There is a basket which contains apples and pears on Mrs. Putri’s kitchen table. One day, all of her grandchildren came to visit and she gave each one of them the same number of fruits without keeping track which kind it is. If Dewi received $\frac15$ of all the apples and $\frac17$ of all the pears, what is the minimum number of grandchildren can Mrs. Putri have?
Anggi is 140 cm tall and she can grab any object 40 cm above her head. She wants to take a book from the top of a cupboard which is 2.8 meters from the floor. She has several chairs with the same height, which can be stacked without overlap. If she uses one chair and stands on it, the distance between the tip of her hand and the book is 65 cm. What is the minimum number of chairs she needs to use to be able to grab the book?
Consider the sequence $\frac11,\frac12,\frac21,\frac13,\frac22,\frac31,\frac14,\frac23,\frac32,\frac41,\ldots,\frac1k,\frac2{k-1},\frac3{k-2},\ldots,\frac{k-1}2,\frac k1,\ldots$. If the 2022nd term of this sequence is in the form $a/b$, in simplest form, what is the value of $a+b$?
An old static CCTV camera, which can only move horizontally, covers the area shown in the figure below. If the distance from the CCTV camera to the ends of the wall are 20 m and 30 m, respectively, what is the total area, in $\mathrm{m}^2$, that is covered by the CCTV camera?
(If the answer is in the form of $a\sqrt b$ where b is the smallest non-square number, write the answer in the form $a;b$)
Mr. Andi maintains two gardens namely A and B, where the grass grows at a rate of 1 cm every 4 and 5 days, respectively. The initial height of the grass for both gardens is 1 cm. He needs to mow the garden only if the grass reaches 6 cm in height, and that after each mowing session, the height of the grass will be reduced back to 1 cm. On the days that he has to mow only one garden, he earns 15 dollars per session, while on some days where he needs to mow two gardens in one day, he will get 10 dollars for each garden mowed. How much dollars will Mr. Andi get in one year?
A vendor is selling three kinds of drinks namely: milk, juice, and soda. It is known that he has one bucket of soda and the total number of buckets of milk and juice is five. If the volumes of the buckets are 18, 19, 21, 23, 25 and 34 litres respectively and he has twice as much milk as he has juice. What is the volume, in litres, of the bucket containing soda?
In the figure below, it is given that $AB\parallel CD$, $\angle EFA=30^\circ$, $\angle FGH=90^\circ$, $\angle HMN=30^\circ$ and $\angle CNP=50^\circ$. What is the measure, in degrees, of $\angle GHM$?
All students in a class, including Amy, stand in a line. One at a time, they starting counting the numbers consecutively starting from 1, 2, 3, …. The sum of the numbers from all students minus twice of Amy’s number is 100. If Amy’s number is A and the number of all students is B, what is the value of $A+B$?
The figure shown below is dissected into six different squares. If the area of the smallest square is $1\ \mathrm{cm}^2$, what is the area, in $\mathrm{cm}^2$, of the shaded square?
In a town festival, there is a horse parade event where all of the horses were assigned numbers starting from 1, 2, 3, …. Ria took part in the event and rode the horse which has the largest sum of the digits from all the assigned numbers. If the total number of digits used in numbering the horses is 2022, then what is the number of the horse that Ria rode?
What is the maximum number of $1\times1\times4$ blocks that can fit inside a $6\times6\times6$ box such that each of the faces of the blocks are parallel to the corresponding faces of the box?
A panel of judges is set to review a movie shown in a cinema which has 50 rows of seats. There are 10 seats in the first row and each subsequent row has one more seat than the previous row. In each row, judges are not allowed to sit next to each other. What is the maximum number of judges that the cinema can accommodate?
In the figure below, $\triangle ABC$, $\triangle ACD$, $\triangle ADE$, and $\triangle AEF$ are all isosceles right triangles. If the area of pentagon BCDEF is $30\ \mathrm{cm}^2$, what is the length, in cm, of $AB+AD+AF$?
In the figure below, ABCD is a trapezoid having an area $70\ \mathrm{cm}^2$, $AD=10$ cm, and M is the midpoint of BC. What is the distance, in cm, from M to the side AD?
