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MEMEG0D
Username
MEMEG0D
Score
226
Membership
Stats
Questions
57
Answers
1
57 Questions
1 Answers
0
1
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+226
Number Theory
A four-digit hexadecimal integer is written on a napkin such that the units digit is illegible. The first three digits are 2, $F$, and 1. If the integer is a multiple of $19_{10}$, what is the units digit?
MEMEG0D
6 hours ago
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0
+226
Number Theory
The numbers $24^2 = 576$ and $56^2 = 3136$ are examples of perfect squares that have a units digits of $6.$
If the units digit of a perfect square is $5,$ then what are the possible values of the tens digit?
MEMEG0D
6 hours ago
0
1
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+226
Number Theory
Which of the residues 0, 1, 2, ..., 11 satisfy the congruence 3x = 1 mod 12?
MEMEG0D
6 hours ago
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1
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+226
Number Theory
Which of the residues 0, 1, 2, 3, 4 satisfy the congruence x^5 = 0 mod 5?
MEMEG0D
6 hours ago
+1
2
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+226
Number Theory
What are the first 5 digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{7}$ is written in base $16$?
MEMEG0D
Oct 28, 2024
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+226
Number Theory
Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim
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MEMEG0D
Oct 28, 2024
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+226
Number Theory
What is the largest positive integer $n$ such that $1457$, $1797$, $709$, $15$, $24$, $197$, $428$ all leave the same remainder when divided by $n$?
MEMEG0D
Oct 28, 2024
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1
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+226
Number Theory
A four-digit hexadecimal integer is written on a napkin such that the units digit is illegible. The first three digits are $7$, $D$, and $3$. If the integer is a multiple of $25_{10}$, what is the units digit?
MEMEG0D
Oct 28, 2024
0
2
1
+226
Algebra
Find the sum of all positive integers less than 1000 ending in 3 or 4 or 6 or 9.
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MEMEG0D
Oct 24, 2024
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1
+226
Algebra
In a geometric sequence, the 23rd term is 16 and the 24th term is 1/4. What is the 30th term?
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MEMEG0D
Oct 24, 2024
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+226
Geometry
In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11
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MEMEG0D
Oct 18, 2024
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+226
Geometry
In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?
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MEMEG0D
Oct 18, 2024
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+226
Geometry
In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.
MEMEG0D
Oct 18, 2024
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1
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+226
Geometry
Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?
MEMEG0D
Oct 18, 2024
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+226
Number Theory
You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $5$ pieces of candy per scoop to the vat, and another machine that can remove exactly $3$ pieces of candy with a different scoop from
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MEMEG0D
Oct 14, 2024
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2
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+226
Algebra
Simplify \dfrac{1}{\sqrt2+sqrt3}+\dfrac{1}{\sqrt2-sqrt3}.
MEMEG0D
Oct 9, 2024
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+226
Algebra
Find all ordered pairs x, y of real numbers such that x+y=10 and x^2+y^2=64.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).
MEMEG0D
Oct 9, 2024
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