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If n is the product of all integers from 1 to 10 inclusive, which of the following

must be a factor of n?

i. 15

ii. 77

iii. 210

a. Only i

b. i and ii

c. i and iii

d. ii and iii

e. All three

Number Properties (5)

1.- If the remainder is 1 when m is divided by 2 and the remainder is 3 when n is divided by 4, which of the

following must be true?

(A) m is even

(B) n is even

(C) m + n is even

(D) mn is even

(E) m/n is even

2.- If m is a positive integer and 75^3 is a multiple of 5^m, what is the largest possible values for m?

A. 3

B. 4

C. 5

D. 6

E. 7

3.- What is the average (arithmetic mean) of all multiples of 10 from 10 to 400 inclusive?

(A) 190

(B) 195

(C) 200

(D) 205

(E) 210

4.- The greatest common factor of positive integers m and n is 12. What is the greatest common factor of

(2m^2, 2n^2)?

A. 2

B. 12

C. 24

D. 144

E. 288