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We are looking for statements which are DEFINITELY TRUE.
A: If ab < ac then b < c – FALSE. If a is negative, then b > c
B: If a2b < a2c then b < c – TRUE a2 is positive so dividing both sides by a2 gives b <c
C: If b2 < c2 then b < c – FALSE for b = 2 and a = -3, b2 < c2 but b > c
Answer: C, E
We need to find how many of these numbers have a perfect square as a factor.
12 is divisible by 4
25 is divisible by 25
38 is divisible by 2, 19, and 38 NO SQUARES
32 is divisible by 4 as well as 16
42 is divisible by 2, 3, 6, 7, 14, 21, 42 NO SQUARES
Answer: D, E
N divided by 6, leaves a remainder = 3
So N is of the form 6a + 3
A: N – 3 = 6a DIVISIBLE
B: N + 3 = 6a + 6 DIVISIBLE
C: 2N = 12a + 6 DIVISIBLE
D: 3N = 18a + 9 NOT DIVISIBLE
E: 3N + 18 = 3(N + 6) and N + 6 is 6a + 9 so NOT DIVISIBLE
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