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.) (7, 9, 257) (10, 3, 170)
(6, 9, 226)
Analyzing the Given Number Sets to Find the Pattern
The question asks us to identify a set of numbers that shares the same relationship between its elements as the two given sets. The given sets are:
- (7, 9, 257)
- (10, 3, 170)
We need to find a mathematical operation or relationship that connects the first two numbers of each set to the third number. Let's denote the numbers in a set as A, B, and C, where C is the third number related to A and B.
Discovering the Number Pattern
Let's examine the first set (7, 9, 257). We need to find a relation between 7, 9, and 257. Let's try combining the first two numbers using basic arithmetic operations and see if they relate to the third number.
- Sum: \(7 + 9 = 16\). The third number is 257. Is 257 related to 16? Notice that \(16^2 = 256\). The third number 257 is \(256 + 1\). This suggests a possible pattern: \((\text{First number} + \text{Second number})^2 + 1 = \text{Third number}\).
Let's test this potential pattern with the second set (10, 3, 170). Here, the first number is 10, the second number is 3, and the third number is 170.
- Using the pattern: \((\text{First number} + \text{Second number})^2 + 1 = (10 + 3)^2 + 1 = 13^2 + 1 = 169 + 1 = 170\).
This matches the third number in the second set. So, the pattern is consistently applied to both given sets.
The established number pattern is: \((\text{First number} + \text{Second number})^2 + 1 = \text{Third number}\), or using A, B, C notation: \((A + B)^2 + 1 = C\).
Applying the Number Pattern to the Options
Now we will check each option provided to see which set follows the same pattern \((A + B)^2 + 1 = C\).
Option 1: (7, 9, 256)
- First number (A) = 7
- Second number (B) = 9
- Third number (C) = 256
- Apply the pattern: \((7 + 9)^2 + 1 = 16^2 + 1 = 256 + 1 = 257\).
- The calculated third number is 257, but the given third number in the set is 256. This option does not follow the pattern.
Option 2: (8, 9, 256)
- First number (A) = 8
- Second number (B) = 9
- Third number (C) = 256
- Apply the pattern: \((8 + 9)^2 + 1 = 17^2 + 1 = 289 + 1 = 290\).
- The calculated third number is 290, but the given third number in the set is 256. This option does not follow the pattern.
Option 3: (6, 9, 226)
- First number (A) = 6
- Second number (B) = 9
- Third number (C) = 226
- Apply the pattern: \((6 + 9)^2 + 1 = 15^2 + 1 = 225 + 1 = 226\).
- The calculated third number is 226, which matches the given third number in the set. This option follows the pattern.
Option 4: (7, 6, 246)
- First number (A) = 7
- Second number (B) = 6
- Third number (C) = 246
- Apply the pattern: \((7 + 6)^2 + 1 = 13^2 + 1 = 169 + 1 = 170\).
- The calculated third number is 170, but the given third number in the set is 246. This option does not follow the pattern.
Identifying the Correct Set
Based on the analysis, only Option 3 (6, 9, 226) follows the number pattern \((\text{First number} + \text{Second number})^2 + 1 = \text{Third number}\) observed in the initial sets.
Revision Table: Checking the Number Pattern
| Set | First Number (A) | Second Number (B) | Third Number (C) | Pattern Check \((A+B)^2 + 1\) | Result |
|---|---|---|---|---|---|
| Given Set 1 | 7 | 9 | 257 | \((7+9)^2 + 1 = 16^2 + 1 = 256 + 1 = 257\) | Matches C |
| Given Set 2 | 10 | 3 | 170 | \((10+3)^2 + 1 = 13^2 + 1 = 169 + 1 = 170\) | Matches C |
| Option 1 | 7 | 9 | 256 | \((7+9)^2 + 1 = 257\) | Does not match C |
| Option 2 | 8 | 9 | 256 | \((8+9)^2 + 1 = 290\) | Does not match C |
| Option 3 | 6 | 9 | 226 | \((6+9)^2 + 1 = 226\) | Matches C |
| Option 4 | 7 | 6 | 246 | \((7+6)^2 + 1 = 170\) | Does not match C |
Additional Information: Types of Number Patterns
Finding number patterns is a common type of logical reasoning question in aptitude tests. These patterns can involve various mathematical operations and sequences. Some common types of number patterns include:
- Arithmetic Progressions: Numbers increase or decrease by a constant difference.
- Geometric Progressions: Numbers are multiplied or divided by a constant ratio.
- Square and Cube Series: Numbers are squares or cubes of natural numbers, or involve operations on squares/cubes.
- Fibonacci Series: Each number is the sum of the two preceding ones.
- Mixed Operations: Patterns involving a combination of addition, subtraction, multiplication, division, squares, cubes, etc., often applied to the position of the number in the sequence or relationships between numbers in a set, as seen in this question.
- Difference Series: Finding the difference between consecutive terms reveals a simpler pattern.
Solving these types of questions requires careful observation and systematic testing of possible relationships between the numbers.
Similar Questions
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)
(52, 34, 43)
(61, 33, 47)
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)
(221, 144, 73)
(222, 153, 75)
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.)
(13, 52, 91)
(19, 76, 133)
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.)
(111, 117, 123)
(169, 200, 231)
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)
(137, 95, 67)
(246, 204, 176)
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.)
(17, 87, 104)
(20, 102, 122)
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 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 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 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)
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 : ?
