Part I Problem 1 Let \(XZ\) be a diameter of circle \(\omega\). Let Y be a point on \(XZ\) such that \(XY=7\) and \(YZ=1\). Let W be a point on \(\omega\) such that \(WY\) is perpendicular to \(XZ\). What is the square of the length of the line segment \(WY\) ? (a) 7(b) 8(c) 10(d) […]
PART I Problem 1 Answer: A Problem 2 Answer: D Problem 3 Answer: D Problem 4 Answer: A Problem 5 Answer: D Problem 6 Answer: D Problem 7 Answer: D Problem 8 Answer: C Problem 9 Answer: B Problem 10 For positive real numbers a and b, the minimum value of\( \left18 a+\frac{1}{3 b}\right\left3 b+\frac{1}{8 […]
Problem 1 Let $\mathbb{N}$ be the set of all positive integers and $S=\left\{(a, b, c, d) \in \mathbb{N}^4: a^2+b^2+c^2=d^2\right\}$. Find the largest positive integer $m$ such that $m$ divides $a b c d$ for all $(a, b, c, d) \in S$. Solution Notice that $(2, 2, 1, 3)\in S\Rightarrow m$ is a divisor of $12 […]
Try this ISI BStat - BMath Entrance 2023, Problem no. 2 with hints and final solution.
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.
Question 1 Kate bakes 20 -inch by 18 -inch pan of cornbread. The cornbread is cut into pieces that measure 2 inches by 2 inches. How many pieces of cornbread does the pan contain? (a) 90 (b) 100 (c) 180 (d) 200 (e) 360 Question 2 Sam drove 96 miles in 90 minutes. His average […]
Question 1 What is the value of $$ 1-(-2)-3-(-4)-5-(-6) ? $$ (a) -20 (b) -3 (c) 3 (d) 5 (e) 21 Question 2 Carl has 5 cubes each having side length 1 , and Kate has 5 cubes each having side length 2 . What is the total volume of these 10 cubes? (a) 24 […]
Question 1 How many integer values of $x$ satisfy $|x|<3 \pi$ ? (a) 9 (b) 10 (c) 18 (d) 19 (e) 20 Question 2 What is the value of $\sqrt{(3-2 \sqrt{3})^{2}}+\sqrt{(3+2 \sqrt{3})^{2}}$ ? (a) 0 (b) $4 \sqrt{3}-6$ (c) 6 (d) $4 \sqrt{3}$ (e) $4 \sqrt{3}+6$ Question 3 In an after-school program for juniors and […]
Question 1 What is the value of $1234+2341+3412+4123$ ? (a) 10,000 (b) 10,010 (c) 10,110 (d) 11,000 (e) 11,110 Question 2 What is the area of the shaded figure shown below? (a) 4 (b) 6 (c) 8 (d) 10 (e) 12 Question 3 The expression $\frac{2021}{2020}-\frac{2020}{2021}$ is equal to the fraction $\frac{p}{q}$ in which $p$ […]
Question 1 Define $x \diamond y$ to be $|x-y|$ for all real numbers $x$ and $y$. What is the value of $$ (1 \diamond(2 \diamond 3))-((1 \diamond 2) \diamond 3) ? $$ (a) -2 (b) -1 (c) 0 (d) 1 (e) 2 Question 2 In rhombus $A B C D$, point $P$ lies on segment […]
Question 1 Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely full but runs out of juice when the fourth glass is only $\frac{1}{3}$ full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into the […]
Question 1 In a long line of people arranged left to right, the $1013^{\text {th }}$ person from the left is also the $1010^{\text {th }}$ person from the right. How many people are in the line? (a) 2021 (b) 2022 (c) 2023 (d) 2024 (e) 2025 Question 2 What is $10!-7!\cdot 6!$ ? (a) […]
Question 1 The instructions on a $350-$ gram bag of coffee beans say that proper brewing of a large mug of pour-over coffee requires 20 grams of coffee beans. What is the greatest number of properly brewed large mugs of coffee that can be made from the coffee beans in that bag? (a) 16 (b) […]
Question 1 Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at $1: 30$, traveling due north at a steady 8 miles per hour. Betsy leaves on her bicycle from the same point at $2: 30$, traveling due east at a steady 12 miles per hour. At what time will they […]
Question 1 In the year 2001, the United States will host the International Mathematical Olympiad. Let $I, M$, and $O$ be distinct positive integers such that the product $I \cdot M \cdot O=2001$. What's the largest possible value of the sum $I+M+O$ ? (a) 23 (b) 55 (c) 99 (d) 111 (e) 671 Question 2 […]