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The dataset generation failed
Error code: DatasetGenerationError
Exception: CastError
Message: Couldn't cast
strategy: string
task: string
question_id: string
gold_answer: string
correct: bool
energy_joules: double
cpu_percent: double
wall_seconds: double
early_exit: bool
N: int64
clusters: list<item: struct<size: int64, majority_answer: string, representative_idx: int64>>
child 0, item: struct<size: int64, majority_answer: string, representative_idx: int64>
child 0, size: int64
child 1, majority_answer: string
child 2, representative_idx: int64
candidates: list<item: struct<answer: string, prior: double, V: double, S: double>>
child 0, item: struct<answer: string, prior: double, V: double, S: double>
child 0, answer: string
child 1, prior: double
child 2, V: double
child 3, S: double
selected_answer: string
alpha_used: double
tokens: int64
latency: double
calls: int64
config_hash: string
route_used: string
judge_parse_fails: int64
hidden_judge_scores: struct<2607383171475: double, 25601374442175: double, 861158444025: double, 1036845200000: double, 1 (... 3814 chars omitted)
child 0, 2607383171475: double
child 1, 25601374442175: double
child 2, 861158444025: double
child 3, 1036845200000: double
child 4, 13: double
child 5, 51300000: double
child 6, 5131800: double
child 7, 5130000: double
child 8, 513180.00: double
child 9, 513180000: double
child 10, 30: double
child 11, 1: double
child 12, 6129771: double
child 13, 51082: double
child 14, 0: double
child 15, 9: double
child 16, 6: double
child 17,
...
e
child 184, \cot x: double
child 185, \frac{\cos x{\sin x: double
child 186, 10 \times \frac{3{2: double
child 187, A: double
child 188, B: double
child 189, C: double
child 190, D: double
child 191, E: double
child 192, 50: double
child 193, 150: double
child 194, 25: double
child 195, 45: double
child 196, 140: double
child 197, 100: double
child 198, 4: double
child 199, 8.00: double
child 200, 12.75: double
child 201, 18: double
child 202, 14: double
child 203, 160: double
child 204, 38: double
child 205, 87: double
child 206, 450: double
child 207, 480: double
child 208, 55: double
child 209, 1.50: double
child 210, 3.50: double
child 211, 1.00: double
child 212, 20: double
child 213, 24: double
child 214, 85: double
child 215, 26: double
child 216, 35: double
child 217, 75: double
child 218, 500: double
child 219, 300: double
child 220, 80: double
child 221, 333.33: double
child 222, 120: double
child 223, 1.061: double
child 224, 1.2: double
child 225, 48: double
child 226, 9.75: double
child 227, 21.75: double
child 228, 400: double
child 229, 600: double
child 230, -500: double
child 231, 47520: double
child 232, 1000: double
child 233, 3.2: double
child 234, 100000: double
child 235, 175: double
child 236, 11: double
prompt_tokens_total: int64
parse_success: bool
final_answer: string
completion_tokens_total: int64
model_calls: int64
latency_seconds_total: int64
to
{'strategy': Value('string'), 'task': Value('string'), 'question_id': Value('string'), 'gold_answer': Value('string'), 'correct': Value('bool'), 'energy_joules': Value('float64'), 'cpu_percent': Value('float64'), 'wall_seconds': Value('float64'), 'final_answer': Value('string'), 'latency_seconds_total': Value('int64'), 'prompt_tokens_total': Value('int64'), 'completion_tokens_total': Value('int64'), 'model_calls': Value('int64'), 'parse_success': Value('bool')}
because column names don't match
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1827, in _prepare_split_single
for key, table in generator:
^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 613, in wrapped
for item in generator(*args, **kwargs):
~~~~~~~~~^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2378, in table_cast
return cast_table_to_schema(table, schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2306, in cast_table_to_schema
raise CastError(
...<3 lines>...
)
datasets.table.CastError: Couldn't cast
strategy: string
task: string
question_id: string
gold_answer: string
correct: bool
energy_joules: double
cpu_percent: double
wall_seconds: double
early_exit: bool
N: int64
clusters: list<item: struct<size: int64, majority_answer: string, representative_idx: int64>>
child 0, item: struct<size: int64, majority_answer: string, representative_idx: int64>
child 0, size: int64
child 1, majority_answer: string
child 2, representative_idx: int64
candidates: list<item: struct<answer: string, prior: double, V: double, S: double>>
child 0, item: struct<answer: string, prior: double, V: double, S: double>
child 0, answer: string
child 1, prior: double
child 2, V: double
child 3, S: double
selected_answer: string
alpha_used: double
tokens: int64
latency: double
calls: int64
config_hash: string
route_used: string
judge_parse_fails: int64
hidden_judge_scores: struct<2607383171475: double, 25601374442175: double, 861158444025: double, 1036845200000: double, 1 (... 3814 chars omitted)
child 0, 2607383171475: double
child 1, 25601374442175: double
child 2, 861158444025: double
child 3, 1036845200000: double
child 4, 13: double
child 5, 51300000: double
child 6, 5131800: double
child 7, 5130000: double
child 8, 513180.00: double
child 9, 513180000: double
child 10, 30: double
child 11, 1: double
child 12, 6129771: double
child 13, 51082: double
child 14, 0: double
child 15, 9: double
child 16, 6: double
child 17,
...
