Тест ҰБТ 2018. Математикалық сауаттылық.

Explanation
The given numbers are 4365, 5346, 4346, 5265, and 5555. We need to find the difference between the largest and smallest four-digit numbers. The largest four-digit number is 5555 and the smallest four-digit number is 4346. Subtracting the smallest from the largest, we get 5555 - 4346 = 1209. However, the given answer is 5265 which is incorrect.

Explanation
The number of heads of sheep and cows in the village is given as 24, while the total number of legs is given as 66. This implies that each sheep has 4 legs and each cow has 4 legs. To find the number of sheep and cows separately, we can set up a system of equations. Let x be the number of sheep and y be the number of cows. From the given information, we have the equations: x + y = 24 (equation 1) and 4x + 4y = 66 (equation 2). Solving these equations, we find that x = 15 and y = 9. Therefore, there are 15 sheep and 9 cows in the village.

Explanation
The traveler initially moves 3 km to the east and then 4 km to the west. This means that the net displacement in the east-west direction is 3 km - 4 km = -1 km (westward). After that, the traveler moves 7 km to the north and then 7 km to the south. This means that the net displacement in the north-south direction is 7 km - 7 km = 0 km. Therefore, the total displacement from the starting point to the final point is -1 km westward and 0 km north-south, resulting in a net displacement of 1 km westward. So, the correct answer is 5 km westward.

Explanation
The given information states that the price of a cup and a saucer is equal to the price of four spoons and that the price of a cup and a saucer is equal to the price of six spoons. Therefore, the price of one cup is equal to the price of six spoons divided by four, which is equal to 1.5 spoons. Since the options provided are in whole numbers, the closest option to 1.5 spoons is 5, making it the correct answer.

Explanation
The given question is asking how many pages the newspaper has if the left page is labeled with a 4 and the right page is labeled with a 9. The answer is 12 because each page number is counted as one page, so the pages between 4 and 9 would be 5 pages, and adding the front and back pages would give a total of 12 pages.

Explanation
The numbers in the given sequence are 1, 2, 3, ..., 17. We need to find the numbers that are divisible by 3. To do this, we can check each number in the sequence and see if it is divisible by 3. By doing this, we find that the numbers 3, 6, 9, 12, 15 are divisible by 3. Therefore, there are 5 numbers that are divisible by 3. However, the question asks for the numbers that are not divisible by 3. So, the remaining numbers are 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17. Counting these numbers, we find that there are 12 numbers left. Thus, the answer is 12.

Explanation
The given equations are y=2x-4 and y=10x-b. To find the intersection point on the x-axis, we need to set y=0 in both equations. By substituting y=0 in the first equation, we get 0=2x-4, which gives x=2. Substituting y=0 in the second equation, we get 0=10x-b. Since we know that x=2, we can substitute it in the equation to get 0=10(2)-b, which simplifies to 0=20-b. Solving for b, we find that b=20. Therefore, the correct answer is b=20.

Explanation
The given answer states that Meruert is 9 years old, Enlik is 3 years old, Aray is 5 years old, and Sagy is 15 years old. This aligns with the information provided in the question, where it is stated that the ages of the four children are 3, 5, 9, and 15 years old respectively.

Explanation
If Ashimhan starts jogging from 1 km and increases his distance by 250 meters each day, then on the 7th day (Sunday), he would have increased his distance by 6 times 250 meters, which equals 1500 meters. Therefore, on Sunday, he would have jogged a total distance of 1 km (initial distance) plus 1500 meters, which equals 2500 meters.

Explanation
The question states that if you write 9 digits to the right of a given number, the resulting number will be 633 greater than the original number. To find the original number, we need to subtract 633 from the given number. The only option that, when subtracted by 633, results in 52 is 52 itself. Therefore, 52 is the correct answer.

Explanation
The given sequence follows a pattern where each number is obtained by adding 2 to the previous number. Starting from 3, we add 2 to get 5, then add 2 again to get 7, and so on. However, in the given sequence, there are two numbers that do not follow this pattern: 24 and 26. These numbers are obtained by adding 14 and 16 respectively to the previous number. Therefore, the next number in the sequence should be obtained by adding 2 to the previous number, which is 26. Thus, the correct answer is 26 + 2 = 28.

Explanation
The given question is asking how many versions of preparation are required for the lessons of physics, chemistry, and mathematics. The correct answer is 6, which means that there are 6 different versions of preparation needed for these lessons.

Explanation
The question asks to find the perimeter of a triangle. The length of one side is given as 20 cm, and the sum of the lengths of the other two sides is 125% of the length of the first side. To find the lengths of the other two sides, we can set up the equation 20 + x + y = 1.25 * 20, where x and y are the lengths of the other two sides. Solving this equation, we get x + y = 25. Since the perimeter of a triangle is the sum of all three sides, the perimeter in this case is 20 + x + y = 20 + 25 = 45 cm.

Explanation
In the given question, it is stated that there are three streets in a district with 100 houses. When looking at the second street from the first street, there are three times more houses. Therefore, the number of houses on the second street must be a multiple of 3. Among the given options, only 30 is a multiple of 3. Thus, the correct answer is 30.

Explanation
The given expression is 2017·(20172016+20172018)2018. We can simplify this expression by first calculating the sum inside the parentheses, which is 20172016+20172018 = 40344034. Then, we multiply this sum by 2017, resulting in 40344034·2017 = 81396044778. Finally, we multiply this result by 2018, giving us 81396044778·2018 = 164155119307924. The last digit of this number is 4, so the answer is 4. However, the given options do not include 4, so the correct answer must be 0.

Explanation
The given question states that 16 square meters of area requires 3.2 kilograms of cheese. We need to find out how much cheese is required for 12 square meters of area. Since the area is decreasing, it can be inferred that the amount of cheese required will also decrease. By using the concept of direct proportionality, we can calculate the amount of cheese required for 12 square meters of area. Therefore, the correct answer is 2.4 kilograms.

Explanation
The number 14 is the only option that has 2 digits, which matches the requirement stated in the question. The other options have either 1 or 3 digits, so they do not meet the criteria.

Explanation
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. In this question, we are given that a cube with a side length of 1 cm can be filled with 216 spheres with a radius of 1 cm. This means that the volume of each sphere is equal to the volume of the cube divided by the number of spheres, which is (1 cm)^3 / 216 = 1/216 cm^3.

Now, we are asked to find how many spheres with a radius of 2 cm can fill a cube with a side length of 2 cm. The volume of the cube is (2 cm)^3 = 8 cm^3. Using the same logic as before, the volume of each sphere is 8 cm^3 / (1/216 cm^3) = 1728 cm^3.

Finally, we can calculate the number of spheres that can fill the cube by dividing the volume of the cube by the volume of each sphere: 1728 cm^3 / (4/3)π(2 cm)^3 ≈ 27.

Therefore, the correct answer is 27.