The BStat and BMath Entrance of ISI Entrance is ‘different’ from IIT JEE or other engineering entrances. It tests creativity and ingenuity of the problem solver that requires more than mechanical application of formulae. Many of these problems are inspired from erstwhile Soviet Union math contests and other math olympiads. The entrance has two sections: […]
NMTC 2010 Primary Stage 1 Question 1 $\mathrm{n}, \mathrm{a}$ are natural numbers each greater than 1 . If $a+a+a+a+\ldots+a=2010$, and there are $n$ terms on the left hand side, then the number of ordered pairs $(a, n)$ is NMTC 2019 Primary Stage 1 Question 10 Sum of the odd numbers from 1 to 2019 both […]
NMTC 2019 Stage 1 Sub junior Question 10 How many positive integers smaller than 400 can you get as a sum of eleven consecutive positive integers? NMTC 2019 Stage 1 Sub junior Question 11 Let $x, y$ and $z$ be positive real numbers and let $x \geq y \geq z$ so that $x+y+z=20.1$. Which of […]
NMTC 2010 Primary Stage 1 Question 1 $\mathrm{n}, \mathrm{a}$ are natural numbers each greater than 1 . If $a+a+a+a+\ldots+a=2010$, and there are $n$ terms on the left hand side, then the number of ordered pairs $(a, n)$ is NMTC 2019 Inter Stage 1 Question 17 The number of times the digit occurs in the result […]
NMTC 2019 Stage 1 Inter Question 5 The area of the curve enclosed by $|x-2 \sqrt{2}|+|y-\sqrt{5}|=2$ is : (A) 16(B) 12(C) 8(D) 4 NMTC 2019 Inter Stage 1 Question 11 In a rectangle $A B C D$, point $E$ lies on $B C$ such that $\frac{B E}{E C}=2$ and point $F$ lies on $C D$ […]
Try these AMC 10 Geometry Questions and check your knowledge! Two right circular cones with vertices facing down as shown in the figure below contains the same amount of liquid. The radii of the tops of the liquid surfaces are $3$ cm and $6$ cm. Into each cone is dropped a spherical marble of radius […]
Author: Kazi Abu Rousan C is hard but fast But you need to be on guard to last. Python is easy but slow But you can use it to glow. But if you have julia Beautiful rhythms will flow. ---Me Julia is a high-level, high-performance, dynamic programming language. Most of you guys have heard or […]
Dear student, In the past few years several Cheenta students reached the top 300 universities in the world. These universities include Oxford, UCLA, NUS, MIT and University of Edinburgh. We have gradually shaped a success pathway for students that works in the long run. This pathway can be useful for you as well.There two components of this success path: Component 1: Performance […]
Author: Kazi Abu Rousan There are some problems in number theory which are very important not only because they came in exams but also they hide much richer intuition inside them. Today, we will be seeing one of such problems. Sources: B.Stat. (Hons.) and B.Math. (Hons.) I.S.I Admission Test 2012 problem-2. B.Stat. (Hons.) and B.Math. […]
Author: Kazi Abu Rousan Where are the zeros of zeta of s? G.F.B. Riemann has made a good guess; They're all on the critical line, saith he, And their density's one over 2 p log t. Source https://www.physicsforums.com/threads/a-poem-on-the-zeta-function.16280/ If you are a person who loves to read maths related stuff then sure you have came […]
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 […]
Question 1 What is the value of \(\left(2^{0}-1+5^{2}+0\right)^{-1}\times 5\)? (a) \(-125\) (b) \(-120\) (c) \(\frac{1}{5}\) (d) \(\frac{5}{24}\) (e) \(25\) Question 2 A box contains a collection of triangular and square tiles. There are 25 tiles in the box, containing 84 edges total. How many square tiles are there in the box? (a) 3 (b) 5 […]
Question 1 What is the value of \(\frac{11!-10!}{9!}\)? (a) 99 (b) 100 (c) 110 (d) 121 (e) 132 Question 2 For what value of \(x\) does \(10^{x}\cdot 100^{2x}=1000^{5}\)? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 Question 3 For every dollar Ben spent on bagels, David spent 25 cents less. Ben paid \($12.50\) […]
Question 1 A taxi ride costs \($1.50\) plus \($0.25\) per mile traveled. How much does a 5-mile taxi ride cost? (a) \($2.25\) (b) \($2.50\) (c) \($2.75\) (d) \($3.00\) (e) \($3.25\) Question 2 Alice is making a batch of cookies and needs \(2\frac{1}{2}\) cups of sugar. Unfortunately, her measuring cup holds only \(\frac{1}{4}\) cup of sugar. […]
Question 1 Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds. Working together, how many cupcakes can they frost in 5 minutes? (a) 10 (b) 15 (c) 20 (d) 25 (e) 30 Question 2 A square with side length 8 is cut in half, creating two congruent […]
Question 1 A cell phone plan costs \($20\) each month, plus \($0.05\) per text message sent, plus \($0.10\) for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay? (a) \($24.00\) (b) \($24.50\) (c) \($25.50\) (d) \($28.00\) (e) \($30.00\) Question […]
Question 1 One ticket to a show costs \($20\) at full price. Susan buys 4 tickets using a coupon that gives her a \(25%\) discount. Pam buys 5 tickets using a coupon that gives her a \(30%\) discount. How many more dollars does Pam pay than Susan? (a) 2 (b) 5 (c) 10 (d) 15 […]
Question 1 What is the value of \((2(2(2(2(2(2+1)+1)+1)+1)+1)+1)\) (a) 70 (b) 97 (c) 127 (d) 159 (e) 729 Question 2 Pablo buys popsicles for his friends. The store sells single popsicles for \($ 1\) each, 3popsicle boxes for \($ 2\) each, and 5-popsicle boxes for \($ 3\). What is the greatest number of popsicles that […]
Problem 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) $\frac{15}{8}$ Answer: (B) $\frac{11}{7}$ Problem 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) Liliane has $20 \%$ […]
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 […]
Question 1 The median of the list \[ n, n+3, n+4, n+5, n+6, n+8, n+10, n+12, n+15 \] is 10 . What is the mean? (a) 4 (b) 6 (c) 7 (d) 10 (e) 11 Question 2 A number \(x\) is 2 more than the product of its reciprocal and its additive inverse. In which […]