{"id":"aqua_rat:4dcae488725b842f894068fa0d2dde84","source_id":"aqua_rat","source_item_id":"4dcae488725b842f894068fa0d2dde84","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":"There are N numbers of gold biscuits in the house, in which four people are lived. If the first men woke up and divided the biscuits into 5 equal piles and found one extra biscuit. He took one of those piles along with the extra biscuit and hid them. He then gathered the 4 remaining piles into a big pile, woke up the second person and went to sleep. Each of the other 3 persons did the same one by one i.e. divided the big pile into 5 equal piles and found one extra biscuit. Each hid one of the piles along with the extra biscuit and gathered the remaining 4 piles into a big pile. If N>1000, what could be the least value of N?","stimulus":"","stimulus_html":null,"stem_html":"

There are N numbers of gold biscuits in the house, in which four people are lived. If the first men woke up and divided the biscuits into 5 equal piles and found one extra biscuit. He took one of those piles along with the extra biscuit and hid them. He then gathered the 4 remaining piles into a big pile, woke up the second person and went to sleep. Each of the other 3 persons did the same one by one i.e. divided the big pile into 5 equal piles and found one extra biscuit. Each hid one of the piles along with the extra biscuit and gathered the remaining 4 piles into a big pile. If N>1000, what could be the least value of N?

","rationale_html":"

Let, each equal part is x and N be the total number of biscuits.

Thus, N=5x+1.

A took (x+1) biscuit.

Now 4x is of the form 5y+1 then x must be in the form 5z+4

⇒4(5z+4)=5y+1

⇒y=4z+3 and x=5z+4

The ratio of number of biscuits that A and B took is

[(5z+4)+1]:[(4z+3)+1]=5:4.

So, we can say that any two successive persons A, B, C and D take coins in the ratio of 5:4

Let the number of biscuits that A, B, C and D took be a, b, c and d respectively.

=>a:b=b:c=c:d=5:4.

=>a:b:c:d=125:100:80:64.

=>a=125k.

=>x=125k−1 and N=5x+1=625k−4.

As, N>1000, the least value of N is when k=2.

=>N= 1246.

B

","correct_answer":["B"],"equiv_key":"da5b0a773e6697dbc0d56e30","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"

1249

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

1246

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

1202

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

1000

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

None of these

","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":[]}