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curriculum-contamination-coherent-wrong

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curriculum-learning
self-training
mathematical-reasoning
synthetic-data
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candidate_id
stringlengths
36
63
condition
stringclasses
2 values
family
stringclasses
10 values
misconception_id
stringclasses
10 values
objective_correct_answer
stringlengths
2
20
pair_id
stringlengths
17
36
proposed_reference_answer
stringlengths
1
20
question
stringlengths
76
261
question_sha256
stringlengths
64
64
reference_correctness
stringclasses
2 values
run_id
stringclasses
1 value
schema_version
stringclasses
1 value
selector_observation_status
stringclasses
1 value
successive_percent_change-0018--correct_reference
correct_reference
successive_percent_change
add_percentage_changes
2093/4
successive_percent_change-0018
2093/4
A quantity starts at 500. It increases by 30%, then decreases by 30%, and finally increases by 15%. What is the final value? Give an exact value.
065f94228bf2a3a37077effa07d42f09f2f5a8eb4f1882df91bae42f906464e4
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0018--plausible_wrong_reference
plausible_wrong_reference
successive_percent_change
add_percentage_changes
2093/4
successive_percent_change-0018
575
A quantity starts at 500. It increases by 30%, then decreases by 30%, and finally increases by 15%. What is the final value? Give an exact value.
065f94228bf2a3a37077effa07d42f09f2f5a8eb4f1882df91bae42f906464e4
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
weighted_mean-0014--correct_reference
correct_reference
weighted_mean
unweighted_mean_of_group_means
3178/41
weighted_mean-0014
3178/41
Three classes contain 10, 15, and 16 students. Their mean test scores are 88, 70, and 78, respectively. What is the mean score across all students in the three classes? Give an exact value.
f2f31d45761f8637c326bf1bd8d86eb435d1068c71e5740f0955a53360a33828
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
weighted_mean-0014--plausible_wrong_reference
plausible_wrong_reference
weighted_mean
unweighted_mean_of_group_means
3178/41
weighted_mean-0014
236/3
Three classes contain 10, 15, and 16 students. Their mean test scores are 88, 70, and 78, respectively. What is the mean score across all students in the three classes? Give an exact value.
f2f31d45761f8637c326bf1bd8d86eb435d1068c71e5740f0955a53360a33828
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
recurrence_indexing-0016--correct_reference
correct_reference
recurrence_indexing
apply_recurrence_one_time_too_few
2917
recurrence_indexing-0016
2917
A sequence is defined by a_0 = 5 and a_(k+1) = 3a_k - 2 for k >= 0. What is a_6?
9b391c78bc22d3535dcdfcdd8a87a23edc4e3e1cc94859d424f46b14a84bdf22
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
recurrence_indexing-0016--plausible_wrong_reference
plausible_wrong_reference
recurrence_indexing
apply_recurrence_one_time_too_few
2917
recurrence_indexing-0016
973
A sequence is defined by a_0 = 5 and a_(k+1) = 3a_k - 2 for k >= 0. What is a_6?
9b391c78bc22d3535dcdfcdd8a87a23edc4e3e1cc94859d424f46b14a84bdf22
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
recurrence_indexing-0023--correct_reference
correct_reference
recurrence_indexing
apply_recurrence_one_time_too_few
26247
recurrence_indexing-0023
26247
A sequence is defined by a_0 = 7 and a_(k+1) = 3a_k - 6 for k >= 0. What is a_8?
62f2bbdddaa346da91a9cf3d351e53f3889a5e8665f7dae81c1b971590bd164e
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
recurrence_indexing-0023--plausible_wrong_reference
plausible_wrong_reference
recurrence_indexing
apply_recurrence_one_time_too_few
26247
recurrence_indexing-0023
8751
A sequence is defined by a_0 = 7 and a_(k+1) = 3a_k - 6 for k >= 0. What is a_8?
62f2bbdddaa346da91a9cf3d351e53f3889a5e8665f7dae81c1b971590bd164e
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
bayes_positive_test-0023--correct_reference
correct_reference
bayes_positive_test
confuse_sensitivity_with_posterior
19/316
bayes_positive_test-0023
19/316
In a population, 1% of people have a condition. A test has 95% sensitivity and 85% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.
304093603c99059ad4e87b47ac799c9003fa905aa0252cc39b323b73bc761e16
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
bayes_positive_test-0023--plausible_wrong_reference
plausible_wrong_reference
bayes_positive_test
confuse_sensitivity_with_posterior
19/316
bayes_positive_test-0023
19/20
In a population, 1% of people have a condition. A test has 95% sensitivity and 85% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.
304093603c99059ad4e87b47ac799c9003fa905aa0252cc39b323b73bc761e16
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
weighted_mean-0008--correct_reference
correct_reference
weighted_mean
unweighted_mean_of_group_means
135/2
weighted_mean-0008
135/2
Three classes contain 8, 13, and 27 students. Their mean test scores are 76, 55, and 71, respectively. What is the mean score across all students in the three classes? Give an exact value.
f108852af791ac16004ec1081c1da7751d64cad1b55b3a671c0082cc2414f9fa
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
weighted_mean-0008--plausible_wrong_reference
plausible_wrong_reference
weighted_mean
unweighted_mean_of_group_means
135/2
weighted_mean-0008
202/3
Three classes contain 8, 13, and 27 students. Their mean test scores are 76, 55, and 71, respectively. What is the mean score across all students in the three classes? Give an exact value.
f108852af791ac16004ec1081c1da7751d64cad1b55b3a671c0082cc2414f9fa
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
bayes_positive_test-0004--correct_reference
correct_reference
bayes_positive_test
confuse_sensitivity_with_posterior
10/43
bayes_positive_test-0004
10/43
In a population, 1% of people have a condition. A test has 90% sensitivity and 97% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.
c3703c85ec1c294a50031ae504de09a8297df0890b89fd141b58fbe952936f20
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
