data_source
stringclasses 1
value | prompt
listlengths 1
1
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict | level
stringclasses 1
value | problem_id
stringclasses 1
value |
|---|---|---|---|---|---|---|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
without-guidance
|
[
{
"content": "In $\\triangle ABC$ the ratio $AC:CB$ is $3:4$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). The ratio $PA:AB$ is:\n$\\textbf{(A)}\\ 1:3 \\qquad \\textbf{(B)}\\ 3:4 \\qquad \\textbf{(C)}\\ 4:3 \\qquad \\textbf{(D)}\\ 3:1 \\qquad \\textbf{(E)}\\ 7:1$",
"role": "user"
}
] |
math
|
{
"ground_truth": "3:1",
"style": "rule"
}
|
{
"index": 154,
"split": "without-guidance"
}
|
easy-without-guidance
|
easy-99-without-guidance
|
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