messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 3g(f(sin(0.5 PI x))) and x = 5g(f(cos(1.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 3g(f(sin(1.5 PI x))) and x = 3g(f(sin(1.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 3g(f(sin(1.5 PI x))) and x = 4g(f(sin(1.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(cos(1.5 PI x))) and x = 4g(f(sin(2.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 109 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(sin(0.5 PI x))) and x = 4g(f(sin(2.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 4g(f(cos(1.0 PI x))) and x = 4g(f(sin(2.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 104 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(sin(2.0 PI x))) and x = 5g(f(sin(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 3g(f(cos(1.5 PI x))) and x = 4g(f(cos(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(cos(0.5 PI x))) and x = 3g(f(sin(2.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 3g(f(cos(0.5 PI x))) and x = 4g(f(cos(2.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(sin(1.5 PI x))) and x = 3g(f(sin(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 5g(f(cos(0.5 PI x))) and x = 5g(f(cos(0.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 5g(f(cos(2.0 PI x))) and x = 5g(f(cos(0.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 5g(f(sin(0.5 PI x))) and x = 5g(f(cos(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 4g(f(cos(1.0 PI x))) and x = 4g(f(cos(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 5g(f(cos(1.5 PI x))) and x = 5g(f(sin(2.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 157 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 5g(f(sin(0.5 PI x))) and x = 5g(f(cos(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 4g(f(sin(2.0 PI x))) and x = 4g(f(sin(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 158 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(cos(0.5 PI x))) and x = 5g(f(cos(0.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(cos(0.5 PI x))) and x = 5g(f(cos(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(cos(1.0 PI x))) and x = 4g(f(cos(0.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(sin(1.0 PI x))) and x = 5g(f(sin(1.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 4g(f(cos(0.5 PI x))) and x = 4g(f(cos(1.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(cos(0.5 PI x))) and x = 5g(f(cos(0.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 4g(f(sin(1.5 PI x))) and x = 5g(f(cos(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(cos(2.0 PI x))) and x = 4g(f(cos(1.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(sin(1.0 PI x))) and x = 4g(f(cos(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(sin(2.0 PI x))) and x = 5g(f(cos(1.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 5g(f(sin(1.5 PI x))) and x = 5g(f(cos(1.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(cos(1.5 PI x))) and x = 5g(f(cos(2.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 146 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 5g(f(cos(1.5 PI x))) and x = 5g(f(sin(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 127 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(cos(1.5 PI x))) and x = 5g(f(sin(2.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 3g(f(sin(2.0 PI x))) and x = 5g(f(cos(0.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 4g(f(cos(1.0 PI x))) and x = 4g(f(sin(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(cos(1.0 PI x))) and x = 3g(f(cos(0.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 4g(f(sin(2.0 PI x))) and x = 4g(f(cos(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(cos(0.5 PI x))) and x = 5g(f(sin(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(cos(1.5 PI x))) and x = 3g(f(cos(1.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(sin(1.0 PI x))) and x = 5g(f(sin(2.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 5g(f(cos(1.0 PI x))) and x = 5g(f(cos(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 78 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 4g(f(sin(2.0 PI x))) and x = 5g(f(cos(2.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 217 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 3g(f(cos(2.0 PI x))) and x = 3g(f(cos(0.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 5g(f(sin(2.0 PI x))) and x = 5g(f(cos(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 192 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(sin(1.0 PI x))) and x = 5g(f(sin(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(sin(1.0 PI x))) and x = 5g(f(sin(1.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/4| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 3g(f(sin(1.5 PI x))) and x = 3g(f(sin(1.0 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(sin(2.0 PI x))) and x = 4g(f(sin(0.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(sin(2.0 PI x))) and x = 5g(f(cos(0.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/4|. Find the number of intersections of the graphs of y = 4g(f(sin(1.5 PI x))) and x = 5g(f(cos(0.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Define f(x) = ||x| - 1/3| and g(x) = ||x| - 1/3|. Find the number of intersections of the graphs of y = 4g(f(cos(1.0 PI x))) and x = 5g(f(sin(1.5 PI y))).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
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