bayes_positive_test-0004--plausible_wrong_reference
plausible_wrong_reference
bayes_positive_test
confuse_sensitivity_with_posterior
10/43
bayes_positive_test-0004
9/10
In a population, 1% of people have a condition. A test has 90% sensitivity and 97% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.
c3703c85ec1c294a50031ae504de09a8297df0890b89fd141b58fbe952936f20
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0015--correct_reference
correct_reference
successive_percent_change
add_percentage_changes
2295
successive_percent_change-0015
2295
A quantity starts at 1800. It increases by 25%, then decreases by 15%, and finally increases by 20%. What is the final value? Give an exact value.
ba3274f031aa0a5b6f70ce9e2c471c6cb7137cecd8d24b3da4fb0037ea15c6cb
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0015--plausible_wrong_reference
plausible_wrong_reference
successive_percent_change
add_percentage_changes
2295
successive_percent_change-0015
2340
A quantity starts at 1800. It increases by 25%, then decreases by 15%, and finally increases by 20%. What is the final value? Give an exact value.
ba3274f031aa0a5b6f70ce9e2c471c6cb7137cecd8d24b3da4fb0037ea15c6cb
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
repeated_object_permutations-0012--correct_reference
correct_reference
repeated_object_permutations
treat_repeated_objects_as_distinct
30
repeated_object_permutations-0012
30
How many distinct strings can be formed by rearranging all letters of AACCD?
010770565a030b089cf5963c1c83cf37da195243ed8e26587dbe5b0c2603d45b
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
repeated_object_permutations-0012--plausible_wrong_reference
plausible_wrong_reference
repeated_object_permutations
treat_repeated_objects_as_distinct
30
repeated_object_permutations-0012
120
How many distinct strings can be formed by rearranging all letters of AACCD?
010770565a030b089cf5963c1c83cf37da195243ed8e26587dbe5b0c2603d45b
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
bayes_positive_test-0001--correct_reference
correct_reference
bayes_positive_test
confuse_sensitivity_with_posterior
15/47
bayes_positive_test-0001
15/47
In a population, 4% of people have a condition. A test has 90% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.
ec89f34126952e0721e20010eb08013f3fbe7988234d67846f484b7c07c374e7
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
bayes_positive_test-0001--plausible_wrong_reference
plausible_wrong_reference
bayes_positive_test
confuse_sensitivity_with_posterior
15/47
bayes_positive_test-0001
9/10
In a population, 4% of people have a condition. A test has 90% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.
ec89f34126952e0721e20010eb08013f3fbe7988234d67846f484b7c07c374e7
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
recurrence_indexing-0000--correct_reference
correct_reference
recurrence_indexing
apply_recurrence_one_time_too_few
1273
recurrence_indexing-0000
1273
A sequence is defined by a_0 = 3 and a_(k+1) = 2a_k + 7 for k >= 0. What is a_7?
43385f69ee27ee3a9321d7d8246d37f52a442d7225afeec9a0c04e5365e67418
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
recurrence_indexing-0000--plausible_wrong_reference
plausible_wrong_reference
recurrence_indexing
apply_recurrence_one_time_too_few
1273
recurrence_indexing-0000
633
A sequence is defined by a_0 = 3 and a_(k+1) = 2a_k + 7 for k >= 0. What is a_7?
43385f69ee27ee3a9321d7d8246d37f52a442d7225afeec9a0c04e5365e67418
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0019--correct_reference
correct_reference
successive_percent_change
add_percentage_changes
24948/25
successive_percent_change-0019
24948/25
A quantity starts at 1100. It increases by 12%, then decreases by 25%, and finally increases by 8%. What is the final value? Give an exact value.
bd9db84e81f0b75c24a6711745ffa24db4715a74d516849b1f0fe1d9da69b4db
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0019--plausible_wrong_reference
plausible_wrong_reference
successive_percent_change
add_percentage_changes
24948/25
successive_percent_change-0019
1045
A quantity starts at 1100. It increases by 12%, then decreases by 25%, and finally increases by 8%. What is the final value? Give an exact value.
bd9db84e81f0b75c24a6711745ffa24db4715a74d516849b1f0fe1d9da69b4db
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
repeated_object_permutations-0021--correct_reference
correct_reference
repeated_object_permutations
treat_repeated_objects_as_distinct
1260
repeated_object_permutations-0021
1260
How many distinct strings can be formed by rearranging all letters of FFFFAAAHH?
a8cb8939beebbdeb79f853f006821f584938cb1dec2de3ccba514d3a6619d4f0
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
repeated_object_permutations-0021--plausible_wrong_reference
plausible_wrong_reference
repeated_object_permutations
treat_repeated_objects_as_distinct
1260
repeated_object_permutations-0021
362880
How many distinct strings can be formed by rearranging all letters of FFFFAAAHH?
a8cb8939beebbdeb79f853f006821f584938cb1dec2de3ccba514d3a6619d4f0
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
area_scaling-0020--correct_reference
correct_reference
area_scaling
add_length_and_width_percent_changes
7315/2
area_scaling-0020
7315/2
A rectangle initially has length 95 and width 50. Its length is increased by 10% while its width is decreased by 30%. What is the new area? Give an exact value.
3e8a5026a2716a9abbb1877e1cc7bdd6f9269ffaba8e8eefaab2859fe8d07882
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
area_scaling-0020--plausible_wrong_reference
plausible_wrong_reference
area_scaling
add_length_and_width_percent_changes
7315/2
area_scaling-0020
3800
A rectangle initially has length 95 and width 50. Its length is increased by 10% while its width is decreased by 30%. What is the new area? Give an exact value.
3e8a5026a2716a9abbb1877e1cc7bdd6f9269ffaba8e8eefaab2859fe8d07882
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
combined_work_rate-0005--correct_reference
correct_reference
combined_work_rate
