problem stringlengths 10 5.15k | answer stringlengths 0 1.23k |
|---|---|
Find the numerical value of $k$ for which
\[\frac{7}{x + y} = \frac{k}{x + z} = \frac{11}{z - y}.\] | 18 |
Amanda’s garden contains 20 flowers and Peter’s garden contains three times as many flowers as Amanda's. If Peter gave 15 flowers to his brother, how many flowers are left in his garden? | The number of flowers in Peter’s garden is 20 * 3 = <<20*3=60>>60 flowers.
The number of flowers left after he gave his brother 15 flowers is 60 – 15 = <<60-15=45>>45 flowers.
#### 45 |
Let \( OP \) be the diameter of the circle \( \Omega \), and let \( \omega \) be a circle with center at point \( P \) and a radius smaller than that of \( \Omega \). The circles \( \Omega \) and \( \omega \) intersect at points \( C \) and \( D \). A chord \( OB \) of the circle \( \Omega \) intersects the second circ... | \sqrt{5} |
For what positive value of $t$ is $|6+ti| = 10$? | 8 |
Given that $\overrightarrow {a}|=4$, $\overrightarrow {e}$ is a unit vector, and the angle between $\overrightarrow {a}$ and $\overrightarrow {e}$ is $\frac {2π}{3}$, find the projection of $\overrightarrow {a}+ \overrightarrow {e}$ on $\overrightarrow {a}- \overrightarrow {e}$. | \frac {5 \sqrt {21}}{7} |
What is equivalent to $\sqrt{\frac{x}{1-\frac{x-1}{x}}}$ when $x < 0$? | -x |
Given a circle of radius $3$, there are multiple line segments of length $6$ that are tangent to the circle at their midpoints. Calculate the area of the region occupied by all such line segments. | 9\pi |
Simplify: $$\sqrt[3]{9112500}$$ | 209 |
Integers $x$ and $y$ with $x>y>0$ satisfy $x+y+xy=104$. What is $x$? | 34 |
At an exchange point, there are two types of transactions:
1) Give 2 euros - receive 3 dollars and a candy as a gift.
2) Give 5 dollars - receive 3 euros and a candy as a gift.
When the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had fewer dollars, he did not get any euros, but h... | 10 |
Let the real numbers \(a_{1}, a_{2}, \cdots, a_{100}\) satisfy the following conditions: (i) \(a_{1} \geqslant a_{2} \geqslant \cdots \geqslant a_{100} \geqslant 0\); (ii) \(a_{1}+a_{2} \leqslant 100\); (iii) \(a_{3}+a_{4} + \cdots + a_{100} \leqslant 100\). Find the maximum value of \(a_{1}^{2}+a_{2}^{2}+\cdots+a_{100... | 10000 |
Let $S_{7}$ denote all the permutations of $1,2, \ldots, 7$. For any \pi \in S_{7}$, let $f(\pi)$ be the smallest positive integer $i$ such that \pi(1), \pi(2), \ldots, \pi(i)$ is a permutation of $1,2, \ldots, i$. Compute \sum_{\pi \in S_{7}} f(\pi)$. | 29093 |
Given a sequence $\{a_n\}$, the sum of the first $n$ terms $S_n$ satisfies $a_{n+1}=2S_n+6$, and $a_1=6$.
