01 Number Properties

22. If x is a positive even number, then each of the following is odd except:

(A) (x + 3) (x + 5) (B) x2 + 5 (C) x2 + 6x + 9 (D) 3x2 + 4 (E) None of these

V19. If x and y are positive odd integers and z is an even integer, which one of the following statements cannot be true?

(A) (x - z)y2 is odd (B) (x - z)2y is even (C) (x - z)y is odd (D) (x - y)2z is even (E) none of these

© 13. M is a set of 5 consecutive integers whose average is 4. N is a set of 7 consecutive integers whose average is 7. How many members of set N are also members of set M?

(A) 0 (B) 1 (C) 2 (D) 3 (E) None of these

21. In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 75 bricks in that wall, how many bricks does the bottom row contain?

(A) 12 (B) 17 (C) 14 (D) 15 (E) None of these

© 14. x, y & z are consecutive integers. If 0<x<y<z and (x+y+z) is an odd integer, which of the following could be the value of z?

(A) 2 (B) 3 (C) 4 (D) 5 (E) None of these

© 11. Five consecutive integers are given. If the sum of the first three integers is 24, what is the sum of the last three?

(A) 27 (B) 28 (C) 29 (D) 30 (E) None of these

□ 2. If x is not a negative number, what is the maximum possible value of 2 - 3x?

(A) 4 (B) 3 (C) 2 (D) 1 (E) None

30. What is the largest integer, n, that satisfies the inequality (n2+ 7n-3) < (n2 + 5n + 9)?

(A) 4 (B) 5 (C) 6 (D) 7 (E) none of these

© 9. If the 1st number in a series of consecutive odd numbers is 8 less than the last number in the series, how many numbers are there in the series?

(A) 4 (B) 5 (C) 7 (D) 8 (E) None of these

□ 4. The sum of six consecutive odd number exceeds twice the largest by 38. Find the sum of the six numbers.

(A) 43 (B) 50 (C) 64 (D) 72 (E) None of these

© 7. If n is an even integer, which of the following must be an odd integer?

(A) 7n - 2 (B) 5(n-2) (C) (16n+24)/8 (D) (6n+12)/3 (E) none of these

© 16. The product of two consecutive numbers is 12 more than the square of the smaller number. Find the greater number.

(A) 9 (B)ll (C) 12 (D) 13 (E) None of these

© 6. The average of four consecutive odd positive integers is always

(A) An odd number (B) Divisible by 4 (C) an even number (D) Both (b) & (c) (E) Either (b) & (c)

© 15. If X is an odd integer and Y is an even integer, which of the following statements is (are) always true? (I) X + Y is odd (II) XY is odd (III) 2X + Y is even

(A) I only (B) II and III only (C) III only (D) I and III only (E) None of these

V20. If a and b are integers such that a + b = 5, which of the following must be true? I. The product of a and b is odd. II. If a is odd then b must be even. III. If a is negative, then b must be positive.

(A) I only (B) II only (C) I and II only (D) II and III only (E) I, II and III

24. If x is a non-zero integer which of the following must be a negative integer? I. - (3x2 + 4) II. - (- x) III.(-x)3

(A) None (B) I only (C) III only (D) I and III only (E) I, II and III

□ 1. Which of the following must be odd? I. Even x Even II. Odd x Odd III. Even + Odd

(A) None (B) I only (C) II and III only (D) I and III only (E) I, II and III

25. If x is an odd integer, in which of the following equations must y be an even integer? I. xy = 5 II. x+2y=l 1 III. 2x+y=12

(A) Only I (B) Only II (C) Only III (D) both II and III (E) all of these

© 10. If a, b and c arc 3 consecutive integers and a>b>c, which of the following has the maximum value?

(A) a+b/c (B) b+c/a (C) c+b/a (D) c+ad> (E) a+c/b

29. If a, b and c are odd integers, which of the following expressions must be an even integer?

(A) ab + bc + ca (B) a(b + c - 1) (C) a2- b2 + c2 (D) 3(ac-bc) (E) none of these

□ 5. If n and p are both odd numbers, which of the following must be an even number?

(A) n + p + 1 (B) np (C) np + 2 (D) n + p (E) 2n + p

© 12. If m is an even integer and n is an odd integer and both are positive numbers, which of the following must be even?

(A) nr + n2 (B) mn + n2 (C) m3 + n2 (D) mn + m2 (E) None of these

26. If x and y are integers and (xy + x) is odd, which of the following must be even?

(A) x + y (B) xy - x (C) x (D) y (E) any of these

V17. If x, y and z are consecutive non-zero integers, and if x < y < z, which of the following must be a positive odd integer?

(A) x - z (B) x + y + 1 (C) x + y + z (D) xz - y (E) none of these

V18. If x/y > 0, which of the following must be true?

(A) x > 0 (B) y > 0 (C) xy > 0 (D) x - y > 0 (E) all of these

23. Which of the following must be an integer if x is a positive integer and (4/x+5/x+6/x) is also an integer?

(A) x/5 (B) 5/x (C) x/30 (D) 30/x (E) none of these

© 8. If x is an odd integer, for which of the following equations must y be an even integer?

(A) xy = 5 (B) x + y = 8 (C) x + 2y = 7 (D) 2x + y = 6 (E) none of these

27. If xy < 0 and y > 0 which of the following must be positive?

(A)x-y (B)2x + 3y (C) (x+10)/(x+2) (D) (-y-2)/x (E)2y*y + x

28. If m is an integer, and y = (m —1) (m + 2) —(m —1) (m —2), then which of the following must be true?

(A)y is odd only when m is odd (B) y is odd only when m is even (C) y is even only when m is even (D) y is even only when m is odd (E) None of these

3. If x and y are both odd integers, which of the following numbers must be an even integer':

A) x2 + y -i (B) xy + y2 (C) x + y + 1 (D) xy + 2 (E) none of these