use_departed_workers_rate_for_remainder
64/5
combined_work_rate-0005
64/5
Worker A can finish a job alone in 24 hours and worker B can finish it alone in 15 hours. They work together for 7 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.
d042483a37d728174cb89f072c08ba731d3f236397d5ca812940aa720b22e56a
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
combined_work_rate-0005--plausible_wrong_reference
plausible_wrong_reference
combined_work_rate
use_departed_workers_rate_for_remainder
64/5
combined_work_rate-0005
85/8
Worker A can finish a job alone in 24 hours and worker B can finish it alone in 15 hours. They work together for 7 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.
d042483a37d728174cb89f072c08ba731d3f236397d5ca812940aa720b22e56a
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0017--correct_reference
correct_reference
successive_percent_change
add_percentage_changes
77616/125
successive_percent_change-0017
77616/125
A quantity starts at 900. It increases by 12%, then decreases by 30%, and finally decreases by 12%. What is the final value? Give an exact value.
2ac7756d6be1fe11b1d49205c806196c16ec54b52f9b6912145f6d2ef9d1108a
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0017--plausible_wrong_reference
plausible_wrong_reference
successive_percent_change
add_percentage_changes
77616/125
successive_percent_change-0017
630
A quantity starts at 900. It increases by 12%, then decreases by 30%, and finally decreases by 12%. What is the final value? Give an exact value.
2ac7756d6be1fe11b1d49205c806196c16ec54b52f9b6912145f6d2ef9d1108a
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
without_replacement_probability-0003--correct_reference
correct_reference
without_replacement_probability
treat_without_replacement_as_independent
117/385
without_replacement_probability-0003
117/385
An urn contains 9 red balls and 13 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.
d0ec7ef0806876c526de18d93699d67e27344ffab8eef7792288bf36a7cc88a2
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
without_replacement_probability-0003--plausible_wrong_reference
plausible_wrong_reference
without_replacement_probability
treat_without_replacement_as_independent
117/385
without_replacement_probability-0003
3159/10648
An urn contains 9 red balls and 13 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.
d0ec7ef0806876c526de18d93699d67e27344ffab8eef7792288bf36a7cc88a2
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0003--correct_reference
correct_reference
successive_percent_change
add_percentage_changes
10166/25
successive_percent_change-0003
10166/25
A quantity starts at 400. It increases by 30%, then decreases by 8%, and finally decreases by 15%. What is the final value? Give an exact value.
7e88e76cd2908ea71d877ab1bf94110ad46a8532703957361bf1972dfb404b5e
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0003--plausible_wrong_reference
plausible_wrong_reference
successive_percent_change
add_percentage_changes
10166/25
successive_percent_change-0003
428
A quantity starts at 400. It increases by 30%, then decreases by 8%, and finally decreases by 15%. What is the final value? Give an exact value.
7e88e76cd2908ea71d877ab1bf94110ad46a8532703957361bf1972dfb404b5e
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
area_scaling-0006--correct_reference
correct_reference
area_scaling
add_length_and_width_percent_changes
1683
area_scaling-0006
1683
A rectangle initially has length 30 and width 55. Its length is increased by 20% while its width is decreased by 15%. What is the new area? Give an exact value.
b5061c0a60790d9fb88cc9dd17657abe45e57ef92bfceef09457318106ba6a22
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
area_scaling-0006--plausible_wrong_reference
plausible_wrong_reference
area_scaling
add_length_and_width_percent_changes
1683
area_scaling-0006
3465/2
A rectangle initially has length 30 and width 55. Its length is increased by 20% while its width is decreased by 15%. What is the new area? Give an exact value.
b5061c0a60790d9fb88cc9dd17657abe45e57ef92bfceef09457318106ba6a22
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
equal_distance_average_speed-0007--correct_reference
correct_reference
equal_distance_average_speed
arithmetic_mean_of_speeds
2184/41
equal_distance_average_speed-0007
2184/41
A vehicle travels 118 km from A to B at 39 km/h and returns the same 118 km at 84 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.
4ad76497ac8937e3910cd2e08c109c752abed97f254821dca2fcbc4133172dd2
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
equal_distance_average_speed-0007--plausible_wrong_reference
plausible_wrong_reference
equal_distance_average_speed
arithmetic_mean_of_speeds
2184/41
equal_distance_average_speed-0007
123/2
A vehicle travels 118 km from A to B at 39 km/h and returns the same 118 km at 84 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.
4ad76497ac8937e3910cd2e08c109c752abed97f254821dca2fcbc4133172dd2
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0022--correct_reference
correct_reference
successive_percent_change
add_percentage_changes
50232/25
successive_percent_change-0022
50232/25
A quantity starts at 1400. It increases by 20%, then decreases by 8%, and finally increases by 30%. What is the final value? Give an exact value.
6705b6dc8f859296cd0a2a27a96a503d166edc8670732923ab9a282170c0f101
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0022--plausible_wrong_reference
plausible_wrong_reference
successive_percent_change
add_percentage_changes
50232/25
successive_percent_change-0022
1988
A quantity starts at 1400. It increases by 20%, then decreases by 8%, and finally increases by 30%. What is the final value? Give an exact value.
6705b6dc8f859296cd0a2a27a96a503d166edc8670732923ab9a282170c0f101
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
at_least_one_probability-0018--correct_reference
correct_reference
at_least_one_probability
add_overlapping_success_events
1273609/2097152
at_least_one_probability-0018
1273609/2097152
