Analyze the logical forms of the following statements:(a) 3 is a common divisor of 6, 9, and 15. (Note: You did this in exercise2 of Section 1.1, but you should be able to give a better answer now.)(b) x is divisible by both 2 and 3 but not 4.(c) x and y are natural numbers, and exactly one of them is prime.

In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer A) Only I is sufficient. B) Only II is sufficient. C) Both the statements I and II together is necessary. D) Either Statement I or Statement II alone is sufficient. E) Both the statements I and II together is not sufficient Read the instructions carefully If X is a natural number then find whether X is divisible by 6 or not. (1) If X is a multiple of 243 (2) If X is not an odd number OPTIONS A B C D E

1. Determine whether each of these integers is prime.a) 21 b) 29 c) 71 d) 97e) 111 f ) 143 g) 93 h) 1012. Find the prime factorization of each of these integers.a) 39 b) 81 c) 101d) 143 e) 289 f ) 899

Given:(1) If n is an even number, then 5n + 2 is always an even number.(2) If n is an integer larger than 1, then 2^n − 1 is always a prime number.Select one of the following choices:Question 16Answera.(1) and (2) are True.b.(1) is True and (2) is False.c.(1) and (2) are False.d.(1) is False and (2) is True.

In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer A) Only I is sufficient. B) Only II is sufficient. C) Both the statements I and II together is necessary. D) Either Statement I or Statement II alone is sufficient. E) Both the statements I and II together is not sufficient Read the instructions carefully Y is a 5 digit natural number. Find whether it is divisible by 11 or not. (1) Sum of digits at odd positions is 15 (2) Sum of digits at even positions is 4 OPTIONS A B C D E

In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer A) Only I is sufficient. B) Only II is sufficient. C) Both the statements I and II together is necessary. D) Either Statement I or Statement II alone is sufficient. E) Both the statements I and II together is not sufficient Read the instructions carefully Find whether ABCD is divisible by 99 or not. (1) If A+C = B+D = 11 (2) If A+B =C+D = 18 OPTIONS A B C D E