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- Which of the following must be true?

Select__all__that apply.

- If ab < ac then b < c .
- If a
^{2}b < a^{2}c then b < c . - If b
^{2}< c^{2}then b < c .

Answer: B

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 a^{2}b < a^{2}c then b < c – TRUE a^{2} is positive so dividing both sides by a^{2} gives b <c

C: If b^{2} < c^{2} then b < c – FALSE for b = 2 and a = -3, b^{2} < c^{2} but b > c

- If x and y are two consecutive even integers and 2x + y = 2(x – y) , what is the value of x + y ?

- -6
- -2
- 2
- 6
- 10

Answer: B

Let y = x + 2

2x + x + 2 = 2(x – (x+2))

3x + 2 = -4

x = – 2

y = 0

- Which of the following integers do NOT have a divisor greater than 1 that is the square of
an integer?

Select__all__that apply.

- 12
- 25
- 38
- 32
- 42

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

- When the integer N is divided by 6, the remainder is 3. Which of the following is NOT a multiple of 6?

Select__all__that apply.

- N – 3
- N + 3
- 2N
- 3N
- 3N + 18

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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- 3a + 5
- 3a – 9
- 3a + 10
- 3a – 4
- 3a + 4

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