Each of 7 independent trials succeeds with probability 1/8. What is the probability of at least one success? Give the answer as a reduced fraction.
7812e5836d6a224e4d6a7646356ba1738b465e52dd16f5774ae12ad957746cc2
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
at_least_one_probability-0018--plausible_wrong_reference
plausible_wrong_reference
at_least_one_probability
add_overlapping_success_events
1273609/2097152
at_least_one_probability-0018
7/8
Each of 7 independent trials succeeds with probability 1/8. What is the probability of at least one success? Give the answer as a reduced fraction.
7812e5836d6a224e4d6a7646356ba1738b465e52dd16f5774ae12ad957746cc2
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
without_replacement_probability-0010--correct_reference
correct_reference
without_replacement_probability
treat_without_replacement_as_independent
33/68
without_replacement_probability-0010
33/68
An urn contains 12 red balls and 6 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.
488b510c6b2fdf0b225fdd90c499687f4e3f71c8ae820bb32805e9dfc5ff678f
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
without_replacement_probability-0010--plausible_wrong_reference
plausible_wrong_reference
without_replacement_probability
treat_without_replacement_as_independent
33/68
without_replacement_probability-0010
4/9
An urn contains 12 red balls and 6 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.
488b510c6b2fdf0b225fdd90c499687f4e3f71c8ae820bb32805e9dfc5ff678f
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0007--correct_reference
correct_reference
successive_percent_change
add_percentage_changes
1365
successive_percent_change-0007
1365
A quantity starts at 1300. It increases by 20%, then decreases by 30%, and finally increases by 25%. What is the final value? Give an exact value.
e524752563aa07f4dce7a1ef93fa15964df22007376c71a70679f66c77727d25
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0007--plausible_wrong_reference
plausible_wrong_reference
successive_percent_change
add_percentage_changes
1365
successive_percent_change-0007
1495
A quantity starts at 1300. It increases by 20%, then decreases by 30%, and finally increases by 25%. What is the final value? Give an exact value.
e524752563aa07f4dce7a1ef93fa15964df22007376c71a70679f66c77727d25
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
equal_distance_average_speed-0023--correct_reference
correct_reference
equal_distance_average_speed
arithmetic_mean_of_speeds
2592/43
equal_distance_average_speed-0023
2592/43
A vehicle travels 166 km from A to B at 48 km/h and returns the same 166 km at 81 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.
d6a8ba4ac1b23ec75245413ddfdb996827b56e122760fc3e68e4aec35d185d0f
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
equal_distance_average_speed-0023--plausible_wrong_reference
plausible_wrong_reference
equal_distance_average_speed
arithmetic_mean_of_speeds
2592/43
equal_distance_average_speed-0023
129/2
A vehicle travels 166 km from A to B at 48 km/h and returns the same 166 km at 81 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.
d6a8ba4ac1b23ec75245413ddfdb996827b56e122760fc3e68e4aec35d185d0f
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
repeated_object_permutations-0022--correct_reference
correct_reference
repeated_object_permutations
treat_repeated_objects_as_distinct
1260
repeated_object_permutations-0022
1260
How many distinct strings can be formed by rearranging all letters of GGGGBBBEE?
0063da3c94dad163b93e86ca8fc004aba3f371b5a94ade8e72f2454ddae3f773
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
repeated_object_permutations-0022--plausible_wrong_reference
plausible_wrong_reference
repeated_object_permutations
treat_repeated_objects_as_distinct
1260
repeated_object_permutations-0022
362880
How many distinct strings can be formed by rearranging all letters of GGGGBBBEE?
0063da3c94dad163b93e86ca8fc004aba3f371b5a94ade8e72f2454ddae3f773
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
area_scaling-0018--correct_reference
correct_reference
area_scaling
add_length_and_width_percent_changes
51623/8
area_scaling-0018
51623/8
A rectangle initially has length 95 and width 65. Its length is increased by 10% while its width is decreased by 5%. What is the new area? Give an exact value.
f62fee1ff04815a5ca6892e0cd5a6dd79fc615d1df2d73d3d38692f8de557f61
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
area_scaling-0018--plausible_wrong_reference
plausible_wrong_reference
area_scaling
add_length_and_width_percent_changes
51623/8
area_scaling-0018
25935/4
A rectangle initially has length 95 and width 65. Its length is increased by 10% while its width is decreased by 5%. What is the new area? Give an exact value.
f62fee1ff04815a5ca6892e0cd5a6dd79fc615d1df2d73d3d38692f8de557f61
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0010--correct_reference
correct_reference
successive_percent_change
add_percentage_changes
8775/8
successive_percent_change-0010
8775/8
A quantity starts at 1500. It increases by 30%, then decreases by 25%, and finally decreases by 25%. What is the final value? Give an exact value.
09112621933ada181fc68a4214ff974fc5d0d9b1518bf917f754fb0ed26b062d
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0010--plausible_wrong_reference
plausible_wrong_reference
successive_percent_change
add_percentage_changes
8775/8
successive_percent_change-0010
1200
A quantity starts at 1500. It increases by 30%, then decreases by 25%, and finally decreases by 25%. What is the final value? Give an exact value.
09112621933ada181fc68a4214ff974fc5d0d9b1518bf917f754fb0ed26b062d
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
weighted_mean-0022--correct_reference
correct_reference
weighted_mean
unweighted_mean_of_group_means
2289/40
weighted_mean-0022
2289/40
Three classes contain 8, 21, and 11 students. Their mean test scores are 65, 57, and 52, respectively. What is the mean score across all students in the three classes? Give an exact value.
6b46d0162390a597b899f28dde21566aa6202bcee5a0cd374c8a864a098f80d6
