03 Divisibility

V11. If y is an integer divisible by 3 but not by 2 then which of the following will never be an integer?

(A) (Y-1)/2 (B) Y/7 (C) Y/24 (D) Y3/3 (E) none of these

□ 2. How many integers between 110 and 120 are prime numbers?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

© 7. What is the minimum number of chocolates that must be added to the existing stock of 270 chocolates so that the total stock can equally be divided among 6, 8 or 12 persons?

(A) 12 (B) 16 (C) 18 (D) 20 (E) none of these

□ 1. How many prime numbers are there between 1 and 10?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

V14. Mr. Saif has n luxury apartments, where n is an integer such that 20 < n < 50. If he divides the apartments equally among his 5 children, he will have 2 apartments remaining. If he divides the apartments among 6 children, he will have 1 apartment remaining. How many apartments will remain if he divides the apartments among 7 children?

(A) 3 (B) 2 (C) 4 (D) 1 (E) none of these

©6. 180 students in a group are to be seated in rows so that there are an equal number of students in each row. Each of the following could be the number of rows EXCEPT

(A) 4 (B) 20 (C) 30 (D) 40 (E) 90

□ 4. If y/3, y/4 and y/7 represent integers, then y can be

(A) 42 (B) 56 (C) 70 (D) 84 (E) 126

V9. One third, one fourth, one fifth and one-seventh of the human population of Island X, which has fewer than 5000 human inhabitants, are all whole numbers and their sum is exactly the population of Island Y. What is the population of Island Y?

(A) 4200 (B)4279 (C)4581 (D) 4800 (E) Cannot be determined

© 8. What is the smallest number of apples that can distributed equally among 4, 6, 9 or 15 students having a surplus of two apples each time?

(A) 422 (B) 362 (C) 182 (D) 62 (E) none of these

V12. (4^41+4^42+4^43) is divisible by-

(A) 7 (B) 13 (C) 15 (D) 17 (E) none of these

□ 3. How many prime numbers are there between 56 and 100?

(A) 8 (B) 9 (C) 10 (D) 11 (E) none of these

V10. The greatest common factor of two positive integers is A. The least common multiple of the two integers is B. If one of the integers is C, what is the other number?

(A) AB/C (B) BC/A (C) (A/C)+B (D) A + (B/C) (E) none of these

□ 5. If n is an integer divisible by 6 but not by 4, then which of the following CANNOT be ' an integer'?

(A) n/2 (B) n/3 (C) n/6 (D) n/10 (E) n/12

V 13. If x and y are two distinct positive integers divisible by 4, then which of the following is necessarily divisible by 8?

(A) x + y (B) x - y (C) x2 + y2 (D) 2x + y (E) none of these