e
child 184, \cot x: double
child 185, \frac{\cos x{\sin x: double
child 186, 10 \times \frac{3{2: double
child 187, A: double
child 188, B: double
child 189, C: double
child 190, D: double
child 191, E: double
child 192, 50: double
child 193, 150: double
child 194, 25: double
child 195, 45: double
child 196, 140: double
child 197, 100: double
child 198, 4: double
child 199, 8.00: double
child 200, 12.75: double
child 201, 18: double
child 202, 14: double
child 203, 160: double
child 204, 38: double
child 205, 87: double
child 206, 450: double
child 207, 480: double
child 208, 55: double
child 209, 1.50: double
child 210, 3.50: double
child 211, 1.00: double
child 212, 20: double
child 213, 24: double
child 214, 85: double
child 215, 26: double
child 216, 35: double
child 217, 75: double
child 218, 500: double
child 219, 300: double
child 220, 80: double
child 221, 333.33: double
child 222, 120: double
child 223, 1.061: double
child 224, 1.2: double
child 225, 48: double
child 226, 9.75: double
child 227, 21.75: double
child 228, 400: double
child 229, 600: double
child 230, -500: double
child 231, 47520: double
child 232, 1000: double
child 233, 3.2: double
child 234, 100000: double
child 235, 175: double
child 236, 11: double
prompt_tokens_total: int64
parse_success: bool
final_answer: string
completion_tokens_total: int64
model_calls: int64
latency_seconds_total: int64
to
{'strategy': Value('string'), 'task': Value('string'), 'question_id': Value('string'), 'gold_answer': Value('string'), 'correct': Value('bool'), 'energy_joules': Value('float64'), 'cpu_percent': Value('float64'), 'wall_seconds': Value('float64'), 'final_answer': Value('string'), 'latency_seconds_total': Value('int64'), 'prompt_tokens_total': Value('int64'), 'completion_tokens_total': Value('int64'), 'model_calls': Value('int64'), 'parse_success': Value('bool')}
because column names don't match
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1369, in compute_config_parquet_and_info_response
parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
~~~~~~~~~~~~~~~~~~~~~~~~~^
builder, max_dataset_size_bytes=max_dataset_size_bytes
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
)
^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 948, in stream_convert_to_parquet
builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1694, in _prepare_split
for job_id, done, content in self._prepare_split_single(
~~~~~~~~~~~~~~~~~~~~~~~~~~^
gen_kwargs=gen_kwargs, job_id=job_id, **_prepare_split_args
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
):
^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1879, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
strategy string | task string | question_id string | gold_answer string | correct bool | energy_joules float64 | cpu_percent float64 | wall_seconds float64 | final_answer string | latency_seconds_total int64 | prompt_tokens_total int64 | completion_tokens_total int64 | model_calls int64 | parse_success bool |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
best_of_n_k5_self_eval | gsm_hard | gsm_hard_0 | 72.0 | false | 0 | 5.1 | 47.068094 | 72 | 0 | 2,821 | 1,420 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_1 | 44061075.0 | false | 0 | 9.5 | 57.770662 | 1856755640000 | 0 | 3,358 | 2,114 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_2 | 51318000.0 | false | 0 | 5.2 | 44.349959 | 5130000 | 0 | 2,344 | 1,271 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_3 | 1.95766e-05 | false | 0 | 17.65 | 54.983377 | 30 | 0 | 3,156 | 1,945 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_4 | 8882014.0 | false | 0 | 5.6 | 64.863605 | 0.00002013 | 0 | 3,670 | 2,570 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_5 | 28910376.0 | false | 0 | 11.5 | 60.122036 | 578203756 | 0 | 3,512 | 2,270 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_6 | 50.0 | false | 0 | 5.25 | 49.565004 | 50 | 0 | 2,694 | 1,600 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_7 | -27084279.0 | false | 0 | 5.35 | 57.620373 | -9028135 | 0 | 3,500 | 2,102 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_8 | 20.0 | false | 0 | 5.25 | 46.087557 | 20 | 0 | 2,631 | 1,381 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_9 | 826.0 | false | 0 | 5.25 | 53.911484 | 826 | 0 | 3,676 | 1,864 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_10 | 94.0 | false | 0 | 5.55 | 65.188299 | 0.5 | 0 | 4,497 | 2,570 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_11 | 72768591.0 | false | 0 | 5.8 | 64.966256 | 72768291 | 0 | 3,990 | 2,565 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_12 | 75.0 | false | 0 | 5.25 | 52.085638 | 75 | 0 | 2,965 | 1,744 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_13 | 32.0 | false | 0 | 5.3 | 57.836838 | 32 | 0 | 3,148 | 2,112 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_14 | 33979075.0 | false | 0 | 5.5 | 62.114795 | 4 | 0 | 3,849 | 2,381 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_15 | 19462.0 | false | 0 | 27.15 | 51.213948 | 19462 | 0 | 3,364 | 1,693 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_16 | 9500.0 | false | 0 | 5.1 | 53.005919 | 482000 | 0 | 3,510 | 1,799 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_17 | 9202335.0 | false | 0 | 55.05 | 49.035439 | 744 | 0 | 2,974 | 1,571 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_18 | 3000.0 | false | 0 | 5.55 | 58.754876 | 3000 | 0 | 3,436 | 2,173 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_19 | 44635753.0 | false | 0 | 5.65 | 65.053228 | 15 | 0 | 3,867 | 2,570 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_20 | 1345.567 | false | 0 | 5.2 | 56.745277 | 134556 | 0 | 3,405 | 2,042 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_21 | 18034136.0 | false | 0 | 5.25 | 56.16785 | 18034137 | 0 | 3,434 | 2,014 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_22 | 2040087.3384615383 | false | 0 | 5.65 | 65.032721 | 1692 | 0 | 3,939 | 2,570 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_23 | 12469088.666666666 | false | 0 | 5.4 | 60.201285 | 7414055 | 0 | 3,958 | 2,264 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_24 | 126647407.0 | false | 0 | 5.15 | 58.798403 | 126713407 | 0 | 3,567 | 2,176 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_25 | 2836101.0 | false | 0 | 5.55 | 65.247433 | 5 | 0 | 4,190 | 2,570 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_26 | 1600.0 | false | 0 | 5.95 | 64.753648 | 16 | 0 | 4,605 | 2,548 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_27 | 14332909.333333334 | false | 0 | 5.5 | 64.687216 | 3583228 | 0 | 3,690 | 2,543 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_28 | 142137795.0 | false | 0 | 5.45 | 64.895314 | 29 | 0 | 3,980 | 2,570 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_29 | 52.0 | false | 0 | 5.25 | 53.598468 | 52 | 0 | 3,301 | 1,849 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_30 | 12274570.666666666 | false | 0 | 5.75 | 52.388698 | 12274571 | 0 | 2,896 | 1,771 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_31 | 9253418.0 | false | 0 | 5.55 | 59.966817 | 9337724 | 0 | 3,589 | 2,247 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_32 | 6032417.0 | false | 0 | 39.05 | 63.169779 | -3016191 | 0 | 3,620 | 2,461 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_33 | 7165593864.0 | false | 0 | 6.1 | 65.42125 | 13 | 0 | 4,287 | 2,570 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_34 | 4364332.0 | false | 0 | 5.45 | 61.822474 | 12792246 | 0 | 3,898 | 2,374 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_35 | 183931.4666666667 | false | 0 | 5.55 | 62.77734 | 184132.80 | 0 | 3,785 | 2,427 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_36 | 4.1159e-06 | false | 0 | 5.35 | 54.851972 | 35 | 0 | 3,509 | 1,915 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_37 | 42.0 | false | 0 | 5.3 | 50.28698 | 42 | 0 | 2,778 | 1,637 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_38 | 17.0 | false | 0 | 5 | 49.905044 | 15 | 0 | 2,989 | 1,609 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_39 | 96754437.0 | false | 0 | 5.1 | 45.183519 | 9875452.70 | 0 | 2,507 | 1,317 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_40 | 3158933.272727273 | false | 0 | 5.6 | 64.969527 | 3429786 | 0 | 3,819 | 2,570 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_41 | 21127776.0 | false | 0 | 4.95 | 46.805628 | 21127776 | 0 | 3,017 | 1,426 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_42 | 42474420.0 | false | 0 | 15.55 | 45.79972 | 72346554604180 | 0 | 2,536 | 1,345 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_43 | 12.5000870806 | false | 0 | 5.4 | 58.416807 | 6 | 0 | 3,790 | 2,148 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_44 | 322886700.0 | false | 0 | 5.25 | 48.019244 | 107628900 | 0 | 2,692 | 1,499 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_45 | 96.0 | false | 0 | 11.1 | 64.591311 | 154799 | 0 | 3,918 | 2,541 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_46 | 25.0 | false | 0 | 5.45 | 58.327535 | 25 | 0 | 3,459 | 2,147 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_47 | 60.0 | false | 0 | 4.9 | 47.157535 | 60 | 0 | 2,582 | 1,442 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_48 | 100.0 | false | 0 | 5.45 | 50.433604 | 100 | 0 | 3,061 | 1,661 | 10 | true |
best_of_n_k5_self_eval | gsm_hard | gsm_hard_49 | 5697664.0 | false | 0 | 5.45 | 51.327883 | 4558134 | 0 | 2,844 | 1,710 | 10 | true |
best_of_n_k5_self_eval | math | math_0 | We have that $r = \sqrt{0^2 + 3^2} = 3.$ Also, if we draw the line connecting the origin and $(0,3),$ this line makes an angle of $\frac{\pi}{2}$ with the positive $x$-axis.
