If ‘A’ means ‘+’, ‘B’ means ‘–’, ‘C’ means ‘×’, and ‘D’ means ‘÷’, what will come in place of the question mark (?) in the following equation? 44 A 36 B 60 D 30 C 5 = ?
70
Evaluating Expressions with Operator Substitution
This question requires us to substitute the given letters with their corresponding mathematical operators and then evaluate the resulting expression according to the order of operations.
The mapping of letters to operators is as follows:
- 'A' means '+' (Addition)
- 'B' means '–' (Subtraction)
- 'C' means '×' (Multiplication)
- 'D' means '÷' (Division)
The given expression is:
\(44 \text{ A } 36 \text{ B } 60 \text{ D } 30 \text{ C } 5 = ?\)
Now, let's replace the letters with their respective operators:
\(44 + 36 - 60 \div 30 \times 5 = ?\)
To solve this expression, we must follow the order of operations, commonly known as BODMAS or PEMDAS. The order is: Brackets (or Parentheses), Orders (or Exponents), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
Let's evaluate the expression step by step:
- Division: Perform the division first.
\(60 \div 30 = 2\)
The expression becomes: \(44 + 36 - 2 \times 5\) - Multiplication: Next, perform the multiplication.
\(2 \times 5 = 10\)
The expression becomes: \(44 + 36 - 10\) - Addition and Subtraction: Now, perform addition and subtraction from left to right. First, the addition.
\(44 + 36 = 80\)
The expression becomes: \(80 - 10\) - Subtraction: Finally, perform the subtraction.
\(80 - 10 = 70\)
So, the value of the expression is \(70\).
Let's verify the steps:
\(44 + 36 - 60 \div 30 \times 5\)
First, division:
\(44 + 36 - 2 \times 5\)
Next, multiplication:
\(44 + 36 - 10\)
Then, addition:
\(80 - 10\)
Finally, subtraction:
\(70\)
Revision Table: Operator Mapping
| Letter | Operator | Meaning |
|---|---|---|
| A | + | Addition |
| B | – | Subtraction |
| C | × | Multiplication |
| D | ÷ | Division |
Additional Information: Order of Operations (BODMAS/PEMDAS)
The order of operations is a set of rules that dictates the sequence in which operations should be performed in a mathematical expression to ensure a unique result. The acronyms BODMAS and PEMDAS are commonly used to remember this order:
- BODMAS: Brackets, Orders (powers/roots), Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right).
- PEMDAS: Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right).
It is crucial to follow this order; otherwise, you will likely get an incorrect answer when evaluating expressions with multiple operations.
Important Questions from Logical Puzzle
Below is given a figure, in which a horse is placed on one of the boxes in a square grid of size $5 \times 5$. The horse can move in either of the following ways in a single move:
(i) two boxes to either left or right side and one box to either up or down side
(ii) two boxes to either up or down side and one box to either left or right side
(iii) the horse cannot step on a grey box. The horse has to stay within the grid and any move to out of the grid is NOT legal.
How many white boxes are there which cannot be covered by horse within 3 moves?
- Six persons Raj, Rohit, Rachit, Rajat, Rishu, and Rinku are working in an office. Each of them has a favorite car viz. P, Q, R, S, T, and U, but not necessarily in the same order. Each of them got a different salary - 1000, 2000, 2500, 3000, 3500, and 4000, but not necessarily in the same order. Rajat gets a salary of 2500 and his favorite car is U. The one who likes car Q gets a salary of 3000. Rachit likes car P and gets a salary of 3500. The one who gets a salary of 1000 does not like car R or S. Rinku does not like car Q or S but gets a salary of 2000. Rishu gets a salary of 4000 and does not like a car R. Rohit does not get a salary of 1000. Who gets a salary of 3000?
- Six friends P, Q, R, S, T, and U are sitting at different positions in a row of the company, and each of them get a different salary viz – 500, 800, 1000, 1500, 1800 & 2000, but not necessary in the same order. The friend who gets a salary of 2000 does not sit at the extreme end of the row. Q sits immediately before R and gets a salary of 800. T sits between U and S. Q is second to the left of S. P sits at the left end of the row and gets a salary of 1000. T gets a salary of 1500. R gets a salary neither of 2000 nor of 1800. How much salary does U get?
- Seven men A, B, C, D, E, F and G are standing in a queue, one behind the other in that order. That is, A is first in queue while G brings up the rear. Each of them is wearing a hat of a different colour of the rainbow - Violet, Indigo, Blue, Green, Yellow, Orange, and Red, but not necessarily in that order. It is also known that:
• D can see in front of him green and blue hats, but not the violet hat.
• E can see violet and yellow hats, but not the red hat.
• G can see hats of all the colours except Orange.
• E is wearing the Indigo coloured hat.
What colour hat is worn by F? - Who amongst the females arrived third?
