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. 3 - Operations on 3 such as adding /deleting /multiplying etc. to 3 can be performed, Breaking down 3 into | and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(144, 12, 6)
(210, 15, 7)
(96, 8, 6)
Understanding the Number Set Relationship
The question asks us to identify the relationship between the numbers in the given example sets and then find the option that follows the same pattern. We are given two example sets:
- Set 1: (144, 12, 6)
- Set 2: (210, 15, 7)
A key instruction is that operations must be performed on the whole numbers, not on their individual digits.
Analyzing the Example Sets
Let's examine the relationship between the three numbers (let's call them A, B, and C) in each set.
Set 1 Analysis: (144, 12, 6)
We need to find a consistent mathematical operation linking 144, 12, and 6.
Let's try dividing the first number by the second number:
\( \frac{144}{12} = 12 \)
Now, let's see how this result (12) relates to the third number (6).
If we divide this result by the third number:
\( \frac{12}{6} = 2 \)
So, the relationship appears to be: \( (\frac{A}{B}) \div C = 2 \).
Set 2 Analysis: (210, 15, 7)
Let's test if the same relationship holds true for the second set.
First, divide the first number by the second:
\( \frac{210}{15} = 14 \)
Now, divide this result by the third number:
\( \frac{14}{7} = 2 \)
The relationship \( (\frac{A}{B}) \div C = 2 \) holds true for both example sets. This is the pattern we need to find in the options.
Evaluating the Options
Now, let's apply the derived relationship \( (\frac{A}{B}) \div C = 2 \) to each option.
We will check if \( (\frac{\text{First Number}}{\text{Second Number}}) \div \text{Third Number} = 2 \).
| Option | Calculation | Result | Matches Pattern? |
|---|---|---|---|
| 1. (100, 10, 4) | \( (\frac{100}{10}) \div 4 = 10 \div 4 \) | 2.5 | No |
| 2. (156, 13, 7) | \( (\frac{156}{13}) \div 7 = 12 \div 7 \) | Approx 1.71 | No |
| 3. (180, 9, 11) | \( (\frac{180}{9}) \div 11 = 20 \div 11 \) | Approx 1.82 | No |
| 4. (96, 8, 6) | \( (\frac{96}{8}) \div 6 = 12 \div 6 \) | 2 | Yes |
Identifying the Matching Set
Based on the calculations in the table, the set (96, 8, 6) is the only one where the relationship \( (\frac{A}{B}) \div C = 2 \) holds true.
- For (96, 8, 6): \( (\frac{96}{8}) = 12 \). Then \( \frac{12}{6} = 2 \).
Therefore, this set follows the same pattern as the example sets (144, 12, 6) and (210, 15, 7).
Similar Questions
Select the set, from the given options, 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.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(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.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If ‘A’ stands for ‘\(\div \)', ‘B’ stands for ‘x', ‘C’ stands for ‘+', ‘D’ stands for ‘-', what will come in the place of the question mark '?' in the following equation?
225 B 15 A 15 C 125 D 225 = ?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. 3 - Operations on 3 such as adding /deleting /multiplying etc. to 3 can be performed, Breaking down 3 into | and 3 and then performing mathematical operations on | and 3 is not allowed.)
(9, 6, 56)
(7,8, 58)If A means +, B means -, C means x, D means \(\div \), then what will come in place of the question mark (?) in the following equation?
18 D 2 A 4 C 5 B 15 = ?If 'A' stands for '+', 'B' stands for '×', 'C' stands for '+' and 'D' stands for '-', then what will come in place of the question mark (?) in the following equation?
47 D 25 A 5 C 2 B 9 = ?
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
22 - 5 ÷ 3 + 12 × 3 = ?
Which two numbers should be interchanged to make the given equation correct?
186 - 82 + (129 ÷ 3) − 6 × 8 + (31 - 19) × 2 = 85
(Note: Interchange should be done of entire number and not individual digits of a given number.)
Important Questions from Mathematical Operations
Which two numbers (not digits) should be interchanged to make the given equation correct?
21 × 8 – 18 + (64 ÷ 2) + 32 = 64
The two expressions on either side of the equal sign will have the same value if two numbers on the left-hand side are interchanged and two signs on the right-hand side are interchanged. What are those two numbers (not digits) and the two signs?
9 × 1 ÷ 3 + 8 – 7 = 12 ÷ 3 + 2 × 33 – 13
Select the set, from the given options, 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.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(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.)
X : 649 :: 956 : Y
