Difference between revisions of "AIME 2020(MOCK) Problems"

Latest revision as of 05:45, 23 December 2020

Problem 1

Let $N$ be $112123123412345... (1000 digits)$ . What is the remainder when $N$ is divided by $21$ ?

Problem 2

Let $K$ be a set of polynomials $P(x)$ with integral coefficients such that the roots of $P(x)$ are $cos \frac{\pi}{7}$ , $cos \frac{\pi}{11}$ , and $cos \frac{\pi}{17}$ . What is the least possible sum of the coefficients of $P(x)$ ?

Problem 3

How many $15$ digit base $5$ positive integers consist of exactly $2$ pairs of consecutive $0$ s but no $4$ consecutive $3$ s?

Problem 4

Let $\lfloor\x\rfloor$ (Error compiling LaTeX. Unknown error_msg) denote the greatest integer less than or equal to $x$ . What is the tens digit of $\lfloor\frac{10^{2020}}{10^{101} + 7}\rfloor$

Revision as of 22:06, 25 June 2020 (view source) Shiamk (talk \| contribs) (→‎Problem 4) ← Older edit		Latest revision as of 05:45, 23 December 2020 (view source) Crazyinmath (talk \| contribs) m
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	==Problem 4==		==Problem 4==
−	Let <math>\lfloor\x\rfloor</math> denote the greatest integer less than or equal to <math>x</math>. What is the tens digit of $\lfloor\frac{10^{2020}}{10^{101} + 7}	+	Let <math>\lfloor\x\rfloor</math> denote the greatest integer less than or equal to <math>x</math>. What is the tens digit of <math>\lfloor\frac{10^{2020}}{10^{101} + 7}\rfloor</math>

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