Question

what set of numbers are shaded on the hundred chart?

choose 1 answer:

a only the factors of 4
b only the multiples of 4
c only the factors of 8
d only the multiples of 8

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Factors and Multiples"
],
"new_concepts": [],
"current_concepts": [
"Factors and Multiples"
]
}
</pre_analysis>

<reasoning>

Identify the shaded numbers on the chart

\[
S = \{8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96\}
\]

Analyze the pattern of the shaded set

\[

$$\begin{aligned} 8 &= 8 \times 1 \\ 16 &= 8 \times 2 \\ 24 &= 8 \times 3 \\ &\ \ \vdots \\ 96 &= 8 \times 12 \end{aligned}$$

\]

Match with the given options

\[
\text{The shaded numbers are positive integers divisible by 8, which are the multiples of 8.}
\]
</reasoning>

<answer>
<mcq-option>(A) Only the factors of 4</mcq-option>
<mcq-option>(B) Only the multiples of 4</mcq-option>
<mcq-option>(C) Only the factors of 8</mcq-option>
<mcq-correct>(D) Only the multiples of 8</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Factors and Multiples"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Factors and Multiples"
],
"new_concepts": [],
"current_concepts": [
"Factors and Multiples"
]
}
</pre_analysis>

<reasoning>

Identify the shaded numbers on the chart

\[
S = \{8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96\}
\]

Analyze the pattern of the shaded set

\[

$$\begin{aligned} 8 &= 8 \times 1 \\ 16 &= 8 \times 2 \\ 24 &= 8 \times 3 \\ &\ \ \vdots \\ 96 &= 8 \times 12 \end{aligned}$$

\]

Match with the given options

\[
\text{The shaded numbers are positive integers divisible by 8, which are the multiples of 8.}
\]
</reasoning>

<answer>
<mcq-option>(A) Only the factors of 4</mcq-option>
<mcq-option>(B) Only the multiples of 4</mcq-option>
<mcq-option>(C) Only the factors of 8</mcq-option>
<mcq-correct>(D) Only the multiples of 8</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Factors and Multiples"
]
}
</post_analysis>