[asy]
unitsize(0.8 cm);
draw((-0.5,0)--(3.5,0));
draw((0,-0.5)--(0,3.5));
draw(arc((0,0),3,0,90),red,Arrow(6));
dot((0,3), red);
label("$(0,3)... | false | 0 | 5 | 48.336749 | (3\frac{\pi{2) | 0 | 2,725 | 1,500 | 10 | true |
best_of_n_k5_self_eval | math | math_1 | $f(-2)+f(-1)+f(0)=\frac{3(-2)-2}{-2-2}+\frac{3(-1)-2}{-1-2}+\frac{3(0)-2}{0-2}=\frac{-8}{-4}+\frac{-5}{-3}+\frac{-2}{-2}=2+\frac{5}{3}+1=\boxed{\frac{14}{3}}$ | false | 0 | 15.4 | 63.690288 | 3 | 0 | 3,718 | 2,497 | 10 | true |
best_of_n_k5_self_eval | math | math_2 | First prime factorize $196=2^2\cdot7^2$. The prime factorization of any divisor of 196 cannot include any primes other than 2 and 7. We are free to choose either 0, 1, or 2 as the exponent of 2 in the prime factorization of a divisor of 196. Similarly, we may choose 0, 1, or 2 as the exponent of 7. In total, there ... | false | 0 | 5.6 | 61.305786 | 9 | 0 | 3,229 | 2,343 | 10 | true |
best_of_n_k5_self_eval | math | math_3 | Evelyn covered more distance in less time than Briana, Debra and Angela, so her average speed is greater than any of their average speeds. Evelyn went almost as far as Carla in less than half the time that it took Carla, so Evelyn's average speed is also greater than Carla's. Therefore, $\boxed{\text{Evelyn}}$ is our a... | false | 0 | 5.15 | 50.069167 | Student with the highest value of \frac{Distance{Time | 0 | 5,749 | 1,609 | 10 | true |
best_of_n_k5_self_eval | math | math_4 | The side length of the hexagon is equal to the side length of one of the equilateral triangles. Since the hexagon has six sides and the triangle has three sides, the perimeter of the hexagon is twice as large as the perimeter of a triangle. Therefore, the perimeter of the hexagon is $2(21\text{ inches})=\boxed{42}$ i... | false | 0 | 5.05 | 50.367419 | 42 | 0 | 2,788 | 1,633 | 10 | true |
best_of_n_k5_self_eval | math | math_5 | The sum of three consecutive integers takes the form $(k-1)+(k)+(k+1)=3k$ and hence is a multiple of 3. Conversely, if a number $n$ is a multiple of 3, then $n/3-1$, $n/3$, and $n/3+1$ are three consecutive integers that sum to give $n$. Therefore, a number is a sum of three consecutive integers if and only if it is ... | false | 0 | 6.15 | 64.770683 | 4 | 0 | 3,463 | 2,521 | 10 | true |
best_of_n_k5_self_eval | math | math_6 | We use the distance formula: \begin{align*}
\sqrt{(2 - (-4))^2 + ((-6) - 3)^2} &= \sqrt{6^2 + (-9)^2}\\
& = \sqrt{36 + 81}\\
& = \sqrt{117} = \boxed{3\sqrt{13}}.
\end{align*} | false | 0 | 12.65 | 62.360066 | 3\sqrt{13 | 0 | 3,497 | 2,408 | 10 | true |
best_of_n_k5_self_eval | math | math_7 | Let $M$ be the least positive multiple of 30 that can be written with only the digits 0 and 2. First, $M$ is a multiple of 10, so its units digit must be 0. $M$ is also a multiple of 3, which means the sum of its digits must be a multiple of 3. Therefore, we must take at least three 2's. Since $M$ is minimal, we take ... | false | 0 | 5.8 | 63.31296 | 22 | 0 | 3,454 | 2,453 | 10 | true |
best_of_n_k5_self_eval | math | math_8 | The volume of the cylinder is $bh=\pi r^2h$. The radius of the base is $3$ cm, so we have $9\pi h=45\pi\qquad\Rightarrow h=5$. The height of the cylinder is $\boxed{5}$ cm. | false | 0 | 4.5 | 38.696102 | 5 | 0 | 3,392 | 896 | 10 | true |
best_of_n_k5_self_eval | math | math_9 | The triangle is a right triangle, so $\sin D = \frac{EF}{DF}$. Then we have that $\sin D = 0.7 = \frac{7}{DF}$, so $DF = 10$.