(Ⅰ) Find the general formula for the sequence $\{a_n\}$;
(Ⅱ) Let $b_n=\frac{a_n}{(a_n-2)(a_{n+1}-2)}$, and $T_n$ be the sum of the first $n$ terms of the sequence $\{b_n\}$. Is there a maximum integer $m$ such th... | m=1 |
Find the smallest natural number \( n \) such that the sum of the digits of each of the numbers \( n \) and \( n+1 \) is divisible by 17. | 8899 |
In $\triangle ABC, D$ and $E$ are the midpoints of $BC$ and $CA$, respectively. $AD$ and $BE$ intersect at $G$. Given that $GEC$D is cyclic, $AB=41$, and $AC=31$, compute $BC$. | 49 |
Find the largest integer value of $n$ such that $n^2-9n+18$ is negative. | 5 |
What is the sum of all the four-digit positive integers that end in 0? | 4945500 |
The equation $y=-16t^2+22t+45$ describes the height (in feet) of a ball thrown upwards at $22$ feet per second from $45$ feet above the ground. Find the time (in seconds) when the ball will hit the ground. Express your answer as a common fraction. | \frac{5}{2} |
What is the product of all real numbers that are tripled when added to their reciprocals? | -\frac{1}{2} |
In parallelogram $EFGH$, point $Q$ is on $\overline{EF}$ such that $\frac{EQ}{EF} = \frac{1}{8}$, and point $R$ is on $\overline{EH}$ such that $\frac{ER}{EH} = \frac{1}{9}$. Let $S$ be the point of intersection of $\overline{EG}$ and $\overline{QR}$. Find the ratio $\frac{ES}{EG}$. | \frac{1}{9} |
Find the sum of all positive integers $n$ such that $1.5n - 6.3 < 7.5$. | 45 |
A typesetter scattered part of a set - a set of a five-digit number that is a perfect square, written with the digits $1, 2, 5, 5,$ and $6$. Find all such five-digit numbers. | 15625 |
A circle touches the extensions of two sides \( AB \) and \( AD \) of a square \( ABCD \) with a side length of 4 cm. From point \( C \), two tangents are drawn to this circle. Find the radius of the circle if the angle between the tangents is \( 60^{\circ} \). | 4 (\sqrt{2} + 1) |
The forecast predicts an 80 percent chance of rain for each day of a three-day festival. If it doesn't rain, there is a 50% chance it will be sunny and a 50% chance it will be cloudy. Mina and John want exactly one sunny day during the festival for their outdoor activities. What is the probability that they will get ex... | 0.243 |
Find the radius of the circle with equation $x^2 - 6x + y^2 + 2y + 6 = 0$. | 2 |
Five friends were comparing how much scrap iron they brought to the collection. On average, it was $55 \mathrm{~kg}$, but Ivan brought only $43 \mathrm{~kg}$.
What is the average amount of iron brought without Ivan?
(Note: By how many kilograms does Ivan's contribution differ from the average?) | 58 |
For each of the possible outcomes of rolling three coins (TTT, THT, TTH, HHT, HTH, HHH), a fair die is rolled for each two heads that appear together. What is the probability that the sum of the die rolls is odd? | \frac{1}{4} |
A large rectangle consists of three identical squares and three identical small rectangles. The perimeter of a square is 24, and the perimeter of a small rectangle is 16. What is the perimeter of the large rectangle?
The perimeter of a shape is the sum of its side lengths. | 52 |
What is the 20th digit after the decimal point of the sum of the decimal equivalents for the fractions $\frac{1}{7}$ and $\frac{1}{3}$? | 7 |
The graphs of the equations
$y=k, \qquad y=\sqrt{3}x+2k, \qquad y=-\sqrt{3}x+2k,$
are drawn in the coordinate plane for $k=-10,-9,-8,\ldots,9,10.\,$ These 63 lines cut part of the plane into equilateral triangles of side $2/\sqrt{3}.\,$ How many such triangles are formed?
| 660 |
Determine the smallest odd prime factor of $2021^{10} + 1$. | 61 |
What is the absolute value of the difference between the squares of 103 and 97? | 1200 |
In triangle $\triangle ABC$, it is known that the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, $c$, with $a=\sqrt{6}$, $\sin ^{2}B+\sin ^{2}C=\sin ^{2}A+\frac{2\sqrt{3}}{3}\sin A\sin B\sin C$. Choose one of the following conditions to determine whether triangle $\triangle ABC$ exists. If it exists, find the... | \frac{\sqrt{3}}{2} |
9 judges score a gymnast in artistic gymnastics, with each giving an integer score. One highest score and one lowest score are removed, and the average of the remaining scores determines the gymnast's score. If the score is rounded to one decimal place using the rounding method, the gymnast scores 8.4 points. What woul... | 8.43 |
Let $m$ be the product of all positive integers less than $4!$ which are invertible modulo $4!$. Find the remainder when $m$ is divided by $4!$.
