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Which of the following numbers is farthest from number 1 on the number line?


On the number line shown, the tick marks are equally spaced. Which of the following statements about the numbers x, y and z must be true?

Indicate all such statements.


Note: Figure not drawn to scale

If x and y are numbers on the number line above, which of the following statements must be true?

I. |x+y| < y

II. x + y < 0

III. xy < 0
x > y, xy > 0

Quantity A

|x-y|

Quantity B

y


-1 < x < 1

Quantity A: |1-x|

Quantity B: 1
M > N

Quantity A

|-M| - |-N|

Quantity B

|-N| - |-M|


If x+|x|+y=7 and x+|y|-y=6 , then x+y=
What is the sum of all possible solutions of the equation

$$|x+4|^{2}$$ -10|x+4|=24
y > |x|, xy < 0

Quantity A

x+y

Quantity B

0


If |z| ≤ 1, which of the following statements must be true?

Indicate all such statements.
How many integer values of n satisfy the inequality | 3-n | ≤ 4 ?
If 6 ·| 4-k/3| > 12, which of the following could be the value of k ?

Indicate all such values.
X is the set of all integers n that satisfy the inequality 2 ≤ |n| ≤ 5.

Quantity A

The absolute value of the greatest integer in X

Quantity B

The absolute value of the least integer in X


If |3x+2| < 5, then which of the following statements must be true?

Indicate all such statements.

Quantity A

0.05 percent of 4,000

Quantity B

$$\frac{1}{200}$$ of 4,000


If x > 0, which of the following expressions are equal to 3.6 percent of $$\frac{5x}{12}$$?

Indicate all such expressions.
x is an integer

Quantity A

22 percent of x

Quantity B

$$\frac{2}{9}$$ of x


x and y are integers greater than 5. x is y percent of $$x^{2}$$.

Quantity A

x

Quantity B

10


If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair, what fraction of those who do not have brown hair have red hair?
In a private library, biography books account for 5 per cent of all the paperback books, while paperback biography books account for 3 per cent of all the books, then what`s the percentage of paperback books among all the books?

_____%

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