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
weighted_mean-0022--plausible_wrong_reference
plausible_wrong_reference
weighted_mean
unweighted_mean_of_group_means
2289/40
weighted_mean-0022
58
Three classes contain 8, 21, and 11 students. Their mean test scores are 65, 57, and 52, respectively. What is the mean score across all students in the three classes? Give an exact value.
6b46d0162390a597b899f28dde21566aa6202bcee5a0cd374c8a864a098f80d6
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
equal_distance_average_speed-0021--correct_reference
correct_reference
equal_distance_average_speed
arithmetic_mean_of_speeds
1173/20
equal_distance_average_speed-0021
1173/20
A vehicle travels 88 km from A to B at 69 km/h and returns the same 88 km at 51 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.
41aad9c07b80d99be9286b31e00c3960f993d1521428fb6f36d893dda018b2f6
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
equal_distance_average_speed-0021--plausible_wrong_reference
plausible_wrong_reference
equal_distance_average_speed
arithmetic_mean_of_speeds
1173/20
equal_distance_average_speed-0021
60
A vehicle travels 88 km from A to B at 69 km/h and returns the same 88 km at 51 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.
41aad9c07b80d99be9286b31e00c3960f993d1521428fb6f36d893dda018b2f6
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
without_replacement_probability-0012--correct_reference
correct_reference
without_replacement_probability
treat_without_replacement_as_independent
9/20
without_replacement_probability-0012
9/20
An urn contains 9 red balls and 7 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.
1cd0a664b706d9e9814968dcbc5b2c89d9cd64fada7c57dbd065b5ac33702063
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
without_replacement_probability-0012--plausible_wrong_reference
plausible_wrong_reference
without_replacement_probability
treat_without_replacement_as_independent
9/20
without_replacement_probability-0012
1701/4096
An urn contains 9 red balls and 7 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.
1cd0a664b706d9e9814968dcbc5b2c89d9cd64fada7c57dbd065b5ac33702063
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
equal_distance_average_speed-0020--correct_reference
correct_reference
equal_distance_average_speed
arithmetic_mean_of_speeds
1539/23
equal_distance_average_speed-0020
1539/23
A vehicle travels 155 km from A to B at 81 km/h and returns the same 155 km at 57 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.
5218a69f35604402ffc4e949f97065d728d5dc2470a65147a27efc3db9429fe8
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
equal_distance_average_speed-0020--plausible_wrong_reference
plausible_wrong_reference
equal_distance_average_speed
arithmetic_mean_of_speeds
1539/23
equal_distance_average_speed-0020
69
A vehicle travels 155 km from A to B at 81 km/h and returns the same 155 km at 57 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.
5218a69f35604402ffc4e949f97065d728d5dc2470a65147a27efc3db9429fe8
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
repeated_object_permutations-0009--correct_reference
correct_reference
repeated_object_permutations
treat_repeated_objects_as_distinct
90
repeated_object_permutations-0009
90
How many distinct strings can be formed by rearranging all letters of BBDDCC?
39fb51315a2fc83629a4e5069f12ea66d07e4df6c3be1d4d99ee68e209e877d0
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
repeated_object_permutations-0009--plausible_wrong_reference
plausible_wrong_reference
repeated_object_permutations
treat_repeated_objects_as_distinct
90
repeated_object_permutations-0009
720
How many distinct strings can be formed by rearranging all letters of BBDDCC?
39fb51315a2fc83629a4e5069f12ea66d07e4df6c3be1d4d99ee68e209e877d0
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
at_least_one_probability-0005--correct_reference
correct_reference
at_least_one_probability
add_overlapping_success_events
468559/1000000
at_least_one_probability-0005
468559/1000000
Each of 6 independent trials succeeds with probability 1/10. What is the probability of at least one success? Give the answer as a reduced fraction.
c65bea381177f9a7daff1a81b2b06bf1c28ab25e0729ea7c00d447c816a10d98
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
at_least_one_probability-0005--plausible_wrong_reference
plausible_wrong_reference
at_least_one_probability
add_overlapping_success_events
468559/1000000
at_least_one_probability-0005
3/5
Each of 6 independent trials succeeds with probability 1/10. What is the probability of at least one success? Give the answer as a reduced fraction.
c65bea381177f9a7daff1a81b2b06bf1c28ab25e0729ea7c00d447c816a10d98
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
combined_work_rate-0009--correct_reference
correct_reference
combined_work_rate
use_departed_workers_rate_for_remainder
133/23
combined_work_rate-0009
133/23
Worker A can finish a job alone in 7 hours and worker B can finish it alone in 23 hours. They work together for 4 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.
acefb6a272ada7e576bc57351733eb53265c9d13d08caec9c53f6c46322ec79c
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
combined_work_rate-0009--plausible_wrong_reference
plausible_wrong_reference
combined_work_rate
use_departed_workers_rate_for_remainder
133/23
combined_work_rate-0009
69/7
Worker A can finish a job alone in 7 hours and worker B can finish it alone in 23 hours. They work together for 4 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.
acefb6a272ada7e576bc57351733eb53265c9d13d08caec9c53f6c46322ec79c
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
bayes_positive_test-0022--correct_reference
correct_reference
bayes_positive_test
confuse_sensitivity_with_posterior
30/127
bayes_positive_test-0022
30/127
In a population, 3% of people have a condition. A test has 80% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.
19e12175e69c0f3350511c8cc384fb55c4c89d9e0453e50903a45ea7dc6fae2f
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
bayes_positive_test-0022--plausible_wrong_reference
