Four consecutive odd integers add up to 80. What is the least of these integers?

 

39. If a set of 2x consecutive numbers has y even numbers and the first number in the set is 1, which of the following must be the largest odd number in the set?

A. y 1

B. y

C. 2y 1

D. 2y

E. y + 1

 

 

40. When the integer Y is divided by 11, the remainder is 3. Which of the following can't be a multiple of (Y+l)?

a) 2Y + 2.

b) 1.5Y + 9.

c) 2.5Y-5.

d) 3Y + 3.

e) 3Y-5.

 

41. If a and b are positive integers such that a – b and a /b are both even integers, which of the following must be an odd integer?

A.  a/2

B.  b/2

C. (a + b)/2

D.  (a + 2)/2

E. (b + 2)/2

 

 

42. The average of (54,820)² and (54,822)² =

(A) (54,821)²

(B) (54,821.5)²

(C) (54,820.5)²

(D) (54,821)² + 1

(E) (54,821)² – 1

 

Which of the following fractions is the greatest?

A.

B.

C.

D.

E.

 

 

44. If X and Y are consecutive numbers (Y > X), which of the following statements could be false ?

1. The multiplication XY is an even number.

2. (Y/X)> 1.

3. (X + Y) is always an odd number.

a) 1 only.

b) 2 only.

c) 1 and 2 only.

d) 1 and 3 only.

e) 1, 2and3.

 

 

A is even and В is odd. Which of the following expressions can't be an integer?

a) (A+1)/(B+1)

b) (A+1)/B

c) (B-1)/(A²)

d) (A)/(64)

e) (A⁴)/(AB)

46. A and В are integers. The expression (A+1)(B+1) is even. What can be said about A and B?

a) They are both even numbers.

b) At least one of them is even.

c) At least one of them is odd.

d) They are both odd.

e) Nothing can be said surly on A and B.

 

 

47. When n is divided by 13, the remainder is 2 and the quotient is k. When n is divided by 17, the remainder is 2. What is the remainder when k is divided by 17?

(A)    0

(B)    2

(C)     4

(D)   13

(E)  15

 

48. The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder of Y divided by 5?

a) 1.

b) 2.

c) 3.

d) 4.

e) 5.

 

 

49. When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the

value of y?

A. 96

B. 75

C. 48

D. 25

E. 12

 

50. If n is a positive integer, what is the maximum possible number of prime numbers in the following sequences: n + 1, n + 2, n + 3, n + 4, n + 5, and n + 6?

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

 

 

51. If n and p are different positive prime numbers, which of the integers , and np has (have) exactly 4 positive divisors?

(A) n⁴ only

(B) p³ only

(C) np only

(D) n⁴ and np

(E) p³ and np

 

 

52. V, W, X, Y and Z are numbers between 0 and 9. If XYZ /15 = WV and V-W=X (WV is a 2 digit number,

XYZ is a 3 digit number), which of the following numbers can represent XYZ?

a) 321

b) 215

c) 633

d) 570

e) 414

 

 

Homework

 

1. If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10

B. 12

C. 14

D. 16

E. 18

 

A and В are numbers between 1 and 9. What is ABAB/AB? (AB is a two-digit number and ABAB is a 4-digit number).

a) 11

b) BAB

c) 101

d) AB

e) 100.

3. A positive integer n is said to be “prime-saturated” if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two-digit prime-saturated integer?

A. 99

B. 98

C. 97

D. 96

E. 95

 

Q, R, S, and T are four consecutive positive numbers. Which of the following expressions must be odd?

a) QR + ST.

b) Q + R + S + T.

c) Q² + S³.

d) Q² + R².

e) Q² + 2R

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