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Counting & Probability | When Payel goes outside, she wears a shirt and pants. She has a red, a black, and a blue shirt, and a red, a black, and a blue pair of pants. She follows a specific rule when wearing her shirt and pants. She doesn't wear the same color shirt and pants (for example, she doesn't wear a red shirt with red pants). Now, how many ways can she wear her shirt and pants? | 6 |
Prealgebra | You have 5 positive integers whose average is 7. You gave 3 of those numbers to your first friend, and the average of those three numbers is 5. You gave the remaining two numbers to your second friend. What is the average of the two numbers with the second friend? | 10 |
Prealgebra | Sadia and Moma came to the caf茅 for snacks. Here, 9 chocolates are served per box when ordered. Moma challenged Sadia, saying, 'If you can eat more than 15 chocolates, I will give you 30 Taka for each one after the 15th.' Since Sadia completed the challenge, she received 120 Taka from Moma. What is the minimum number of boxes of chocolates that Sadia had to order to complete the challenge? | 3 |
Algebra | If the sum of 4 consecutive integers is 634, find the largest integer. | 160 |
Prealgebra | In a class, $ rac{3}{7}$ of the students prefer statistics and $ rac{4}{5}$ prefer geometry. What is the minimum number of students who prefer both subjects? | 8 |
Algebra | Payel builds a robot that can do her one day's work in $n$ days. The Payel robot creates another robot that can do its one day's work in $n$ days as well. Each Payel robot creates copies of itself. Payel never wants the robots to unite and become more efficient than her to rebel against her. What should the minimum value of this be to make her plan successful? | 2 |
Intermediate Algebra | $\lceil {\frac{n+(n+1)}{n+2}} \rceil + \lceil {\frac{(n + 1) + (n + 2)}{(n + 3)}} \rceil + \lceil {\frac{(n + 2) + (n + 3)}{n + 4}} \rceil + \dots + \lceil {\frac{(n+m-2)+(n+m-1)}{n+m}} \rceil =301$, where $0 < n < 1$. Determine the value of $m$. The symbol $\lceil \rceil$ denotes the ceiling function, which refers to the next integer of any decimal number. For example, $\left\lceil {2.1} \right\rceil = 3, \left\lceil {3} \right\rceil = 3, \left\lceil {2.6} \right\rceil = 3$. | 152 |
Prealgebra | In a village, there are 8 houses labeled 1, 2, 3, 4, 5, 6, 7, and 8. Each house is connected to all the others, and any two houses are connected by only one road. The construction cost of each road is equal to the label value of the larger of the two connected houses. What is the total cost to build all the roads in the village? | 168 |
Prealgebra | The length of a diagonal of a rectangle with integer sides is 5 units. Adding 22 to the perimeter of this rectangle gives the perimeter of a rhombus whose height is equal to the smaller side of the rectangle. Find the area of the rhombus. | 27 |