In the math world, a unique challenge emerges, combining algebra and number theory. The goal: show that specific equation solutions aren't simple fractions. We reveal a key insight about b² - 4ac: it's always a distinct odd perfect square. Using "parity check," No matter the numbers, the left side remains even, while the right side stays odd. The result: these solutions differ from simple fractions, highlighting math's power in problem-solving.
In 2023, the following Cheenta students are successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 100 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 times every week. CMI B.Sc. Math Entrance I.S.I. […]
The leaders in the IOQM, ISI Entrance, American Math Competitions and Math Kangaroo mock contests in Cheenta
Please use the following form to contribute problems of CMI BSc Math Entrance 2023. We will work on the solutions. Also come back to this page to see the updates on Problems and Solutions of CMI BSc Math Entrance 2023. B1. Let \( n \) be an odd positive number greater than 1. We have […]
Questions, Solutions and discussions on ISI BStat-BMath Entrance 2023.
Solutions of INMO 2023 Problem 1 Let $S$ be a finite set of positive integers. Assume that there are precisely $2023$ ordered pairs $(x, y)$ in $S \times S$ so that the product $xy$ is a perfect square. Prove that one can find at least four distinct elements in $S$ so that none of their […]
Understand how Cheenta Math Circles are critical for training students for math olympiads and other advanced mathematical competitions.
Problems, solutions and discussion on IOQM 2022 (India).
Question 1 What is the value of $9901 \cdot 101-99 \cdot 10101$ ? (a) 1 (b) 20 (c) 200 (d) 202 (e) 2020 Question 2 A model used to estimate the time it will take to hike to the top of the mountain on a trail is of the form $T=a L+b G$, where $a$ […]
Question 1 What is the value of $$ 3+\frac{1}{3+\frac{1}{3+\frac{1}{3}} ?} $$ (a) $\frac{31}{10}$ (b) $\frac{49}{15}$ (c) $\frac{33}{10}$ (d) $\frac{109}{33}$ (e) $\frac{15}{4}$ Question 2 Mike cycled 15 laps in 57 minutes. Assume he cycled at a constant speed throughout. Approximately how many laps did he complete in the first 27 minutes? (a) 5 (b) 7 (c) […]
Question 1 What is the value of $$ \left(2^{2}-2\right)-\left(3^{2}-3\right)+\left(4^{2}-4\right) ? $$ (a) 1 (b) 2 (c) 5 (d) 8 (e) 12 Question 2 Portia's high school has 3 times as many students as Lara's high school. The two high schools have a total of 2600 students. How many students does Portia's high school have? (a) […]
Question 1 What value of $\boldsymbol{x}$ satisfies $$ x-\frac{3}{4}=\frac{5}{12}-\frac{1}{3} ? $$ (a) $-\frac{2}{3}$ (b) $\frac{7}{36}$ (c) $\frac{7}{12}$ (d) $\frac{2}{3}$ (e) $\frac{5}{6}$ Question 2 The numbers $3,5,7, a$ and $b$ have an average (arithmetic mean) of 15 . What is the average of $a$ and $b$ ? (a) 0 (b) 15 (c) 30 (d) 45 (e) […]
Question 1 Cities $A$ and $B$ are 45 miles apart. Alice and Barbara start biking from $A$ and $B$ at speeds of 18 mph and 12 mph , respectively. How far away from city $A$ will they be when they meet? (a) 20 (b) 24 (c) 25 (d) 26 (e) 27 Question 2 The weight […]
Question 1 What is the value of \[ 2^{\left(0^{\left(1^{9}\right)}\right)}+\left(\left(2^{0}\right)^{1}\right)^{9}? \] (a) 0 (b) 1 (c) 2 (d) 3 (e) 4 Question 2 What is the hundreds digit of \((20!-15!)\)? (a) 0 (b) 1 (c) 2 (d) 4 (e) 5 Question 3 Ana and Bonita were born on the same date in different years, \(n\) years […]
Question 1 What is the value of $$ \left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1 ? $$ (a) $\frac{5}{8}$ (b) $\frac{11}{7}$ (c) $\frac{8}{5}$ (d) $\frac{18}{11}$ (e) $\frac{15}{8}$ Question 2 Liliane has $50 %$ more soda than Jacqueline, and Alice has $25 %$ more soda than Jacqueline. What is the relationship between the amounts of soda that Liliane and Alica have? (a) […]
Question 1 Mary's top book shelf holds five books with the following widths, in centimeters: \(6, \frac{1}{2}, 1,2.5\), and 10. What is the average book width, in centimeters? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 Question 2 Four identical squares and one rectangle are placed together to form one large square as […]
Question 1 One can holds 12 ounces of soda. What is the minimum number of cans to provide a gallon (128 ounces) of soda? (a) 7 (b) 8 (c) 9 (d) 10 (e) 11 Question 2 Four coins are picked out of a piggy bank that contains a collection of pennies, nickels, dimes, and quarters. […]
Question 1 A bakery owner turns on his doughnut machine at 8:30 AM. At 11:10 AM the machine has completed one third of the day's job. At what time will the doughnut machine complete the job? (a) 1:50 PM (b) 3:00 PM (c) 3:30 PM (d) 4:30 PM (e) 5:50 PM Question 2 A square […]