Difference between revisions of "2025 AMC 8 Problems/Problem 2"
Jadon jung (talk | contribs) |
m |
||
| (39 intermediate revisions by 21 users not shown) | |||
| Line 1: | Line 1: | ||
| − | The 2025 | + | == Problem == |
| + | |||
| + | The table below shows the ancient Egyptian hieroglyphs that were used to represent different numbers. | ||
| + | |||
| + | [[File:mathh.PNG]] | ||
| + | |||
| + | For example, the number <math>32</math> was represented by the hieroglyphs <math>\cap \cap \cap ||</math>. What number is represented by the following combination of hieroglyphs? | ||
| + | |||
| + | [[File:Amc8 2025 prob 2 pic.PNG]] | ||
| + | |||
| + | <math>\textbf{(A)}\ 1,423 \qquad \textbf{(B)}\ 10,423 \qquad \textbf{(C)}\ 14,023 \qquad \textbf{(D)}\ 14,203 \qquad \textbf{(E)}\ 14,230</math> | ||
| + | |||
| + | == Solution 1 == | ||
| + | |||
| + | The first hieroglyph is worth <math>10,000</math>, the next 4 are worth <math>100 \cdot 4 = 400</math>, the next <math>2</math> are worth <math>10 \cdot 2 = 20</math>, and the last <math>3</math> are worth <math>1 \cdot 3 = 3</math>. Therefore, the answer is <math>10,000 + 400 + 20 + 3 = \boxed{\textbf{(B)}\ 10,423}</math> | ||
| + | |||
| + | == Solution 2 == | ||
| + | |||
| + | Simply notice that the first hieroglyph represents <math>10,000</math>, and the next ones represent <math>4</math> hundreds. They only answer choice with a <math>1</math> in the thousands place and a <math>4</math> in the hundreds place is answer choice <math>\boxed{\textbf{(B)}\ 10,423}</math> | ||
| + | |||
| + | ~Avy11 | ||
| + | |||
| + | == Solution 3 (fast version of Solution 2) == | ||
| + | |||
| + | From a first inspection, you may notice that there is no thousands hieroglyph. The only option with zero in the thousands place is <math>\boxed{\textbf{(B)}\ 10,423}</math> | ||
| + | |||
| + | ~thatmathsguy | ||
| + | |||
| + | == Video Solution by Pi Academy == | ||
| + | |||
| + | https://youtu.be/Iv_a3Rz725w?si=E0SI_h1XT8msWgkK | ||
| + | |||
| + | == Video Solution 1 == | ||
| + | |||
| + | [//youtu.be/j20JsyEXKcs ~ ChillGuyDoesMath] | ||
| + | |||
| + | == Video Solution 2 by SpreadTheMathLove == | ||
| + | |||
| + | https://www.youtube.com/watch?v=jTTcscvcQmI | ||
| + | |||
| + | == Video Solution 3 == | ||
| + | |||
| + | [//youtu.be/VP7g-s8akMY?si=eptV4vO-YstwSQy1&t=105 ~hsnacademy] | ||
| + | |||
| + | == Video Solution 4 by Daily Dose of Math == | ||
| + | |||
| + | [//youtu.be/rjd0gigUsd0 ~Thesmartgreekmathdude] | ||
| + | |||
| + | == Video Solution 5 by Thinking Feet == | ||
| + | |||
| + | https://youtu.be/PKMpTS6b988 | ||
| + | |||
| + | == Video Solution 6 by CoolMathProblems == | ||
| + | |||
| + | https://youtu.be/biB8GlB54oI | ||
| + | |||
| + | == See Also == | ||
| + | |||
| + | {{AMC8 box|year=2025|num-b=1|num-a=3}} | ||
| + | {{MAA Notice}} | ||
| + | [[Category:Introductory Number Theory Problems]] | ||
Latest revision as of 08:53, 16 February 2025
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3 (fast version of Solution 2)
- 5 Video Solution by Pi Academy
- 6 Video Solution 1
- 7 Video Solution 2 by SpreadTheMathLove
- 8 Video Solution 3
- 9 Video Solution 4 by Daily Dose of Math
- 10 Video Solution 5 by Thinking Feet
- 11 Video Solution 6 by CoolMathProblems
- 12 See Also
Problem
The table below shows the ancient Egyptian hieroglyphs that were used to represent different numbers.
For example, the number 
was represented by the hieroglyphs 
. What number is represented by the following combination of hieroglyphs?
Solution 1
The first hieroglyph is worth 
, the next 4 are worth 
, the next 
are worth 
, and the last 
are worth 
. Therefore, the answer is 
Solution 2
Simply notice that the first hieroglyph represents , and the next ones represent 
hundreds. They only answer choice with a 
in the thousands place and a in the hundreds place is answer choice 
~Avy11
Solution 3 (fast version of Solution 2)
From a first inspection, you may notice that there is no thousands hieroglyph. The only option with zero in the thousands place is
~thatmathsguy
Video Solution by Pi Academy
https://youtu.be/Iv_a3Rz725w?si=E0SI_h1XT8msWgkK
Video Solution 1
Video Solution 2 by SpreadTheMathLove
https://www.youtube.com/watch?v=jTTcscvcQmI
Video Solution 3
Video Solution 4 by Daily Dose of Math
Video Solution 5 by Thinking Feet
Video Solution 6 by CoolMathProblems
See Also
| 2025 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