(Here $n!$ denotes $1\times\cdots\times n$ for each positive integer $n$.) | 1 |
Let $a$ and $b$ be the two real values of $x$ for which\[\sqrt[3]{x} + \sqrt[3]{20 - x} = 2\]The smaller of the two values can be expressed as $p - \sqrt{q}$, where $p$ and $q$ are integers. Compute $p + q$.
| 118 |
A box contains 5 white balls and 5 black balls. I draw them out of the box, one at a time. What is the probability that all of my draws alternate colors, starting and ending with the same color? | \frac{1}{126} |
Find $73^{-1} \pmod{74}$, as a residue modulo 74. (Give an answer between 0 and 73, inclusive.) | 73 |
There are 7 trucks that have 20 boxes. There are 5 trucks that have 12 boxes. Each box holds 8 containers of oil. If all of the oil is evenly redistributed onto 10 trucks, how many containers of oil will each truck have? | Boxes of oil = 7 * 20 + 5 * 12 = <<7*20+5*12=200>>200 boxes
Containers of oil = 200 boxes * 8 containers = <<200*8=1600>>1600 containers of oil
1600/10 = <<1600/10=160>>160
Each truck will carry 160 containers of oil.
#### 160 |
What is the least four-digit positive integer, with all different digits, that is divisible by each of its digits? | 1236 |
Vivi bought fabric to make new pillows for her bed. She spent $75 on checkered fabric and $45 on plain fabric. If both fabrics cost $7.50 per yard, how many total yards of fabric did she buy? | The total yards of the checkered fabric is $75 / 7.50 = <<75/7.50=10>>10.
The total yards of the plain fabric is 45 / 7.50 = <<45/7.50=6>>6.
So, Vivi bought a total of 10 + 6 = <<10+6=16>>16 yards of fabric.
#### 16 |
Trevor's older brother was twice his age 20 years ago. How old was Trevor a decade ago if his brother is now 32 years old? | If Trevor's brother is 32 years old today then 20 years ago he was = 32-20 = <<32-20=12>>12 years old
If Trevor's brother was 12 years old and he was twice Trevor's age, then Trevor was 12/2 = <<12/2=6>>6 years old
If Trevor was 6 years old 20 years ago, then he must be 6 + 20 = <<6+20=26>>26 years old today
If Trevor ... |
For how many non-negative real values of $x$ is $\sqrt{169-\sqrt[4]{x}}$ an integer? | 14 |
Jack is on the phone with a scammer who says the IRS will arrest Jack if he doesn't send them the codes from 6 $500 Best Buy gift cards and 9 $200 Walmart gift cards. After sending the codes for 1 Best Buy gift card and 2 Walmart gift cards, Jack wises up and hangs up. How many dollars' worth of gift cards can he still... | First find the number of Best Buy gift cards Jack needs to return: 6 cards - 1 cards = <<6-1=5>>5 cards
Then multiply that number by the cost per card to find the total refund Jack gets from Best Buy: 5 cards * $500/card = $<<5*500=2500>>2500
Then find the number of Walmart gift cards Jack needs to return: 9 cards - 2 ... |
There is a lot of dust in Susie's house. It takes her 2 hours to vacuum the whole house. She can vacuum each room in 20 minutes. How many rooms does she have in her house? | Susie spends 2*60 = <<2*60=120>>120 minutes vacuuming.
Since she can vacuum each room in 20 minutes, she has 120/20 = <<120/20=6>>6 rooms in her house.
#### 6 |
A polynomial with integer coefficients is of the form
\[9x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 15 = 0.\]Find the number of different possible rational roots of this polynomial. | 16 |
Compute $\dbinom{10}{5}$. | 252 |
Alice and Bob are stuck in quarantine, so they decide to play a game. Bob will write down a polynomial $f(x)$ with the following properties:
(a) for any integer $n$ , $f(n)$ is an integer;
(b) the degree of $f(x)$ is less than $187$ .
Alice knows that $f(x)$ satisfies (a) and (b), but she does not know $f(... | 187 |
What is the largest five-digit integer whose digits have a product equal to the product $(7)(6)(5)(4)(3)(2)(1)$? | 98752 |
A nickel is placed on a table. The number of nickels which can be placed around it, each tangent to it and to two others is: | 6 |
Solve the equation \[\frac{x^2 + 3x + 4}{x + 5} = x + 6.\] | -\frac{13}{4} |
In the fall, a tree drops a tenth of its initial quantity of leaves each day over the course of four days, then abruptly drops the rest on the fifth day. If it had 340 leaves before they started to fall, how many leaves does it drop on the fifth day? | The tree drops 340 / 10 = <<340/10=34>>34 leaves for each of the four days.
Thus, it drops 34 * 4 = <<34*4=136>>136 leaves over the first four days.