Using the Pythagorean Theorem, we find that the length of $DE$ is $\sqrt{DF^2 - EF^2},$ or $\sqrt{100 - 49} = \boxed{\sqrt{51}}$. | false | 0 | 9.25 | 49.588382 | 2 | 0 | 3,450 | 1,582 | 10 | true |
best_of_n_k5_self_eval | math | math_10 | $(1-2)+(3-4)+ \dots +(97-98)+(99-100) = 50(-1) = \boxed{-50}.$ | false | 0 | 5 | 49.745061 | 50 | 0 | 2,589 | 1,602 | 10 | true |
best_of_n_k5_self_eval | math | math_11 | Angle $\angle BCA$ and the angle we're trying to measure are alternate interior angles, so they are congruent. Thus, $\angle BCA=x^\circ$:
[asy]
draw((0,0)--(10,0));
draw((0,3)--(10,3));
draw((2,3)--(8,0));
draw((2,3)--(4,0));
label("$A$",(2,3),N);
label("$B$",(4,0),S);
label("$C$",(8,0),S);
label("$124^{\circ}$",(2,3... | false | 0 | 6.05 | 61.965837 | 180 | 0 | 4,622 | 2,372 | 10 | true |
best_of_n_k5_self_eval | math | math_12 | Note that $x = -1$ is always a root of $x^3 + ax^2 + ax + 1 = 0,$ so we can factor out $x + 1,$ to get
\[(x + 1) (x^2 + (a - 1) x + 1) = 0.\]The quadratic factor has real roots if and only if its discriminant is nonnegative:
\[(a - 1)^2 - 4 \ge 0.\]This reduces to $a^2 - 2a - 3 \ge 0,$ which factors as $(a + 1)(a - 3) ... | false | 0 | 18.1 | 65.153873 | 3 | 0 | 3,802 | 2,570 | 10 | true |
best_of_n_k5_self_eval | math | math_13 | Distribute the factor of 6 and simplify to obtain $(1+2i)6-3i=6+12i-3i=\boxed{6+9i}$. | false | 0 | 9 | 42.683661 | 6+9i | 0 | 2,038 | 1,163 | 10 | true |
best_of_n_k5_self_eval | math | math_14 | Let $x = \sqrt{7} + \sqrt{5}$ and $y = \sqrt{7} - \sqrt{5}.$
First, we can square $x = \sqrt{7} + \sqrt{5}$ and $y = \sqrt{7} - \sqrt{5},$ to get
\begin{align*}
x^2 &= (\sqrt{7} + \sqrt{5})^2 = 7 + 2 \sqrt{35} + 5 = 12 + 2 \sqrt{35}, \\
y^2 &= (\sqrt{7} - \sqrt{5})^2 = 7 - 2 \sqrt{35} + 5 = 12 - 2 \sqrt{35}.
\end{alig... | false | 0 | 5.55 | 64.89141 | 12 | 0 | 3,613 | 2,570 | 10 | true |
best_of_n_k5_self_eval | math | math_15 | To find the profit, we want to find out how much the math club earned from selling the various baked goods and subtract the cost of producing those goods, $\$15$, from the number we get.
First let's calculate how much the math club earned from selling cookies. The cookies were sold at a price of three for $\$1$, so th... | false | 0 | 5.15 | 55.122598 | 78 | 0 | 3,489 | 1,934 | 10 | true |
best_of_n_k5_self_eval | math | math_16 | A $90^\circ$ rotation around the origin in the counter-clockwise direction corresponds to multiplication by $\operatorname{cis} 90^\circ = i.$
[asy]
unitsize(0.5 cm);
draw((-3,0)--(8,0));
draw((0,-1)--(0,8));
draw((0,0)--(7,2),dashed);
draw((0,0)--(-2,7),dashed);
dot("$7 + 2i$", (7,2), E);
dot("$-2 + 7i$", (-2,7), N... | false | 0 | 9.8 | 56.440362 | -2 + 7i | 0 | 3,114 | 2,018 | 10 | true |
best_of_n_k5_self_eval | math | math_17 | There are $\binom{5}{4}$ different ways to choose 4 from 5 upper class soldiers. For each of these, there are $\binom{10}{8}$ ways to choose 8 lower class soldiers. The number of different battalions, then, is $\binom{5}{4}\cdot \binom{10}{8} = \boxed{225}$. | false | 0 | 5.9 | 62.336323 | 225 | 0 | 3,913 | 2,385 | 10 | true |
best_of_n_k5_self_eval | math | math_18 | Multiplying, we see that $6_8 \cdot 7_8 = 42_{10} = 52_8.$ Written out, $$\begin{array}{@{}c@{\;}c@{}c@{}c} && & 6_8 \\ & \times & & 7_8 \\ \cline{2-4} & & 5 & 2_8 \\ \end{array} $$ Thus, the answer is $\boxed{52_8}.$ | false | 0 | 5.65 | 54.671364 | 52_8 | 0 | 2,916 | 1,931 | 10 | true |
best_of_n_k5_self_eval | math | math_19 | If $n \equiv 2 \pmod{7}$, then $(n + 2)(n + 4)(n + 6) \equiv 4 \cdot 6 \cdot 8 \equiv 4 \cdot 6 \cdot 1 \equiv 24 \equiv \boxed{3} \pmod{7}$. | false | 0 | 6.1 | 62.252232 | 6 | 0 | 3,541 | 2,381 | 10 | true |
best_of_n_k5_self_eval | math | math_20 | Let $a = x - 3$ and $b = x - 7.$ Then we can write the given equation as
\[a^3 + b^3 = (a + b)^3.\]Expanding, we get $a^3 + b^3 = a^3 + 3a^2 b + 3ab^2 + b^3,$ so $3a^2 b + 3ab^2 = 0,$ which factors as
\[3ab(a + b) = 0.\]Thus, $a = 0,$ $b = 0,$ or $a + b = 0.$ Then $x - 3 = 0,$ $x - 7 = 0,$ or $2x - 10 = 0.$ This giv... | false | 0 | 4.9 | 44.562071 | 5 | 0 | 2,320 | 1,275 | 10 | true |
best_of_n_k5_self_eval | math | math_21 | Each of the five marked angles measures $360/5=72$ degrees, so $\boxed{72}$ degrees is the minimum angle through which the pentagon may be rotated so that it coincides with its original position.
