Difference between revisions of "Lcz's Mock AMC 10A Problems"

(Problem 3)
(Problem 4)
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==Problem 4==
 
==Problem 4==
  
Find the sum of all integer <math>x</math> and <math>y</math> such that  
+
Find the sum of all positive integer <math>x</math> and <math>y</math> such that  
  
 
(1) <math>|x-y| \geq 0</math>
 
(1) <math>|x-y| \geq 0</math>
  
(2) <math>|x+y| \leq 6</math>
+
(2) <math>x+y \leq 6</math>
  
 
(3) <math>xy \leq 8</math>
 
(3) <math>xy \leq 8</math>

Revision as of 14:07, 30 June 2020

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 $2^{0+1+2}+2+0(1+(2))+20(12)$.

$\textbf{(A)}\ 8 \qquad\textbf{(B)}\ 248 \qquad\textbf{(C)}\ 250 \qquad\textbf{(D)}\ 252 \qquad\textbf{(E)}\ 254$

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 positive integer $x$ and $y$ such that

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

(2) $x+y \leq 6$

(3) $xy \leq 8$

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 $1734$.)