Lcz's Mock AMC 10A Problems

Instructions

1. All rules of a regular AMC 10 apply.

2. Please submit your answers in a DM to me (Lcz).

3. Don't cheat.

Here's the problems!

Problem 1

Find the value of $2^{0+2+1}+2+0(2+(1))+20(21)$ .

$\textbf{(A)}\ 8 \qquad\textbf{(B)}\ 426 \qquad\textbf{(C)}\ 428 \qquad\textbf{(D)}\ 430 \qquad\textbf{(E)}\ 432$

Problem 2

If $|x-2|=0$ , and $|y-3|=1$ , find the sum of all possible values of $|xy|$ .

$\textbf{(A)}\ 0 \qquad\textbf{(B)}\ 4 \qquad\textbf{(C)}\ 8 \qquad\textbf{(D)}\ 12 \qquad\textbf{(E)}\ 16$

Problem 3

What is $1*2+2*3+3*4+4*5+5*6+6*7+7*8$ ?

$\textbf{(A)}\ 84 \qquad\textbf{(B)}\ 120 \qquad\textbf{(C)}\ 138 \qquad\textbf{(D)}\ 150 \qquad\textbf{(E)}\ 168$

Problem 4

Find the sum of all ordered pairs of positive integer $x$ and $y$ such that

(1) $|x-y| \geq 0$

(2) $x,y \leq 3$

(3) $xy \leq 8$

$\textbf{(A)}\ 24 \qquad\textbf{(B)}\ 27 \qquad\textbf{(C)}\ 30 \qquad\textbf{(D)}\ 36 \qquad\textbf{(E)}\ 39$

Problem 5

Find $x$ if $x^3-3x^2+3x-1=x^3-2x^2+15x+35$ .

$\textbf{(A)}\ -6 \qquad\textbf{(B)}\ -4 \qquad\textbf{(C)}\ 0 \qquad\textbf{(D)}\ 4 \qquad\textbf{(E)}\ 6$

Problem 6

Given that $5101$ is prime, find the number of factors of $104060401+20402+1$ .

$\textbf{(A)}\ 2 \qquad\textbf{(B)}\ 4 \qquad\textbf{(C)}\ 5 \qquad\textbf{(D)}\ 6 \qquad\textbf{(E)}\ 8$

Problem 10

Jack and Jill play a (bad) game on a number line which contains the integers. Jack starts at $-1$ , and Jill starts at $18$ . Every turn, the judge flip a standard six sided die. If the number rolled is a square number, Jack moves to the right $10$ units. Otherwise, Jill moves to the left $5$ units. Find the probability for which Jack and Jill pass each other for the first time in $3$ moves.

$\textbf{(A)}\ 4/27 \qquad\textbf{(B)}\ 2/9 \qquad\textbf{(C)}\ 1/3 \qquad\textbf{(D)}\ 4/9 \qquad\textbf{(E)}\ 2/3$

Problem 13

How many $4$ -digit integers contain a substring of digits that is divisible by $4$ ? (For example, count in $1532$ because it contains $32$ , but don't count in $1734$ .)

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