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?
Define \(a @ b = ab-b^2\) and \(a # b = a+b-ab^2\). What is \[ \frac{6 @ 2}{6 # 2}? \]
An aquarium has a rectangular base that measures 100 cm by 40 cm and has a height of 50 cm. It is filled with water to a height of 40 cm. A brick with a rectangular base that measures 40 cm by 20 cm and a height of 10 cm is placed in the aquarium. By how many centimeters does the water rise?
The larger of two consecutive odd integers is three times the smaller. What is their sum?
A school store sells 7 pencils and 8 notebooks for \($4.15\). It also sells 5 pencils and 3 notebooks for \($1.77\). How much do 16 pencils and 10 notebooks cost?
At Euclid High School, the number of students taking the AMC 10 was 60 in 2002, 66 in 2003, 70 in 2004, 76 in 2005, 78 in 2006, and 85 in 2007. Between what two consecutive years was there the largest percentage increase?
Last year Mr.\ John Q.\ Public received an inheritance. He paid \(20%\) in federal taxes on the inheritance, and paid \(10%\) of what he had left in state taxes. He paid a total of \($10{,}500\) for both taxes. How many dollars was the inheritance?
Triangles \(ABC\) and \(ADC\) are isosceles with \(AB=BC\) and \(AD=DC\). Point \(D\) is inside \(\triangle ABC\). \(\angle ABC=40^\circ\), and \(\angle ADC=140^\circ\). What is the degree measure of \(\angle BAD\)?
Real numbers \(a\) and \(b\) satisfy the equations \[ 3^a=81^{b+2} \quad\text{and}\quad 125^b=5^{a-3}. \] What is \(ab\)?
The Dunbar family consists of a mother, a father, and some children. The average age of the members of the family is 20, the father is 48 years old, and the average age of the mother and children is 16. How many children are in the family?
The numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same. What is this common sum?
Two tour guides are leading six tourists. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. How many different groupings of guides and tourists are possible?
Yan is somewhere between his home and the stadium. To get to the stadium he can walk directly to the stadium, or else he can walk home and then ride his bicycle to the stadium. He rides 7 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his home to his distance from the stadium?
A triangle with side lengths in the ratio \(3:4:5\) is inscribed in a circle of radius 3. What is the area of the triangle?
Four circles of radius 1 are each tangent to two sides of a square and externally tangent to a circle of radius 2, as shown. What is the area of the square?
Integers \(a\), \(b\), \(c\), and \(d\), not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that \(ad-bc\) is even?
Suppose that \(m\) and \(n\) are positive integers such that \(75m=n^3\). What is the minimum possible value of \(m+n\)?
Consider the 12-sided polygon \(ABCDEFGHIJKL\), as shown. Each of its sides has length 4, and each two consecutive sides form a right angle. Suppose that \(\overline{AG}\) and \(\overline{CH}\) meet at \(M\). What is the area of quadrilateral \(ABCM\)?
A paint brush is swept along both diagonals of a square to produce the symmetric painted area, as shown. Half the area of the square is painted. What is the ratio of the side length of the square to the brush width?
Suppose that the number \(a\) satisfies the equation \[ 4=a+a^{-1}. \] What is the value of \(a^4+a^{-4}\)?
A sphere is inscribed in a cube that has a surface area of 24 square meters. A second cube is then inscribed within the sphere. What is the surface area in square meters of the inner cube?
A finite sequence of three-digit integers has the property that the tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term. For example, such a sequence might begin with terms 247, 475, and 756 and end with the term 824. Let \(S\) be the sum of all the terms in the sequence. What is the largest prime number that always divides \(S\)?
How many ordered pairs \((m,n)\) of positive integers, with \(m>n\), have the property that their squares differ by 96?
Circles centered at \(A\) and \(B\) each have radius 2, as shown. Point \(O\) is the midpoint of \(\overline{AB}\), and \(OA=2\sqrt{2}\). Segments \(OC\) and \(OD\) are tangent to the circles centered at \(A\) and \(B\), respectively, and \(EF\) is a common tangent. What is the area of the shaded region \(ECODF\)?
For each positive integer \(n\), let \(S(n)\) denote the sum of the digits of \(n\). For how many values of \(n\) is \[ n+S(n)+S(S(n))=2007? \]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
Cheenta students shine at the Purple Comet Math Meet 2025 organized by Titu Andreescu and Jonathan Kanewith top national and global ranks.
Celebrate the success of Cheenta students in the Stanford Math Tournament. The Unified Vectors team achieved Top 20 in the Team Round.