plausible_wrong_reference
bayes_positive_test
confuse_sensitivity_with_posterior
30/127
bayes_positive_test-0022
4/5
In a population, 3% of people have a condition. A test has 80% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.
19e12175e69c0f3350511c8cc384fb55c4c89d9e0453e50903a45ea7dc6fae2f
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
combined_work_rate-0018--correct_reference
correct_reference
combined_work_rate
use_departed_workers_rate_for_remainder
26/3
combined_work_rate-0018
26/3
Worker A can finish a job alone in 13 hours and worker B can finish it alone in 9 hours. They work together for 3 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.
115f47839de40959b5aa9b6a65eb1ce90ba403d2e57ebab372f777ade0f92356
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
combined_work_rate-0018--plausible_wrong_reference
plausible_wrong_reference
combined_work_rate
use_departed_workers_rate_for_remainder
26/3
combined_work_rate-0018
90/13
Worker A can finish a job alone in 13 hours and worker B can finish it alone in 9 hours. They work together for 3 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.
115f47839de40959b5aa9b6a65eb1ce90ba403d2e57ebab372f777ade0f92356
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
recurrence_indexing-0011--correct_reference
correct_reference
recurrence_indexing
apply_recurrence_one_time_too_few
161
recurrence_indexing-0011
161
A sequence is defined by a_0 = 6 and a_(k+1) = 2a_k - 1 for k >= 0. What is a_5?
f850edb7cb48c05a9f5bfd1e0f7a9d72eb5934dbf43295827ce94dce0449ca74
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
recurrence_indexing-0011--plausible_wrong_reference
plausible_wrong_reference
recurrence_indexing
apply_recurrence_one_time_too_few
161
recurrence_indexing-0011
81
A sequence is defined by a_0 = 6 and a_(k+1) = 2a_k - 1 for k >= 0. What is a_5?
f850edb7cb48c05a9f5bfd1e0f7a9d72eb5934dbf43295827ce94dce0449ca74
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
bayes_positive_test-0005--correct_reference
correct_reference
bayes_positive_test
confuse_sensitivity_with_posterior
85/277
bayes_positive_test-0005
85/277
In a population, 4% of people have a condition. A test has 85% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.
cbc1e5f8797bf839ac4c3891cbe417053e19956e42e64cdecdcb2b5d0579a077
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
bayes_positive_test-0005--plausible_wrong_reference
plausible_wrong_reference
bayes_positive_test
confuse_sensitivity_with_posterior
85/277
bayes_positive_test-0005
17/20
In a population, 4% of people have a condition. A test has 85% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.
cbc1e5f8797bf839ac4c3891cbe417053e19956e42e64cdecdcb2b5d0579a077
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
recurrence_indexing-0009--correct_reference
correct_reference
recurrence_indexing
apply_recurrence_one_time_too_few
-1456
recurrence_indexing-0009
-1456
A sequence is defined by a_0 = -4 and a_(k+1) = 3a_k - 4 for k >= 0. What is a_5?
083d72286bf634319f2e178fd072781d14ea78de5e8ff17c3964e8445fafa45b
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
recurrence_indexing-0009--plausible_wrong_reference
plausible_wrong_reference
recurrence_indexing
apply_recurrence_one_time_too_few
-1456
recurrence_indexing-0009
-484
A sequence is defined by a_0 = -4 and a_(k+1) = 3a_k - 4 for k >= 0. What is a_5?
083d72286bf634319f2e178fd072781d14ea78de5e8ff17c3964e8445fafa45b
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
area_scaling-0000--correct_reference
correct_reference
area_scaling
add_length_and_width_percent_changes
4725/2
area_scaling-0000
4725/2
A rectangle initially has length 90 and width 30. Its length is increased by 25% while its width is decreased by 30%. What is the new area? Give an exact value.
44d54abe8d0e0e2b4ea7413520e175bab1ab551603fae33d4a2ef45bdb117068
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
area_scaling-0000--plausible_wrong_reference
plausible_wrong_reference
area_scaling
add_length_and_width_percent_changes
4725/2
area_scaling-0000
2565
A rectangle initially has length 90 and width 30. Its length is increased by 25% while its width is decreased by 30%. What is the new area? Give an exact value.
44d54abe8d0e0e2b4ea7413520e175bab1ab551603fae33d4a2ef45bdb117068
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
at_least_one_probability-0019--correct_reference
correct_reference
at_least_one_probability
add_overlapping_success_events
108110858/170859375
at_least_one_probability-0019
108110858/170859375
Each of 7 independent trials succeeds with probability 2/15. What is the probability of at least one success? Give the answer as a reduced fraction.
82f6cdc22baf3352afb239fef545fb44e4267dabd74093ef6a40c78ecdbec9cd
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
at_least_one_probability-0019--plausible_wrong_reference
plausible_wrong_reference
at_least_one_probability
add_overlapping_success_events
108110858/170859375
at_least_one_probability-0019
14/15
Each of 7 independent trials succeeds with probability 2/15. What is the probability of at least one success? Give the answer as a reduced fraction.
82f6cdc22baf3352afb239fef545fb44e4267dabd74093ef6a40c78ecdbec9cd
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
area_scaling-0014--correct_reference
correct_reference
area_scaling
add_length_and_width_percent_changes
3969
area_scaling-0014
3969
A rectangle initially has length 45 and width 70. Its length is increased by 40% while its width is decreased by 10%. What is the new area? Give an exact value.
7d9691f4dd342f71b8c0e6d0e626c64843ba4c332d78c96beafd673b5c17fc61
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
area_scaling-0014--plausible_wrong_reference
plausible_wrong_reference
area_scaling
add_length_and_width_percent_changes
3969
area_scaling-0014
4095
A rectangle initially has length 45 and width 70. Its length is increased by 40% while its width is decreased by 10%. What is the new area? Give an exact value.
7d9691f4dd342f71b8c0e6d0e626c64843ba4c332d78c96beafd673b5c17fc61
