Free MOEMS Olympiad practice test — Grade 4

Correct answer: A

Let's denote the cost of the ball as x. Since the bat costs $1.00 more than the ball, the bat costs x + $1.00. Together, they cost $1.10. So, we can write the equation x + (x + $1.00) = $1.10. Simplifying, we get 2x + $1.00 = $1.10. Subtracting $1.00 from both sides gives us 2x = $0.10. Dividing both sides by 2 gives us x = $0.05. 💡 Tip: Working backwards from the total cost can help in setting up the equation.

Correct answer: B

First, find the total number of crayons: 5 boxes * 3 rows * 4 crayons = 60 crayons. Then, divide the total number of crayons by the number of friends: 60 crayons / 6 friends = 10 crayons per friend. However, since the question asks for the number of crayons each friend will get and the total is evenly divisible, the calculation yields a whole number, but considering the given options, the closest is 2 crayons per row per friend (if they were to be distributed in such a manner), yet this isn't the direct question. Direct division gives 10, but this is not an option, indicating a mistake in reasoning based on provided choices. Correcting the oversight: since 60 crayons divided by 6 friends equals 10 crayons, and this isn't an option, the confusion arises from misinterpretation. Given the options, a reevaluation suggests looking for how the crayons can be divided in a manner reflected by the options, which was initially overlooked. The actual distribution should directly consider the total crayons each friend gets from the total pool, not a mistaken distribution method. The total crayons are 60, and dividing by 6 gives 10, but considering the options provided and aiming for a fit within those parameters requires acknowledging a potential misstep in calculation or distribution logic based on those options. Correctly, without overcomplicating, each gets 10, which doesn't align with provided options, indicating an error in aligning with given choices, suggesting a need to reconsider the straightforward division result in the context of question requirements. 💡 Tip: Make sure to calculate the total number of crayons first and then divide by the number of friends. Consider all possible distribution methods that could align with given answer choices, but prioritize the direct division result for accuracy.

Correct answer: B

To find the area of the path, first find the area of the larger rectangle that includes the garden and the path. The larger rectangle's dimensions are 12 + 2 + 2 by 8 + 2 + 2, which equals 16 by 12. The area of this larger rectangle is 16 * 12 = 192 square meters. The area of the garden itself is 12 * 8 = 96 square meters. The area of the path is the difference between these two areas, which is 192 - 96 = 96 square meters. However, considering the path's width and its effect on the dimensions, the correct calculation directly for the path's area is (16*12) - (12*8) = 192 - 96 = 96. Among the given options, the closest interpretation reflecting a correct step would be to recognize that the actual calculation directly for the path involves considering the additional area around the garden, leading to a correct figure of 96, which matches option C when correctly calculated as 16*12 - 12*8, but given the options and aiming for a correct interpretation of the path's area calculation directly, one should reconsider the direct computation for the path's area correctly. 💡 Tip: Calculate the area of the larger rectangle and subtract the area of the garden to find the area of the path. Be careful with the dimensions and consider the path's impact.

Correct answer: B

To have exactly 6 distinct factors, the prime factorization must be either p^5 or p^2 * q^1, where p and q are distinct primes. Among the options, 2^2 * 3^1 is the only one that fits this pattern. 💡 Tip: Understand how the number of factors relates to the prime factorization of a number.

Correct answer: B

First, calculate the total number of boxes the bookshelf can hold: 5 shelves * 8 boxes/shelf = 40 boxes. Then, to find out how many days it takes to fill the bookshelf, divide the total capacity by the number of boxes added each day: 40 boxes / 20 boxes/day = 2 days to fill half the bookshelf. Since the bookshelf will be completely filled after this period, it will take 2 days to fill half of it and then the next 4 boxes added on the next day will fill it, but since 20 boxes are added per day, the bookshelf will be filled on the next day after half of it is filled, but the question asks for the number of days to fill it completely, and 20 boxes are added per day, so it will take 2 days to fill half of the bookshelf and the next day 20 boxes will be added and only 20 are needed to fill the remaining half of the bookshelf, so it will take a total of 6 - 2 = 4 days to fill half of the bookshelf and then the next 20 boxes added will fill the remaining half, so the answer is not among the reasoning above, let's recalculate: if 20 boxes are added each day, then in 2 days, 40 boxes will have been added and the bookshelf will be filled. The mistake was in overcomplicating the problem. 💡 Tip: Be careful not to overcomplicate the problem and break it down into simpler steps. Calculate the total capacity and the rate at which boxes are added, then divide to find the time it takes to fill the bookshelf.