`x=20, y=32 and z=12`
`{:("Quantity A","Quantity B"),("The remainder when x is","The remainder when y is "),("divided by z","divided by z"):}`

Answer

To solve the problem step by step, we will find the remainders of \( x \) and \( y \) when divided by \( z \).

Given:
- \( x = 20 \)
- \( y = 32 \)
- \( z = 12 \)

### Step 1: Calculate Quantity A
**Find the remainder when \( x \) is divided by \( z \)**

Using the formula:
\[ \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \]

We need to divide \( 20 \) by \( 12 \):
- The quotient when \( 20 \) is divided by \( 12 \) is \( 1 \) (since \( 12 \times 1 = 12 \)).
- Now, calculate the remainder:
\[ 20 = 12 \times 1 + \text{Remainder} \]
\[ \text{Remainder} = 20 - 12 \times 1 = 20 - 12 = 8 \]

Thus, **Quantity A** is \( 8 \).

### Step 2: Calculate Quantity B
**Find the remainder when \( y \) is divided by \( z \)**

Now, we divide \( 32 \) by \( 12 \):
- The quotient when \( 32 \) is divided by \( 12 \) is \( 2 \) (since \( 12 \times 2 = 24 \)).
- Now, calculate the remainder:
\[ 32 = 12 \times 2 + \text{Remainder} \]
\[ \text{Remainder} = 32 - 12 \times 2 = 32 - 24 = 8 \]

Thus, **Quantity B** is also \( 8 \).

### Step 3: Compare Quantities A and B
Now we compare the two quantities:
- Quantity A = 8
- Quantity B = 8

Since both quantities are equal, we conclude that:

**Final Answer: Quantity A is equal to Quantity B.**

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