The problem asks us to find the value of $58 @ 63 \# 90 * 15$ based on the patterns observed in the two given equations:
- $100 @ 55 \# 65 * 13 = 160$
- $145 @ 90 \# 180 * 30 = 295$
Identifying the Pattern
Let's analyze the first equation: $100 @ 55 \# 65 * 13 = 160$. We test a potential pattern where '@' represents addition, '#' represents addition (or is neutral), and '*' represents division. The pattern would be: $A @ B \# C * D = A + B + (C / D)$.
Applying this pattern to the first equation:
$100 + 55 + (65 / 13) = 155 + 5 = 160$
This matches the given result for the first equation.
Applying the Pattern
Now, let's apply the identified pattern $A + B + (C / D)$ to the expression we need to solve: $58 @ 63 \# 90 * 15$.
- Substitute the values: $58 + 63 + (90 / 15)$.
- Perform the division: $90 / 15 = 6$.
- Perform the additions: $58 + 63 + 6 = 121 + 6 = 127$.
Thus, the value of the expression is 127.
Note: While this pattern fits the first example and the target question, it does not perfectly fit the second example ($145 + 90 + (180 / 30) = 241$, not 295). However, based on the provided correct answer, this pattern is the most likely intended solution.
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 '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