Therefore, it drops 340 - 136 = <<340-136=204>>204 leaves on the fifth day.
#### 204 |
In a box, there are red and black socks. If two socks are randomly taken from the box, the probability that both of them are red is $1/2$.
a) What is the minimum number of socks that can be in the box?
b) What is the minimum number of socks that can be in the box, given that the number of black socks is even? | 21 |
If $q_1(x)$ and $r_1$ are the quotient and remainder, respectively, when the polynomial $x^8$ is divided by $x + \frac{1}{2}$, and if $q_2(x)$ and $r_2$ are the quotient and remainder, respectively, when $q_1(x)$ is divided by $x + \frac{1}{2}$, then $r_2$ equals | -\frac{1}{16} |
In triangle $ABC$, $AB = 16$, $AC = 24$, $BC = 19$, and $AD$ is an angle bisector. Find the ratio of the area of triangle $ABD$ to the area of triangle $ACD$. (Express your answer as a fraction in lowest terms.) | \frac{2}{3} |
When \( n \) is a positive integer, the function \( f \) satisfies \( f(n+3)=\frac{f(n)-1}{f(n)+1} \), with \( f(1) \neq 0 \) and \( f(1) \neq \pm 1 \). Find the value of \( f(8) \cdot f(2018) \). | -1 |
In convex quadrilateral $ABCD$, $AB=8$, $BC=4$, $CD=DA=10$, and $\angle CDA=60^\circ$. If the area of $ABCD$ can be written in the form $\sqrt{a}+b\sqrt{c}$ where $a$ and $c$ have no perfect square factors (greater than 1), what is $a+b+c$? | 259 |
Find all $c$ which satisfy $$\frac{c}{3} \le 2+c < -2(1+c).$$Express your answer in interval notation, simplifying any fractions which occur in your answer. | \left[-3,-\frac{4}{3}\right) |
The NIMO problem writers have invented a new chess piece called the *Oriented Knight*. This new chess piece has a limited number of moves: it can either move two squares to the right and one square upward or two squares upward and one square to the right. How many ways can the knight move from the bottom-left square ... | 252 |
"The Nine Chapters on the Mathematical Art" is an ancient Chinese mathematical text, which records: "If it can be halved, then halve it; if not, juxtapose the numerator and denominator, subtract the lesser from the greater, continue to subtract in turn, seeking their equality. Use the equal number to reduce them." This... | 273 |
Liz's basketball team is down by 20 points in the final quarter of their game. Liz goes on a shooting spree, sinking 5 free throw shots, 3 three-pointers, and 4 other jump shots. The other team only scores 10 points that quarter, and none of Liz's teammates manage to score any points. How much does Liz's team lose b... | Each free throw counts as 1 point, so 5 successful free throws means she scores 5*1= <<5*1=5>>5 points
Each 3 pointer counts as 3 points, so this means Liz scores 3*3= <<3*3=9>>9 points from 3 pointers
Each jump shot counts as 2 points, meaning Liz scores 4*2=<<4*2=8>>8 points of jump shots.
Liz's opponents score 10 po... |
Boris was given a Connect Four game set for his birthday, but his color-blindness makes it hard to play the game. Still, he enjoys the shapes he can make by dropping checkers into the set. If the number of shapes possible modulo (horizontal) flips about the vertical axis of symmetry is expressed as $9(1+2+\cdots+n)$, f... | 729 |
Calculate the sum $1 + 3 + 5 + \cdots + 15 + 17$. | 81 |
How many students are there in our city? The number expressing the quantity of students is the largest of all numbers where any two adjacent digits form a number that is divisible by 23. | 46923 |
A pyramid is formed on a $6\times 8$ rectangular base. The four edges joining the apex to the corners of the rectangular base each have length $13$. What is the volume of the pyramid? | 192 |
In the Cartesian coordinate system \(xOy\), there is a point \(P(0, \sqrt{3})\) and a line \(l\) with the parametric equations \(\begin{cases} x = \dfrac{1}{2}t \\ y = \sqrt{3} + \dfrac{\sqrt{3}}{2}t \end{cases}\) (where \(t\) is the parameter). Using the origin as the pole and the non-negative half-axis of \(x\) to es... | \sqrt{14} |
Points $A(3,5)$ and $B(7,10)$ are the endpoints of a diameter of a circle graphed in a coordinate plane. How many square units are in the area of the circle? Express your answer in terms of $\pi$. | \frac{41\pi}{4} |
What is the greatest common factor of $154$ and $252$? | 14 |
Victor has $3$ piles of $3$ cards each. He draws all of the cards, but cannot draw a card until all the cards above it have been drawn. (For example, for his first card, Victor must draw the top card from one of the $3$ piles.) In how many orders can Victor draw the cards? | 1680 |
In Mr. Fox's class, there are seven more girls than boys, and the total number of students is 35. What is the ratio of the number of girls to the number of boys in his class?
