2025 AMC 8 Problems/Problem 2: Difference between revisions
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==Problem== | == Problem == | ||
The table below shows the ancient Egyptian hieroglyphs that were used to represent different numbers. | 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? | 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> | <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== | == 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. The 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> | |||
~Thesmartgreekmathdude | ~thatmathsguy | ||
== Video Solution 1 (Detailed Explanation) 🚀⚡📊 == | |||
https://www.youtube.com/watch?v=j20JsyEXKcs | |||
~ ChillThingz :) | |||
==Video Solution! Super Easy to understand and very knowledgeable == | |||
https://youtu.be/U_jbKGRR2Ww | |||
== Video Solution by Pi Academy == | |||
https://youtu.be/Iv_a3Rz725w?si=E0SI_h1XT8msWgkK | |||
== 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 | https://youtu.be/PKMpTS6b988 | ||
==See Also== | == Video Solution 6 by CoolMathProblems == | ||
https://youtu.be/biB8GlB54oI | |||
==Video Solution(Quick, fast, easy!)== | |||
https://youtu.be/fdG7EDW_7xk | |||
~MC | |||
== See Also == | |||
{{AMC8 box|year=2025|num-b=1|num-a=3}} | {{AMC8 box|year=2025|num-b=1|num-a=3}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
[[Category:Introductory Number Theory Problems]] | |||
Latest revision as of 10:42, 7 September 2025
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. The 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 1 (Detailed Explanation) 🚀⚡📊
https://www.youtube.com/watch?v=j20JsyEXKcs
~ ChillThingz :)
Video Solution! Super Easy to understand and very knowledgeable
Video Solution by Pi Academy
https://youtu.be/Iv_a3Rz725w?si=E0SI_h1XT8msWgkK
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
Video Solution(Quick, fast, easy!)
~MC
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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing
