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## GRE Practice - Quantitative Reasoning - Set 17

1. Which of the following must be true?
Select all that apply.
1. If ab < ac then b < c .
2. If a2b < a2c then b < c .
3. If b2 < c2 then b < c .

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

1. If x and y are two consecutive even integers and 2x + y = 2(x – y) , what is the value of x + y ?
1. -6
2. -2
3. 2
4. 6
5. 10

Let y = x + 2
2x + x + 2 = 2(x – (x+2))
3x + 2 = -4
x = – 2
y = 0

1. Which of the following integers do NOT have a divisor greater than 1 that is the square of an integer?
Select all that apply.
1. 12
2. 25
3. 38
4. 32
5. 42

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

1. 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.
1. N – 3
2. N + 3
3. 2N
4. 3N
5. 3N + 18

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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