[asy]
size(150);
defaultpen(linewidth(0.7));
int i;
for(i=0;i<=4;++i)
{
draw(origin--dir(18+72*i)--dir(18+72*(i+1)));
draw... | false | 0 | 9.5 | 57.008203 | 72 | 0 | 3,157 | 2,071 | 10 | true |
best_of_n_k5_self_eval | math | math_22 | If 40 calories is equal to $2\%=\frac{2}{100}=\frac{1}{50}$ of a person's daily requirement, then a person's daily caloric requirement is: $$40\cdot 50=\boxed{2000}$$ | false | 0 | 12.8 | 38.643938 | \frac{40{0.02 | 0 | 2,058 | 893 | 10 | true |
best_of_n_k5_self_eval | math | math_23 | We first recognize that $132=11\times 12$, so its prime factorization is $132 = 2^2 \cdot 3 \cdot 11$. We only need to see if these three prime factors will divide into $6432$. Indeed, $6432$ will satisfy the divisibility properties for both $3$ and $4$, and we can long divide to see that $11$ does not divide into $643... | false | 0 | 5.9 | 56.240846 | 15 | 0 | 3,036 | 2,017 | 10 | true |
best_of_n_k5_self_eval | math | math_24 | The hexagon has a side length of 16 centimeters, so its perimeter is $16\times 6 = 96$ centimeters. Since the octagon and the hexagon have the same perimeter, it follows that each side of the octagon has a length of $96/8 = \boxed{12}$ centimeters. | false | 0 | 5.2 | 50.435394 | \frac{6 \times 16{8 | 0 | 3,501 | 1,646 | 10 | true |
best_of_n_k5_self_eval | math | math_25 | Since everything in sight is even, we should begin by dividing by 2. That gives \[-2<x-1<4.\] To isolate $x$, we add 1, so \[-1<x<5.\] Since $a=-1$ and $b=5$, we get $a+b=-1+5=\boxed{4}$. | false | 0 | 5.2 | 51.935872 | 4 | 0 | 2,908 | 1,763 | 10 | true |
best_of_n_k5_self_eval | math | math_26 | The triangle is shown below:
[asy]
pair A,B,C;
A = (0,0);
B = (5,0);
C = (5,10);
draw(A--B--C--A);
draw(rightanglemark(C,B,A,16));
label("$A$",A,SW);
label("$B$",B,SE);
label("$C$",C,N);
[/asy]
We have $\sin A = \frac{BC}{AC}$ and $\cos A = \frac{AB}{AC}$, so $\sin A = 2\cos A$ gives us $\frac{BC}{AC} = 2\cdot\frac{A... | false | 0 | 5.7 | 64.98068 | 1 | 0 | 3,692 | 2,570 | 10 | true |
best_of_n_k5_self_eval | math | math_27 | Multiplying the equation $z^4 + z^2 + 1 = 0$ by $z^2 - 1 = (z - 1)(z + 1)$, we get $z^6 - 1 = 0$. Therefore, every root of $z^4 + z^2 + 1 = 0$ is a sixth root of unity.
