If: 2 × 3 = 13, 4 × 5 = 41, 6 × 7 = ?
Understanding the Number Pattern Puzzle
This question presents a series of equations that don't follow standard multiplication rules. The goal is to identify the underlying pattern or logic connecting the numbers on the left side (operands) to the result on the right side.
We are given:
- \(2 × 3 = 13\)
- \(4 × 5 = 41\)
- \(6 × 7 = ?\)
We need to find the rule that applies to the first two equations and then apply it to the third one.
Identifying the Mathematical Pattern
Let's analyze the first equation: \(2 × 3 = 13\).
Standard multiplication gives \(2 × 3 = 6\). This is not 13.
Let's try squaring the numbers and adding them:
- Square of the first number: \( 2^2 = 4 \)
- Square of the second number: \( 3^2 = 9 \)
- Sum of the squares: \( 4 + 9 = 13 \)
This matches the result given!
Verifying the Pattern with the Second Equation
Let's check if this pattern holds for the second equation: \(4 × 5 = 41\).
Using the same rule (sum of squares):
- Square of the first number: \( 4^2 = 16 \)
- Square of the second number: \( 5^2 = 25 \)
- Sum of the squares: \( 16 + 25 = 41 \)
The pattern \( a \times b = a^2 + b^2 \) works for the second equation as well.
Applying the Pattern to Find the Missing Value
Now, we apply the confirmed pattern \( a \times b = a^2 + b^2 \) to the final equation: \(6 × 7 = ?\).
- Here, \( a = 6 \) and \( b = 7 \).
- Square of the first number: \( 6^2 = 36 \)
- Square of the second number: \( 7^2 = 49 \)
- Sum of the squares: \( 36 + 49 = 85 \)
Therefore, based on the identified pattern, \(6 × 7 = 85\).
Conclusion
The sequence follows the rule where the result is the sum of the squares of the two numbers. Applying this rule to \(6 × 7\) gives 85.
Similar Questions
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?
4 × 3 ÷ 6 + 2 - 8 = 10 + 2 × 3 ÷ 5 - 18
- At a banquet, every 2 people shared a cake, every 6 people shared a bowl of soup, and every 8 people shared a platter of fruit. There were a total of 42 items. How many people were present at the banquet?
If + means ×, × means −, − means ÷, and ÷ means +, what will be the value of the given expression?
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what is 6+ (4*2)-3/1? - Which of the following equations is correct when the numbers 12 and 6 are interchanged and the signs ÷ and + are interchanged?
Which two numbers (not digits) and which two signs should be interchanged to yield the value ‘zero’ for the following expression?
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What will come in place of the question mark (?) in the following equation if '-' means '×', '×' means '+', and '+' means '-'?
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Select the number that will come in the place of the question mark(?), if '+' and ' - ' are interchanged and 'x' and '÷' are interchanged?
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Important Questions from Mathematical Operations
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 = ?
