User:Fura3334
DONT DELETE THIS PAGE, IM WORKING ON SUS MOCK AIME
[hide="the 6 problems for sus mock aime, now in latex"]
[b]Problem 1[/b]
Kube the robot completes a task repeatedly, each time taking minutes. One day, Furaken asks Kube to complete
identical tasks in
hours. If Kube works slower and spends
minutes on each task, it will finish
tasks in exactly
hours. If Kube works faster and spends
minutes on each task, it can finish
tasks in
hours with
minutes to spare. Find
.
Answer: [hide]i'm not putting the answer here, send your answer in this thread then i'll see whether yours is same as mine[/hide]
[b]Problem 2[/b]
Let ,
,
be positive real numbers such that
Find
.
Answer: [hide]i'm not putting the answer here, send your answer in this thread then i'll see whether yours is same as mine[/hide]
[b]Problem 3[/b]
Let be an odd prime such that
. Find
.
Answer: [hide]i'm not putting the answer here, send your answer in this thread then i'll see whether yours is same as mine[/hide]
[b]Problem 4[/b]
[img]https://latex.artofproblemsolving.com/d/4/4/d44b620826b6207a9018efd4b6db89b39b2b9b3c.png[/img]
For triangle , let
be the midpoint of
. Extend
to
such that
. Let
be the point on
such that
, and let
be the point on
such that
. Line
intersects line
at
such that
. Given that
is parallel to
, the maximum possible area of triangle
can be written as
where
and
are relatively prime positive integers. Find
.
Answer: [hide]i'm not putting the answer here, send your answer in this thread then i'll see whether yours is same as mine[/hide]
[b]Problem 5[/b]
Let be a root of the polynomial
where
,
,
,
are integers. Find
.
Answer: [hide]i'm not putting the answer here, send your answer in this thread then i'll see whether yours is same as mine[/hide]
[b]Problem 6[/b]
[img]https://latex.artofproblemsolving.com/4/6/1/461d152569bf18e1c406d5b3c3a3afa4201b4245.png[/img]
Fly has a large number of red, yellow, green and blue pearls. Fly is making a necklace consisting of pearls as shown in the diagram. One slot already has a red pearl, and another slot has a green pearl. Find the number of ways to fill the
remaining slots such that any two pearls that are connected directly have different colors.
Answer: [hide]i'm not putting the answer here, send your answer in this thread then i'll see whether yours is same as mine[/hide][/hide]