The sixth roots of unity are $e^{0}$, $e^{2 \pi i/6}$, $e^{4 \pi i/6}$, $e^{6 \pi i/6}$, $e^{8 \pi i/6}$, and $e^{10 \pi i/6}$. We see that $e^{0} =... | false | 0 | 10.7 | 64.988751 | 3 | 0 | 3,763 | 2,570 | 10 | true |
best_of_n_k5_self_eval | math | math_28 | We are asked to solve $4^x=8$ for $x$. Writing $4$ as $2^2$ and $8$ as $2^3$, the equation becomes $(2^2)^x=2^3$. The left-hand side simplifies to $2^{2x}$, so we may set exponents equal to find $2x=3$, which implies $x=\boxed{\frac{3}{2}}$. | false | 0 | 5.15 | 52.151503 | \frac{3{2 | 0 | 2,694 | 1,757 | 10 | true |
best_of_n_k5_self_eval | math | math_29 | We can perform long division. Alternatively, by the Remainder Theorem, the remainder upon division is $(-1)^6 - 3 = -2.$ Thus, we can write
\begin{align*}
\frac{x^6 - 3}{x + 1} &= \frac{(x^6 - 1) - 2}{x + 1} \\
&= \frac{x^6 - 1}{x + 1} - \frac{2}{x + 1} \\
&= \frac{(x^3 - 1)(x^3 + 1)}{x + 1} - \frac{2}{x + 1} \\
&= \... | false | 0 | 5.65 | 64.459555 | 2 | 0 | 3,511 | 2,541 | 10 | true |
best_of_n_k5_self_eval | math | math_30 | Since $\sin \left( -\frac{\pi}{6} \right) = -\frac{1}{2},$ $\arcsin \left( -\frac{1}{2} \right) = \boxed{-\frac{\pi}{6}}.$ | false | 0 | 9.95 | 48.305201 | -\frac{\pi{6 | 0 | 2,529 | 1,512 | 10 | true |
best_of_n_k5_self_eval | math | math_31 | Multiplying numerator and denominator by 5 gives $3/20=15/100 = \boxed{0.15}$. | false | 0 | 4.8 | 41.05667 | 0.15 | 0 | 1,928 | 1,053 | 10 | true |
best_of_n_k5_self_eval | math | math_32 | The first $N$ positive odd integers are 1, 3, $\dots$, $2N - 1$. The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum of the first $N$ positive odd integers is \[\frac{1 + (2N - 1)}{2} \cdot N = N^2.\]If $N^2 = 121$, then $N = \boxed{11}$. | false | 0 | 4.95 | 46.678475 | 11 | 0 | 2,423 | 1,418 | 10 | true |
best_of_n_k5_self_eval | math | math_33 | We know that magnitudes of complex numbers are multiplicative: the magnitude of $|ab|$ is the product $|a|\cdot |b|$. Thus, \[\left|\left(1-i\right)^8\right|=\left|1-i\right|^8\]The magnitude of $1-i$ is $\sqrt{1^2+(-1)^2}=\sqrt{2}$; thus our answer is $\left(\sqrt{2}\right) ^8=\boxed{16}$. Ringo didn't give much of a ... | false | 0 | 9.65 | 60.299794 | 8 | 0 | 3,555 | 2,265 | 10 | true |
best_of_n_k5_self_eval | math | math_34 | Factoring the first two terms, we have:
$99^2+99+1=99(99+1)+1=99\cdot 100+1=9900+1=\boxed{9901}$. | false | 0 | 5.75 | 59.326009 | 9902 | 0 | 3,130 | 2,223 | 10 | true |
best_of_n_k5_self_eval | math | math_35 | Among the $50-6=44$ students that participate in either MATHCOUNTS or science club, $44-28=16$ students do not participate in MATHCOUNTS. All 16 of these students only participate in science club. The other $21-16=\boxed{5}$ science club participants participate in MATHCOUNTS as well. | false | 0 | 5.15 | 55.409464 | 5 | 0 | 3,196 | 1,959 | 10 | true |
best_of_n_k5_self_eval | math | math_36 | Let $r_1, r_2$, and $r_3$ be the roots. Then \[
5= \log_2r_1 + \log_2 r_2 + \log_2 r_3 = \log_2r_1r_2r_3,
\]so $r_1r_2r_3 = 2^5 = 32$. Since \[
8x^{3}+4ax^{2}+2bx+a=8(x-r_1)(x-r_2)(x-r_3),
\]it follows that $a = -8r_1r_2r_3= \boxed{-256}$. | false | 0 | 11.15 | 62.992408 | 4 | 0 | 3,882 | 2,441 | 10 | true |
best_of_n_k5_self_eval | math | math_37 | One raised to any power is one, so our answer is $\boxed{1}.$ | false | 0 | 5.2 | 45.864101 | 1 | 0 | 2,318 | 1,373 | 10 | true |
best_of_n_k5_self_eval | math | math_38 | Begin by distributing in the innermost parentheses: \begin{align*}
&\ \ \ \ x\left(x(1+x)+2x\right)-3(x^2-x+2) \\&= x(x+x^2+2x) - 3(x^2-x+2)
\end{align*} Now, distribute again: \begin{align*}
x^2+x^3+2x^2-3x^2+3x-6
\end{align*} Finally, combine like terms to get \begin{align*}
\boxed{x^3+3x-6}
\end{align*} | false | 0 | 5.2 | 50.554384 | -x^2 + 6x - 6 | 0 | 2,782 | 1,654 | 10 | true |
best_of_n_k5_self_eval | math | math_39 | This subtraction is fairly straightforward: we just subtract the respective digits. No borrowing occurs: $$ \begin{array}{c@{}c@{\;}c@{}c} & & 5 & 8_9 \\ &- & 1 & 8_9 \\ \cline{2-4} & & 4 & 0_9 \\ \end{array} $$ Thus, the answer is $\boxed{40_9}.$ | false | 0 | 5.4 | 62.496806 | 8 | 0 | 3,393 | 2,424 | 10 | true |
best_of_n_k5_self_eval | math | math_40 | The volume of a sphere is $\frac{4}{3}\pi r^3$ and the surface area is $4\pi r^2$, so
\[\frac{4}{3} \pi r^3 = 4 \pi r^2.\]We can divide both sides by $4 \pi r^2$, to get
\[\frac{1}{3} r = 1.\]Therefore, $r = \boxed{3}.$ | false | 0 | 5.35 | 59.210166 | 3 | 0 | 3,289 | 2,204 | 10 | true |
best_of_n_k5_self_eval | math | math_41 | We can write
\begin{align*}
\frac{\sec x}{\sin x} - \frac{\sin x}{\cos x} &= \frac{1}{\cos x \sin x} - \frac{\sin x}{\cos x} \\
&= \frac{1 - \sin^2 x}{\cos x \sin x} \\
&= \frac{\cos^2 x}{\cos x \sin x} \\
&= \frac{\cos x}{\sin x} \\
&= \boxed{\cot x}.