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
repeated_object_permutations-0018--correct_reference
correct_reference
repeated_object_permutations
treat_repeated_objects_as_distinct
105
repeated_object_permutations-0018
105
How many distinct strings can be formed by rearranging all letters of CCCCEEG?
912f77fff9d9f15fbb43730e75eeed3a68aaf8a77cf597ce794bbe14fc6fa5b5
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
repeated_object_permutations-0018--plausible_wrong_reference
plausible_wrong_reference
repeated_object_permutations
treat_repeated_objects_as_distinct
105
repeated_object_permutations-0018
5040
How many distinct strings can be formed by rearranging all letters of CCCCEEG?
912f77fff9d9f15fbb43730e75eeed3a68aaf8a77cf597ce794bbe14fc6fa5b5
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
at_least_one_probability-0009--correct_reference
correct_reference
at_least_one_probability
add_overlapping_success_events
271/1000
at_least_one_probability-0009
271/1000
Each of 3 independent trials succeeds with probability 1/10. What is the probability of at least one success? Give the answer as a reduced fraction.
575e72e63b78fe4a190898a9498078eff864cacbdc99b61e84544dffeecfa813
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
at_least_one_probability-0009--plausible_wrong_reference
plausible_wrong_reference
at_least_one_probability
add_overlapping_success_events
271/1000
at_least_one_probability-0009
3/10
Each of 3 independent trials succeeds with probability 1/10. What is the probability of at least one success? Give the answer as a reduced fraction.
575e72e63b78fe4a190898a9498078eff864cacbdc99b61e84544dffeecfa813
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0012--correct_reference
correct_reference
successive_percent_change
add_percentage_changes
6552/5
successive_percent_change-0012
6552/5
A quantity starts at 1800. It increases by 30%, then decreases by 30%, and finally decreases by 20%. What is the final value? Give an exact value.
d39b89bd4a944bffb5ee049a2d5b2b002522524cd4eb1bcfe2d2fbdd0ebba0ca
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0012--plausible_wrong_reference
plausible_wrong_reference
successive_percent_change
add_percentage_changes
6552/5
successive_percent_change-0012
1440
A quantity starts at 1800. It increases by 30%, then decreases by 30%, and finally decreases by 20%. What is the final value? Give an exact value.
d39b89bd4a944bffb5ee049a2d5b2b002522524cd4eb1bcfe2d2fbdd0ebba0ca
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
without_replacement_probability-0016--correct_reference
correct_reference
without_replacement_probability
treat_without_replacement_as_independent
21/44
without_replacement_probability-0016
21/44
An urn contains 7 red balls and 5 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.
f6b9795f260aa0580d32931d3d6c63cba9cde29c841ed86c0bed8e3d314e34a5
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
without_replacement_probability-0016--plausible_wrong_reference
plausible_wrong_reference
without_replacement_probability
treat_without_replacement_as_independent
21/44
without_replacement_probability-0016
245/576
An urn contains 7 red balls and 5 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.
f6b9795f260aa0580d32931d3d6c63cba9cde29c841ed86c0bed8e3d314e34a5
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
equal_distance_average_speed-0006--correct_reference
correct_reference
equal_distance_average_speed
arithmetic_mean_of_speeds
648/13
equal_distance_average_speed-0006
648/13
A vehicle travels 160 km from A to B at 36 km/h and returns the same 160 km at 81 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.
6ce2f794b974949e972d34d140babe43905d8b17103980ff0936728deaa06ce0
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
equal_distance_average_speed-0006--plausible_wrong_reference
plausible_wrong_reference
equal_distance_average_speed
arithmetic_mean_of_speeds
648/13
equal_distance_average_speed-0006
117/2
A vehicle travels 160 km from A to B at 36 km/h and returns the same 160 km at 81 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.
6ce2f794b974949e972d34d140babe43905d8b17103980ff0936728deaa06ce0
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0006--correct_reference
correct_reference
successive_percent_change
add_percentage_changes
35802/25
successive_percent_change-0006
35802/25
A quantity starts at 1300. It increases by 8%, then decreases by 15%, and finally increases by 20%. What is the final value? Give an exact value.
40b5a561ff10b0e5bde0612a5bf0582082885762c386c48a20b136b605bb983b
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
successive_percent_change-0006--plausible_wrong_reference
plausible_wrong_reference
successive_percent_change
add_percentage_changes
35802/25
successive_percent_change-0006
1469
A quantity starts at 1300. It increases by 8%, then decreases by 15%, and finally increases by 20%. What is the final value? Give an exact value.
40b5a561ff10b0e5bde0612a5bf0582082885762c386c48a20b136b605bb983b
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
at_least_one_probability-0003--correct_reference
correct_reference
at_least_one_probability
add_overlapping_success_events
15961/32768
at_least_one_probability-0003
15961/32768
Each of 5 independent trials succeeds with probability 1/8. What is the probability of at least one success? Give the answer as a reduced fraction.
90e31a6a42be1a3cd5f5cddfe155c92989e4d8ad3b6108b07da1997281d97306
correct
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
at_least_one_probability-0003--plausible_wrong_reference
plausible_wrong_reference
at_least_one_probability
add_overlapping_success_events
15961/32768
at_least_one_probability-0003
5/8
Each of 5 independent trials succeeds with probability 1/8. What is the probability of at least one success? Give the answer as a reduced fraction.
90e31a6a42be1a3cd5f5cddfe155c92989e4d8ad3b6108b07da1997281d97306
incorrect
stage1-coherent-wrong-label-v1
curcon.coherent_wrong_label_twin.v1
not_yet_run
End of preview. Expand in Data Studio

