{"id":"aqua_rat:070a38653606999a77d735a6a61a8a0e","source_id":"aqua_rat","source_item_id":"070a38653606999a77d735a6a61a8a0e","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"A bag contains 11 candy bars: three cost 50 cents each, four cost $1 each and four cost $2 each. How many ways can 3 candy bars be selected from the 11 candy bars so that the total cost is more than $4?","stimulus":"","stimulus_html":null,"stem_html":"

A bag contains 11 candy bars: three cost 50 cents each, four cost $1 each and four cost $2

each. How many ways can 3 candy bars be selected from the 11 candy bars so that the total cost is more than $4?

","rationale_html":"

The ways of choosing 3 candy bars with a total cost over $4 include: choose 3 out of 4 (2 dollars each); choose 2 out of 4 (2 dollars each) and 1 from the other 7. So, the total number of ways is C4

3 + (7 C4

2 ) = 46. Incidentally, the total number ways of choosing 3 candy bars out of 11 is C11

3 = 165. So the probability of them costing more than $4 if they are randomly chosen is

C4

3 + (7 C4

2 )

C11

3

=

46/165

correct answer C

","correct_answer":["C"],"equiv_key":"5ed44b176fee1e4c227d8b2e","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"

8

","ord":0},{"label":"B","content_html":"

28

","ord":1},{"label":"C","content_html":"

46

","ord":2},{"label":"D","content_html":"

66

","ord":3},{"label":"E","content_html":"

70

","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}