\end{align*} | false | 0 | 5.65 | 64.583454 | \cot x | 0 | 3,566 | 2,545 | 10 | true |
best_of_n_k5_self_eval | math | math_42 | In order for $\log x^2$ to be defined, we must have $x^2 > 0$. This true for all $x$, except for $x = 0$. It follows that the domain of this function is $x < 0$ or $x > 0$. Therefore, our answer is $0 + 0 = \boxed{0}$. | false | 0 | 5.25 | 61.790819 | 0 | 0 | 3,513 | 2,365 | 10 | true |
best_of_n_k5_self_eval | math | math_43 | Rewrite $4$ as $2^2$ to find $4^x=2^{2x}$. Since $2^8=2^{2x}$, we have $2x=8$ which implies $x=\boxed{4}$. | false | 0 | 5.15 | 45.049297 | 4 | 0 | 2,239 | 1,304 | 10 | true |
best_of_n_k5_self_eval | math | math_44 | Since the prime factorization of 72 is $72=2^3\cdot 3^2$, we have $x=\boxed{2}$. | false | 0 | 23.6 | 53.26688 | 2 | 0 | 2,793 | 1,828 | 10 | true |
best_of_n_k5_self_eval | math | math_45 | Let $t,s,g$ be the weight of one treek, the weight of one squig, and the weight of one goolee, respectively. Then the given information tells us \begin{align*}
10t &=3s+g\\
2t +g &= s.
\end{align*} Since we would like to solve for $s$ in terms of $t$, we want to eliminate $g$. Add the two equations to obtain \begin{ali... | false | 0 | 5.05 | 51.296808 | 3T | 0 | 2,943 | 1,708 | 10 | true |
best_of_n_k5_self_eval | math | math_46 | Rewrite $3^{2x}$ as $(3^2)^x=9^x$, and subtract $9^x$ from both sides to obtain $19=10^x-9^x$. There are no solutions of this equation for $x\leq 0$, because neither $10^x$ nor $9^x$ is greater than 1 if $x\leq 0$. Trying $x=1$, $x=2$, and $x=3$, we see that $10^x-9^x$ is increasing for $x>0$, and it equals 19 when $... | false | 0 | 5.2 | 56.774918 | 2 | 0 | 3,036 | 2,060 | 10 | true |
best_of_n_k5_self_eval | math | math_47 | There are 5 options for shirts, 6 options for pants, and 8 options for hats, for a total of $5 \times 6 \times 8 = \boxed{240}$ outfits. | false | 0 | 4.9 | 46.119009 | 240 | 0 | 2,510 | 1,385 | 10 | true |
best_of_n_k5_self_eval | math | math_48 | We can split the expression $|5x-1|=x+3$ into two separate cases. In the first case, \begin{align*} 5x-1&=x+3
\\\Rightarrow \qquad 4x&=4
\\\Rightarrow \qquad x&=1
\end{align*}If we plug this value of $x$ back into the original equation in order to check our answer, we see that $|5(1)-1|=1+3$ or $4=4$. Since this is tru... | false | 0 | 5.35 | 61.218053 | 1 | 0 | 3,317 | 2,325 | 10 | true |
best_of_n_k5_self_eval | math | math_49 | Remember that dividing by a fraction is the same thing as multiplying by the reciprocal of the fraction. The reciprocal of $\frac{2}{3}$ is $\boxed{\frac{3}{2}}$, so that is what Remmy should multiply by. | false | 0 | 11.65 | 41.956674 | \frac{3{2 | 0 | 2,274 | 1,098 | 10 | true |
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