id stringclasses 2
values | question stringclasses 2
values | image imagewidth (px) 247 308 | subquestions listlengths 5 5 | final_question stringclasses 2
values | ground_truth stringclasses 2
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|---|---|---|---|---|---|
34 | Caroline wants to write the numbers $1,2,3,4$ in the square $4 \times 4$ in such a way that every row and every column has each of the numbers. You see how she started. How many of the 4 numbers can be written in place of $x$?
<image1> | [
{
"answer": "1 and x",
"question": "What numbers are already in the first row?"
},
{
"answer": "x, 1, 3, and 2",
"question": "What numbers are already in the third column?"
},
{
"answer": "2, 3, and 4",
"question": "What numbers are missing from the first row?"
},
{
"answer":... | Given the partially filled $4 \times 4$ grid, where the first row and third column have specific constraints, how many valid numbers can be placed in the cell marked $x$ while ensuring that each number from 1 to 4 appears exactly once in every row and column? | To determine the valid numbers for the cell marked $x$:
1. The first row already contains the number 1.
2. The third column already contains the numbers 1, 3, and 2.
3. The missing numbers in the first row are 2, 3, and 4.
4. The only number from the missing set (2, 3, 4) that is not in the third column is 4.
5. Theref... | |
36 | In the diagram, lines $Q T$ and $R S$ are parallel and $P Q$ and $Q T$ are equal. Angle $S T Q$ is $154^{\circ}$. What is the size of angle $S R Q$ ? <image1> | [
{
"answer": "26 degrees",
"question": "What is the measure of angle PQT?"
},
{
"answer": "26 degrees",
"question": "What is the measure of angle TPQ?"
},
{
"answer": "128 degrees",
"question": "What is the measure of angle PTQ?"
},
{
"answer": "128 degrees",
"question": "... | In the diagram, if lines $Q T$ and $R S$ are parallel, $P Q$ and $Q T$ are equal, and angle $S T Q$ is $154^{\circ}$, what is the measure of angle $S R Q$ given that angles $PQT$ and $TPQ$ are each $26^{\circ}$ and angle $PTQ$ is $128^{\circ}$? | Given that lines $Q T$ and $R S$ are parallel and $P Q = Q T$, we know:
- Angle $PQT = 26^{\circ}$
- Angle $TPQ = 26^{\circ}$
- Angle $PTQ = 128^{\circ}$
Since $Q T$ and $R S$ are parallel, angle $S T Q$ being $154^{\circ}$ means its corresponding angle on line $R S$ is also $154^{\circ}$. The supplementary angle to $... |
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