In this type of questions, question is provided with substitutes for various mathematical symbols, followed by a question involving calculation of an expression or choosing the correct/incorrect equation. You have to put the real signs in the given equation and then solve the questions as required. If '&' stands for '+', '^' stands for '-', '!' stands for '÷', '~' stands for '×', then find the value of: 6 ^ 8 ^ 7 ! 5 = ?
\(-\dfrac{17}{5}\)
The question uses coded symbols, so first substitute each symbol with the real mathematical sign it stands for: '&' = +, '^' = −, '!' = ÷, and '~' = ×.
The expression to evaluate is \(6 \, ^\wedge \, 8 \, ^\wedge \, 7 \, ! \, 5\), where only '^' and '!' appear.
Replacing '^' with '−' and '!' with '÷' turns it into \(6 - 8 - 7 \div 5\).
By the BODMAS/order-of-operations rule, division is performed before subtraction, so first compute \(7 \div 5 = \dfrac{7}{5}\).
The expression becomes \(6 - 8 - \dfrac{7}{5}\). Doing the subtraction left to right, \(6 - 8 = -2\).
Then \(-2 - \dfrac{7}{5} = \dfrac{-10}{5} - \dfrac{7}{5} = \dfrac{-10 - 7}{5} = -\dfrac{17}{5}\).
The key concept is that in symbol-substitution problems you must first replace the codes with real signs and then strictly apply BODMAS.
Hence the value of the expression is \(-\dfrac{17}{5}\).
Similar Questions
In this type of questions, question is provided with substitutes for various mathematical symbols, followed by a question involving calculation of an expression or choosing the correct/incorrect equation. You have to put the real signs in the given equation and then solve the questions as required.
If '&' stands for '+', '~' stands for '÷', '?' stands for '-', '$' stands for '×', then find the value of: 6 $ 15 & 11 $ 5 = ?
In this type of questions, question is provided with substitutes for various mathematical symbols, followed by a question involving calculation of an expression or choosing the correct/incorrect equation. You have to put the real signs in the given equation and then solve the questions as required.
If '*' stands for '-', '$' stands for '×', '!' stands for '÷', '~' stands for '+', then find the value of: 14 ! 6 * 3 * 5 = ?
If 'P' means '+', 'Q' means '÷', 'R' means '×' and 'S' means '−', then 42 Q 7 R 3 P 6 S 2 = ?
By interchanging the given two numbers (not digits) which of the following equation will NOT be correct?
3 and 7
I. 7 × 9 + 3 − 8 ÷ 2 = 30
II. 2 × 3 + 7 − 4 ÷ 1 = 13
If 420 ! 21 * 201 = -181 and 728 ! 26 * 905 = -877, then what is the value of 56 ! 2 * 367?
If 'A' means '+', 'B' means '−', 'C' means '÷' and 'D' means '×', then which of the following equation is correct?
I. 45 A 13 B 38 C 19 D 6 = 46
II. 13 A 47 B 36 C 4 D 5 = 15
If '+' means '−', '−' means '×', '×' means '÷' and '÷' means '+', then 12 × 4 ÷ 22 + 5 − 3 = ?
After interchanging the given two numbers (not digits), what will be the value of the given equation?
1 and 5
\(5 \times 7 + 1 - 9 \div 3 = ?\)
By interchanging the given two numbers (not digits) which of the following equation will NOT be correct?
2 and 7
I. \(7 \times 3 + 2 - 6 \div 1 = 9\)
II. \(2 \times 8 + 7 - 9 \div 3 = 40\)
Select the correct combination of mathematical signs to replace (*) signs sequentially and to balance the given equation.
\(64 * 16 * 34 * 8 * 3 = 14\)
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
