 4$ is consistent across both provided sets.
Testing the Pattern Against the Options
Now, we apply the confirmed relationship $c = a \times b + 4$ to each of the given options:
-
Option 1: (5, 2, 49)
- $a=5$, $b=2$.
- Calculation: $5 \times 2 + 4 = 10 + 4 = 14$.
- The result (14) does not match the third number (49).
-
Option 2: (8, 2, 20)
- $a=8$, $b=2$.
- Calculation: $8 \times 2 + 4 = 16 + 4 = 20$.
- The result (20) matches the third number (20).
-
Option 3: (8, 1, 18)
- $a=8$, $b=1$.
- Calculation: $8 \times 1 + 4 = 8 + 4 = 12$.
- The result (12) does not match the third number (18).
-
Option 4: (3, 2, 12)
- $a=3$, $b=2$.
- Calculation: $3 \times 2 + 4 = 6 + 4 = 10$.
- The result (10) does not match the third number (12).
Conclusion on the Correct Number Set
Based on the analysis, the set (8, 2, 20) is the only option that follows the pattern $c = a \times b + 4$, which is consistent with the given examples (4, 3, 16) and (6, 4, 28).
Therefore, the set in which the numbers are related in the same way is (8, 2, 20).
Similar Questions
Select the option in which the numbers are related in the same way as are the numbers of the following set.
(12, 60, 84)
Select the options in which the numbers are related in the same way as are the numbers of the following set.
(541, 14, 737)
Select the option in which the numbers are related in the same way as are the numbers of the following set.
(4, 8, 16)
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(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)
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(8, 44, 784)
Select the set in which the numbers are related in the same way as are the numbers of the given set.
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(5, 98, 9)
(10, 168, 14)
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)
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(11, 185, 8)
Select the option that is related to the fourth term in the same way as the first term is related to the second term and the fifth term is related to the sixth term.
8 : 96 :: ? : 54 :: 12 : 216
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(5, 2, 23)
(6, 2, 34)
(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)
Select the set in which the numbers are related in the same way as are the numbers of the given set.
(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.)
(6, 17, 408)
(13, 27, 1404)
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)
(49, 63, 441)
(7, 14, 14)
Important Questions from Letter and Number Based
Select the related number from the given alternatives that will complete the series:
Y 2 : 4 : : V 2 : ?Select the related number from the given alternatives:
F : 216 : : L : ?Select the option in which the numbers are related in the same way as are the numbers of the following set.
(12, 60, 84)
Three of the following four number-pairs ale alike in a certain way and one is different. Find the odd one out.
In the following question, select the related number from the given alternatives.
52 : 57 ∷ 46 : ?
