1003085203
Level:
B
What is the sum of all positive multiples of $7$ smaller than $100$?
$735$
$637$
$728$
$105$
$686$
Arithmetic sequences
1003085202
Level:
B
What is the sum of all two-digit numbers divisible by five?
$945$
$950$
$1050$
$1045$
$940$
1003085201
Level:
B
Find the sum of all even numbers which are greater than $6$ and smaller than $122$.
$3648$
$3584$
$3654$
$3712$
$3776$
1003107210
Level:
C
Solve the inequality with the variable $x$, where $x$ is a natural number:
$$\sum\limits_{n=1}^x \left(\frac25n-1\right) \leq x $$
$ x\leq9;\ x\in\mathbb{N}$
$x\leq10;\ x\in\mathbb{N}$
$x\in(-\infty;8]$
$x\geq8;\ x\in\mathbb{N}$
there is no solution in $\mathbb{N}$
1003107209
Level:
C
Solve the equation with the real variable $x$:
$$ \sum\limits_{n=1}^{23} xn=92 $$
$\frac13$
$4$
$\frac14$
$1$
$\frac12$
1003107208
Level:
C
Solve the equation with the variable $x$, where $x$ is a natural number:
$$ \sum\limits_{n=1}^x(-3n+10)=-45 $$
$9$
$5$
$10$
$13$
$12$
1003107207
Level:
C
Find the set of all solutions of the given inequality with the variable $x$, where $x$ is a natural number:
$$ 5x+10x+15x+\dots+50x \leq 1000 $$
$ \{1;2;3\} $
$ \{ 2 \} $
$\{ 1;2;3;4;5\} $
$\{ 1 \}$
$\{1;2\}$
1003107206
Level:
C
Solve the equation with the variable $n$, where $n$ is a natural number:
$$ 5+8+11+14+\dots+(3n+2)=735 $$
$21$
$65$
$20$
$68$
$10$
1003107205
Level:
C
Sizes of angles in a triangle form three consecutive arithmetic sequence terms. The size of the largest angle is four times the smallest one. Find the size of the smallest angle of the triangle.
$24^{\circ}$
$30^{\circ}$
$60^{\circ}$
$20^{\circ}$
$35^{\circ}$
1003107204
Level:
C
Positive numbers which when divided by $3$ leave a remainder of $2$ are terms of an increasing arithmetic sequence. The sum of the first $15$ terms is $480$. Find the $3$rd term of this sequence.
$17$
$11$
$20$
$5$
$23$