Solving the Logic Puzzle with the '#' Symbol

This question asks us to figure out the operation represented by the symbol '#' based on the given examples and then apply it to a new expression. This type of problem requires finding a hidden pattern or rule.

Analyzing the Given Patterns

We are given two examples:

1. $$64 \text{ # } 58 \text{ # } 32 = -26$$
2. $$104 \text{ # } 17 \text{ # } 89 = -2$$

Let's examine the first example: $$64 \text{ # } 58 \text{ # } 32 = -26$$. We need to find a combination of mathematical operations (+, -, ×, ÷, etc.) that, when applied to 64, 58, and 32 in that order, results in -26. Let's try some basic operations:

• If we add all numbers: $$64 + 58 + 32 = 154$$. Not -26.
• If we subtract the second and third from the first: $$64 - 58 - 32$$

Let's calculate $$64 - 58 - 32$$:

• First, $$64 - 58 = 6$$.
• Then, $$6 - 32 = -26$$.

This matches the result of the first example!

Testing the Hypothesis with the Second Pattern

Our hypothesis is that the '#' symbol represents subtraction performed sequentially from left to right. Let's test this with the second example: $$104 \text{ # } 17 \text{ # } 89 = -2$$.

According to our hypothesis, this should be calculated as $$104 - 17 - 89$$.

Let's calculate $$104 - 17 - 89$$.

• First, $$104 - 17$$. $$104 - 10 = 94$$, $$94 - 7 = 87$$. So, $$104 - 17 = 87$$.
• Then, $$87 - 89$$. $$87 - 87 = 0$$, $$0 - 2 = -2$$. So, $$87 - 89 = -2$$.

This also matches the result of the second example!

The pattern $$a \text{ # } b \text{ # } c = a - b - c$$ seems correct.

Applying the Pattern to the Question

Now we need to find the value of $$56 \text{ # } 7 \text{ # } 24$$. Using the pattern we discovered, this should be calculated as $$56 - 7 - 24$$.

Let's perform the calculation:

• First, calculate $$56 - 7$$. $$56 - 6 = 50$$, $$50 - 1 = 49$$. So, $$56 - 7 = 49$$.
• Next, calculate $$49 - 24$$. $$49 - 20 = 29$$, $$29 - 4 = 25$$. So, $$49 - 24 = 25$$.

The result is 25.

Conclusion

Based on the analysis of the given examples, the operation represented by '#' is sequential subtraction. Applying this rule to the expression $$56 \text{ # } 7 \text{ # } 24$$ gives us 25.

Revision Table: Key Concepts

Additional Information: Solving Logic Puzzles

Logic puzzles involving symbolic operations or number patterns are common in aptitude tests. Here are some tips for solving them:

• Look for simple patterns first: Start by trying basic arithmetic operations (+, -, ×, ÷) on the numbers in the examples.
• Consider the position: The order of the numbers often matters. Try applying operations sequentially.
• Look at the result: The size and sign of the result can give clues about the operations involved. A negative result often suggests subtraction where the numbers being subtracted are larger than the number being subtracted from.
• Test your hypothesis: Once you think you've found a pattern, test it with all the given examples to make sure it holds true for every case.
• Don't overcomplicate: Most of these puzzles rely on relatively simple, often consistent, rules.
• Break down the problem: If there are multiple numbers or symbols, try to analyze the relationship between them step-by-step.

Practicing different types of number and symbol puzzles helps improve your pattern recognition and problem-solving skills.