MEMEG0D

65 Questions
3 Answers

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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 28.10.2024

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6

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Algebra

Find the sum of all positive integers less than 1000 ending in 3 or 4 or 6 or 9.

MEMEG0D 24.10.2024

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Algebra

In a geometric sequence, the 23rd term is 16 and the 24th term is 1/4. What is the 30th term?

MEMEG0D 24.10.2024

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1

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Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

MEMEG0D 18.10.2024

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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?

MEMEG0D 18.10.2024

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6

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+260

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 18.10.2024

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3

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+260

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 18.10.2024

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4

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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 mehr ..

MEMEG0D 14.10.2024

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Algebra

Simplify \dfrac{1}{\sqrt2+sqrt3}+\dfrac{1}{\sqrt2-sqrt3}.

MEMEG0D 09.10.2024

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5

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+260

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 09.10.2024

+260

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The answer is 19.

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