Question

Shown on the left is a set of equations. Which option belongs to the same set? 

 

• A. A
• B. B
• C. C
• D. D

Hint:

For symbolic equations, identify the relationships between symbols and check if each operation maintains consistency across the options.

Answer 1

The Correct Option is C

Step 1: Analyze the relationship between each symbol. Note that all equations follow a pattern, where certain operations involving symbols result in a specific value. 

Step 2: Using the first equation, we observe that \( \triangle \times \) leads to \( \square \). Next, apply the operations to each option and identify the one that maintains consistency with the pattern in the original set of equations. 

Step 3: Option (C) correctly follows the pattern from the original equations.

Answer 2

Let triangle, square, crossed-square and circled-cross stand for four unknown numbers. From the given equations: triangle times triangle equals square, square plus triangle equals the crossed-square, triangle times circled-cross equals the crossed-square, and crossed-square plus circled-cross equals 25. Solving these together, if triangle is \( a \), then square is \( a^2 \), the crossed-square is \( a^2+a \), and circled-cross is \( \frac{a^2+a}{a}=a+1 \). Substituting into the last equation gives \( (a^2+a)+(a+1)=25 \), which simplifies to \( (a+1)^2=25 \), so \( a+1=5 \) and \( a=4 \). That makes triangle \(=4\), square \(=16\), circled-cross \(=5\), and crossed-square \(=20\).

1. Option A - triangle times circled-cross equals 12: Using the solved values, triangle times circled-cross is \( 4\times5=20 \), not 12, so this equation does not hold.
2. Option B - crossed-square plus triangle equals 20: Using the solved values, this sum is \( 20+4=24 \), not 20, so this equation is false.
3. Option C - circled-cross times circled-cross equals 25: Using the solved value, this is \( 5\times5=25 \), which matches exactly.
4. Option D - square plus circled-cross equals 28: Using the solved values, this sum is \( 16+5=21 \), not 28, so this equation does not hold.

Checking every option against the solved values shows only option C's equation is actually true.

So the correct answer is Option C.