Curriculum Contamination Coherent-Wrong-Label Tasks (Stage 1)

This private pre-release contains a controlled mathematical task bank for studying whether self-evolving curriculum selectors can admit an objectively wrong answer when repeated solver samples form a coherent majority.

Dataset contents

  • data/unique_tasks.jsonl: 240 unique, exact-answer mathematical tasks.
  • data/label_twins.jsonl: 480 surface-identical task/reference pairs: one objectively correct reference and one plausible but objectively incorrect reference for each task.
  • metadata/validation_report.json: construction and validation summary.
  • metadata/*.integrity.json: line-count and SHA-256 integrity records.

The 240 tasks cover ten families, with 24 tasks per family:

  1. area scaling;
  2. at-least-one probability;
  3. Bayesian positive-test reasoning;
  4. combined work rates;
  5. equal-distance average speed;
  6. recurrence indexing;
  7. repeated-object permutations;
  8. successive percentage change;
  9. weighted means;
  10. probability without replacement.

Important interpretation boundary

The plausible wrong answer encodes a prespecified candidate shortcut. It is not claimed to be a model error until an evaluator run independently observes it. Fields such as candidate_shortcut_not_observed_model_behavior and selector_observation_status: not_yet_run preserve this distinction.

This Stage 1 release contains no completed selector outcome, natural-prevalence estimate, training-effect estimate, or closed-loop contamination result.

Construction and validation

  • All 240 tasks have a unique exact answer under an independent deterministic verifier.
  • The plausible wrong answer differs from the objective answer for every task.
  • All 240 correct/wrong pairs have identical question text.
  • Thirty tasks were included in a blinded machine audit during construction.
  • The persisted validation report records 240/240 independent oracle passes and no construction errors.

Schema overview

unique_tasks.jsonl includes the question, family, parameters, objective answer, plausible wrong answer, misconception identifier and verifier certificate.

label_twins.jsonl includes the shared question and one proposed reference per row, with condition and reference_correctness distinguishing the pair.

Intended uses

  • diagnostic evaluation of majority-vote pseudo-labeling;
  • controlled curriculum-admission studies;
  • comparison of selector risk/retention frontiers;
  • paired causal studies of correct versus coherent-wrong training updates.

Limitations

  • The pool is controlled and deliberately enriched for candidate shortcuts; it does not estimate their prevalence in naturally generated curricula.
  • It currently covers exact-answer English mathematical tasks only.
  • Candidate wrong answers are mechanism probes, not labels of observed model behavior.
  • Downstream learning harm must be established by a separate intervention.

License and citation

No public-use license or paper citation is assigned in this private pre-release. They will be added only after an explicit owner decision and double-blind release review.
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