Practice (90/1000)
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A three-digit integer contains one of each of the digits $1$, $3$, and $5$. What is the probability that the integer is divisible by $5$?
How many $3$-digit positive integers have digits whose product equals $24$?
Two angles of an isosceles triangle measure $70^\circ$ and $x^\circ$. What is the sum of the three possible values of $x$?
How many non-congruent triangles have vertices at three of the eight points in the array shown below?
On the last day of school, Mrs. Wonderful gave jelly beans to her class. She gave each boy as many jelly beans as there were boys in the class. She gave each girl as many jelly beans as there were girls in the class. She brought $400$ jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. How many students were in her class?
The letters $A$, $B$, $C$ and $D$ represent digits.
what digit does $D$ represent?
A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cube is $\frac{1}{2}$ foot from the top face. The second cut is $\frac{1}{3}$ foot below the first cut, and the third cut is $\frac{1}{17}$ foot below the second cut. From the top to the bottom the pieces are labeled A, B, C, and D. The pieces are then glued together end to end as shown in the second diagram. What is the total surface area of this solid in square feet?
If $x^2 +2(m-3)x+16$ is a perfect square, find the value of $m$.
If $x^2 +x =m = (x-n)^2$, what is the value of $4(m+n)$?
If $x^m - y^n = (x+y^2)(x-y^2)(x^2+y^4)$, find the value of $m+n$.
If $1+x+x^2+\cdots + x^{2014}+x^{2015}=0$, find the value of $x^{2016}$.
If the value of $(9x^2 + k + y^2)$ is a perfect square for any $x$ and $y$, what value can $k$ take?
If $x^2+4x-4=0$, find the value of $3x^2+12x-5$.
Square ABCD, shown here, has diagonals AC and BD that intersect at E. How many triangles of any size are in the figure?
If $x+y=4$ and $x^2+y^2=6$, find the value of $xy$.
When the integers $1$ to $100$ inclusive are written, what digit is written the fewest number of times?
Evaluate the value of $$\Big(1-\frac{1}{2^2}\Big)\Big(1-\frac{1}{3^2}\Big)\cdots\Big(1-\frac{1}{9^2}\Big)\Big(1-\frac{1}{10^2}\Big)$$
Factorize: $x^4-2x^3-35x^2$
Factorize $3x^6-3x^2$.
Factorize $x^2-4xy-1+4y^2$.
Factorize $ax^2 -bx^2 -bx + ax +b-a$.
Factorize $9x^4-36y^2$.
Factorize $(x+1)(x+2)(x+3)(x+4)-24$.
Prove: for any given positive integer $n$, the value of $(n+7)^2 -(n-5)^2$ must be a multiple of 24.
If $a+b=2$, find the value of $(a^2-b^2)-8(a^2+b^2)$