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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