**A)** $2 : 3$
**B)** $3 : 2$
**C)** $4 : 3$
**D)** $5 : 3$
**E)** $7 : 4$ | 3 : 2 |
In a bag there are $1007$ black and $1007$ white balls, which are randomly numbered $1$ to $2014$ . In every step we draw one ball and put it on the table; also if we want to, we may choose two different colored balls from the table and put them in a different bag. If we do that we earn points equal to the absol... | 1014049 |
The red parabola shown is the graph of the equation $x = ay^2 + by + c$. Find $c$. (The grid lines are spaced one unit apart.)
[asy]
size(150);
real ticklen=3;
real tickspace=2;
real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownle... | -2 |
Find the smallest positive integer $M$ such that the three numbers $M$, $M+1$, and $M+2$, one of them is divisible by $3^2$, one of them is divisible by $5^2$, and one is divisible by $7^2$. | 98 |
Masha has three identical dice, each face of which has one of six different prime numbers with a total sum of 87.
Masha rolled all three dice twice. The first time, the sum of the numbers rolled was 10, and the second time, the sum of the numbers rolled was 62.
Exactly one of the six numbers never appeared. What numb... | 17 |
Compute: $5^2-3(4)+3^2$. | 22 |
From Monday to Friday, Elle practices piano for 30 minutes. On Saturday, she practices piano three times as much as on a weekday. There is no practice on Sunday. How many hours does Elle spend practicing piano each week? | From Monday to Friday, Elle practices 0.50 x 5 = <<0.50*5=2.5>>2.5 hours.
On Saturday, she practices 0.50 x 3 = <<0.50*3=1.5>>1.5 hours.
Each week, Elle practices piano for 2.5 + 1.5 = <<2.5+1.5=4>>4 hours.
#### 4 |
Sandy's daughter has a playhouse in the back yard. She plans to cover the one shaded exterior wall and the two rectangular faces of the roof, also shaded, with a special siding to resist the elements. The siding is sold only in 8-foot by 12-foot sections that cost $\$27.30$ each. If Sandy can cut the siding when she ge... | \$ 54.60 |
What is the value of $\frac{13!-12!+144}{11!}$? | 144 |
What is the value of $x$ in the plane figure shown?
[asy]
pair A;
draw(dir(40)--A); draw(dir(200)--A); draw(dir(300)--A);
label("$160^{\circ}$",A,dir(120)); label("$x^{\circ}$",A,dir(250)); label("$x^{\circ}$",A,dir(350));
[/asy] | 100 |
The circles whose equations are $x^2 + y^2 - 4x + 2y - 11 = 0$ and $x^2 + y^2 - 14x + 12y + 60 = 0$ intersect in the points $A$ and $B.$ Compute the slope of $\overline{AB}.$ | 1 |
Jason has a moray eel that eats 20 guppies a day and 5 betta fish who each eat 7 guppies a day. How many guppies per day does she need to buy? | First find the total number of guppies the betta fish need: 5 fish * 7 guppies/fish = <<5*7=35>>35 guppies
Then add the number of guppies the eel needs to find the total number needed: 35 guppies + 20 guppies = <<35+20=55>>55 guppies
#### 55 |
A group of 25 friends were discussing a large positive integer. ``It can be divided by 1,'' said the first friend. ``It can be divided by 2,'' said the second friend. ``And by 3,'' said the third friend. ``And by 4,'' added the fourth friend. This continued until everyone had made such a comment. If exactly two friends... | 787386600 |
Find the value of $n$ that satisfies $\frac{1}{n+1} + \frac{2}{n+1} + \frac{n}{n+1} = 3$. | 0 |
The equations $x^3 + Ax + 10 = 0$ and $x^3 + Bx^2 + 50 = 0$ have two roots in common. Then the product of these common roots can be expressed in the form $a \sqrt[b]{c},$ where $a,$ $b,$ and $c$ are positive integers, when simplified. Find $a + b + c.$ | 12 |
In isosceles triangle $\triangle ABC$ we have $AB=AC=4$. The altitude from $B$ meets $\overline{AC}$ at $H$. If $AH=3(HC)$ then determine $BC$. | 2\sqrt{2} |
Miranda is stuffing feather pillows. She needs two pounds of feathers for each pillow. A pound of goose feathers is approximately 300 feathers. Her goose has approximately 3600 feathers. How many pillows can she stuff after she plucks the goose? | Miranda will have 3600 / 300 = <<3600/300=12>>12 pounds of feathers from her goose.
