Set 7

A public transport stop is usually served by public transport vans (angkot) from $3$ different routes. Van A with the shortest route passes the stop every $2$ hours, Van B every $3$ hours, while Van C every $x$ hours. The three of them last met at the stop simultaneously at $08.00$, and will meet for the $4$-th time $18$ hours after the first meeting. Then the value of $x$ is....

Panjul is entangled in an online loan (pinjol) of $\text{Rp}3,000,000.00$ with an interest policy of $2\%$ per month. He is optimistic that he can pay off the loan within $10$ months. Then the money he deposits to the online loan provider per month is....

Mr. Umar is an employee of the school cooperative in the procurement department. At the end of every month, Mr. Umar always shops for consumer needs, especially stationery, namely $6$ dozens of notebooks for $\text{Rp}144,000.00$, $5$ dozens of ballpoints for $\text{Rp}90,000.00$, and $6$ dozens of pencils for $\text{Rp}72,000.00$.

Notebooks are sold: $3$ dozens at $\text{Rp}2,500.00$ per copy, $2$ dozens at $\text{Rp}2,300.00$ per copy, and the rest at $\text{Rp}2,100.00$ per copy.

Ballpoints are sold: one dozen at $\text{Rp}2,000.00$ per piece, $3$ dozens at $\text{Rp}1,700.00$ per piece, and the rest at $\text{Rp}1,600.00$ per piece.

Pencils are sold: $4$ dozens at $\text{Rp}1,500.00$ per piece, and the rest at $\text{Rp}1,300.00$ per piece.

The item that provides the most profit is....

A room will be made into a podcast studio. The room is cube-shaped with an edge length of $5$ meters. Four spotlights will be installed at the top corners of the room. Assume the spotlight beams are straight lines.

If the four lights are turned on simultaneously so that the beams intersect at one point, then the distance from the intersection point to the floor is....

A cylinder has a radius of $16 \text{ cm}$ and a height of $20 \text{ cm}$ and is full of water. Then, $n$ balls with a radius of $6 \text{ cm}$ are put into the cylinder. After the balls are inserted, the remaining water volume is $64\pi \text{ cm}^3$.

The number of balls inserted is....

City A is a city located on the coast but surrounded by high hills. The following is a table of air temperature in City A at each altitude of its region.

The temperature in City A decreases by a constant value as the altitude measured from sea level increases.

What is the ratio of the air temperature at an altitude of $800 \text{ m}$ to $1200 \text{ m}$?

Mr. Brikson is a manager at an insurance company. Last year, he received a salary of $\text{Rp}15.000.000,00$ per month. Due to his performance, this year he received a salary increase of $\text{Rp}750.000,00$, so that this year he receives a salary of $\text{Rp}15.750.000,00$ per month. Next year, his salary will increase again to $\text{Rp}16.500.000,00$ per month. Similarly, he receives a salary increase of $\text{Rp}750.000,00$ every year.

If Mr. Brikson is $40$ years old this year, what will be his monthly salary when he is $54$ years old?

A taxi driver has an income regulated by his workplace. The amount of wage he receives is the UMR (Regional Minimum Wage) plus the product of the number of passengers and the customer satisfaction rating (index) each month. The customer satisfaction index in a given month is $100$ less than the number of passengers during that month. The taxi driver's service price is denoted as $y$, the number of passengers is denoted as $x$, and the customer satisfaction index is $z$. The UMR in the place where the driver lives is $\text{Rp}4.680.000,00$.

If in a month a driver gets $200$ passengers, then his income is....

A rocket is fired from an enemy base with the trajectory equation $s(t) = 4000 - t^2$ where $s$ is in meters and $t$ is in seconds. To destroy an enemy aircraft carrier moving with the position function with respect to time $s(t) = 60t$.

The time required until the collision occurs is.... Seconds.

In a warehouse, there are $80$ inventory items. Upon inspection, $20$ items are found to be damaged. If $1$ item is taken at random, the probability that the item taken is not damaged is....

There are two boxes containing balls of different colors. The first box contains $4$ red balls and $3$ blue balls. The second box contains $7$ red balls and $3$ white balls. One ball is taken from each box. The probability of drawing a red ball from the first box and a white ball from the second box is....

A map has a scale of $1:2,000,000$ and on the map, there are several cities with distances as follows:

• City $A$ to city $x$ = $2.5 \text{ cm}$
• City $x$ to city $B$ = $3 \text{ cm}$
• City $A$ to city $y$ = $4 \text{ cm}$
• City $y$ to city $B$ = $4.5 \text{ cm}$

Benu and Mamang will travel from city $A$ to city $B$ via different routes. Benu takes the route passing through city $x$, while Mamang passes through city $y$.

The difference in travel distance between Benu and Mamang is....

A running athlete is training. The training is done in an arena with a circular track. There are $4$ checkpoints on the track, namely $A - B - C - D$, with equal distances between checkpoints. Suppose the runner has passed checkpoint $C$ (from $A$) $3$ times in $12$ minutes.

Then the time required for the runner to reach exactly at checkpoint $C$ for the fourth time is....

A businessman with a capital of $\text{Rp}10,000,000.00$ produces products $A$ and $B$, which provide a profit of $8\%$ and $10\%$ per month, respectively. If both types of products generate a profit of $\text{Rp}904,000.00$ every month, then the capital for product $A$ is....

Two "Semoga Awet" stores both sell meat and fish. The sales of meat and fish from these two stores in one week are shown in the following table.

The price of fish per kilogram at both stores is....

In a study group, there are $22$ participants. Their mathematics average score is $5$ and the range is $4$. If the participant with the lowest score and the participant with the highest score are excluded, the average score becomes $4.9$. The score of the lowest student is....

Two study groups have $4$ members each. Their average weights are $30 \text{ kg}$ and $33 \text{ kg}$. If one child from each group is exchanged, the average weights become equal.

The difference in weight between the two exchanged children is ....

Eagles are a type of bird with terrifying hunting capabilities. They are capable of flying with a wide cruising range and sharp vision. Eagles can spot their prey from a height of $1500$ meters above the surface.

Suppose for a simple case, an eagle flies above the surface of a river and sees a fish at a depth of $3$ meters from the river surface. An angle of $30^\circ$ is formed between the fish and the Eagle's line of sight. If the line of sight distance between the Eagle and the Fish is $18$ meters, then the height of the Eagle above the river surface is .... (ignore the refractive index of water)

A plane is initially at an altitude of $3000 \text{ meters}$ and intends to land on a runway. However, due to bad weather, the ATC (Air Traffic Control) officer requests the pilot to perform a Holding Area, or circle in the air while waiting for the weather to improve.

The plane's position, which initially forms a $30^\circ$ angle with the ATC tower, changes to $45^\circ$ within $30 \text{ seconds}$. Thus, the estimated speed of the plane is ....

In a coastal area, the highest wave reaches $16 \text{ meters}$ from crest to trough. The wave takes $6 \text{ hours } 12 \text{ minutes}$ to move from the highest crest to the trough, so the time required from crest to crest is $12 \text{ hours } 24 \text{ minutes}$.

The following is a possible wave height function $h(t)$ in meters with respect to time $t$ in hours...