Difference between revisions of "Lcz's Mock AMC 10A Problems"
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==Problem 3== | ==Problem 3== | ||
− | Jack and Jill play a (bad) game on a number line which contains the integers. Jack starts at <math>- | + | What is <math>1*2+2*3+3*4+4*5+5*6+6*7+7*8</math>? |
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− | <math>\textbf{(A)}\ | + | <math>\textbf{(A)}\ 84 \qquad\textbf{(B)}\ 120 \qquad\textbf{(C)}\ 138 \qquad\textbf{(D)}\ 150 \qquad\textbf{(E)}\ 168</math> |
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+ | ==Problem 4== | ||
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+ | Jack and Jill play a (bad) game on a number line which contains the integers. Jack starts at <math>-1</math>, and Jill starts at <math>18</math>. Every turn, the judge flip a standard six sided die. If the number rolled is a square number, Jack moves to the right <math>10</math> units. Otherwise, Jill moves to the left <math>5</math> units. Find the probability for which Jack and Jill pass each other for the first time in <math>3</math> moves. | ||
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+ | <math>\textbf{(A)}\ 4/27 \qquad\textbf{(B)}\ 2/9 \qquad\textbf{(C)}\ 1/3 \qquad\textbf{(D)}\ 4/9 \qquad\textbf{(E)}\ 2/3</math> |
Revision as of 12:50, 30 June 2020
Contents
[hide]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 .
Problem 2
If , and , find the sum of all possible values of .
Problem 3
What is ?
Problem 4
Jack and Jill play a (bad) game on a number line which contains the integers. Jack starts at , and Jill starts at . Every turn, the judge flip a standard six sided die. If the number rolled is a square number, Jack moves to the right units. Otherwise, Jill moves to the left units. Find the probability for which Jack and Jill pass each other for the first time in moves.