Thus, Miranda can stuff about 12 / 2 = <<12/2=6>>6 feather pillows after she plucks the goose.
#### 6 |
The national security agency's wiretap recorded a conversation between two spies and found that on a 30-minute tape, starting from the 30-second mark, there was a 10-second segment of conversation containing information about the spies' criminal activities. Later, it was discovered that part of this conversation was er... | \frac{1}{45} |
Six horizontal lines and five vertical lines are drawn in a plane. If a specific point, say (3, 4), exists in the coordinate plane, in how many ways can four lines be chosen such that a rectangular region enclosing the point (3, 4) is formed? | 24 |
Let the ordered triples $(x,y,z)$ of complex numbers that satisfy
\begin{align*}
x + yz &= 7, \\
y + xz &= 10, \\
z + xy &= 10.
\end{align*}be $(x_1,y_1,z_1),$ $(x_2,y_2,z_2),$ $\dots,$ $(x_n,y_n,z_n).$ Find $x_1 + x_2 + \dots + x_n.$ | 7 |
Given the function $f(x)=e^{x}+ \frac {2x-5}{x^{2}+1}$, determine the value of the real number $m$ such that the tangent line to the graph of the function at the point $(0,f(0))$ is perpendicular to the line $x-my+4=0$. | -3 |
The distance from the point $(3,0)$ to one of the asymptotes of the hyperbola $\frac{{x}^{2}}{16}-\frac{{y}^{2}}{9}=1$ is $\frac{9}{5}$. | \frac{9}{5} |
If the perimeter of a rectangle is $p$ and its diagonal is $d$, the difference between the length and width of the rectangle is: | \frac {\sqrt {8d^2 - p^2}}{2} |
A recipe calls for $5 \frac{3}{4}$ cups of flour and $2 \frac{1}{2}$ cups of sugar. If you make one-third of the recipe, how many cups of flour and sugar do you need? Express your answers as mixed numbers. | \frac{5}{6} |
Suppose that $x$ and $y$ are nonzero real numbers such that $\frac{4x-3y}{x+4y} = 3$. Find the value of $\frac{x-4y}{4x+3y}$. | \frac{11}{63} |
If $g(x)=\sqrt[3]{\frac{x+3}{4}}$, for what value of $x$ will $g(2x)=2(g(x))$? Express your answer in simplest form. | -\frac{7}{2} |
Given that the sequence {a<sub>n</sub>} is an arithmetic sequence, a<sub>1</sub> < 0, a<sub>8</sub> + a<sub>9</sub> > 0, a<sub>8</sub> • a<sub>9</sub> < 0. Find the smallest value of n for which S<sub>n</sub> > 0. | 16 |
Annie and Bonnie are running laps around a $400$-meter oval track. They started together, but Annie has pulled ahead, because she runs $25\%$ faster than Bonnie. How many laps will Annie have run when she first passes Bonnie? | 5 |
During the festive season when the moon is full and the country is celebrating together, a supermarket plans to reduce the selling price of grapes that cost $16$ yuan per kilogram. Through statistical analysis, it was found that when the selling price is $26$ yuan per kilogram, $320$ kilograms can be sold per day. If t... | 21 |
Ron ate pizza with his friends the other day. If they ordered a 12-slice pizza and each of them ate 4 slices, how many friends were there with Ron? | Let the number of friends that ate with Ron be represented by F. That means the total amount of people that ate that day were 1 + F
If each of them ate 4 slices, and the pizza only has 12 slices, that means there could only have been 12/4 = 3 people eating
If the total number of people eating was 3, and if was also rep... |
What is the sum of the two smallest prime factors of $250$? | 7 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.