(6) Suppose one type of cicada insect appears every 14 years and another type ap

Question

(6) Suppose one type of cicada insect appears every 14 years and another type appears IntßUI alla the least common multiple of 78 and 52. every 21years. If they both appear this year, when will they appear again in the same ye (7) Two friends go exercising each morning. One is runner and the other a walker. Suppose that the walker takes 12 minutes to go around a circle that the runner takes 9 minutes to run around. If they start at the same point at 6:00 am, then at what time will they mcet again at the starting point for the first time? (8) I have 48 apples and 72 oranges. What is the maximum number of friends can I distribute these fruits to, so that every friend receives the same number of.apples and the same number of oranges so that no fruit is left over? (9) A staff member at a major hotel chain has 120 towels and 90 pillows. What is the maximum number of rooms that the staff member can distribute the towels and pillows so that every room receives the same number of towels and the same number of pillows so that no towel or pillow is left over? (10) A prime p is said to be a Germain prime if 2p+1 is also a prime. Is 29 a Germain prime? (11) Is 41 a Germain prime? (12) Simplify: #3(-2-29-43-2(1-5)] + 13-7] 3(-3+5)2 -21-3(4-7)+12-5 10 12 15 .2V6(v/3 + 5 + V2) . 2V3(6+4+ V15) (13) If a recipe to make 12 cookies requires 2 cups of sugar, then how much sugar will required to make 40 cookies? Write your answer in the form of a mixed number

Explanation / Answer

Question 6

This is a simple question on the concept of LCM. The question is primarily asking us to find out the LCM of 14 and 21 which is 42. So, both types of insects will meet 42 years later.

Question 7

Again a question on LCM asking us to find out the LCM of 9 and 12 which is 36. So, both the friends will meet t 6:36 AM.

I would urge you to try out questions 8 and 9 on your own once you understand these questions.

Question 10 and 11

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

This is a list of first few primes.

Consider 29. 2*29 + 1 = 59 is a prime. Thus, 29 is a Germain Prime.

Consider 41 2*41 + 1 = 83 is a prime. Thus, 41 is a germaon prime as well.

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