1.Read the following SAT test question and then click on a button to select your answer.

If , and , what is ?

Answer Choices

(A)

(B)

(C)

(D)

(E)

2.If and , what is the value of ?

Answer Choices

(A)

(B)

(C)

(D)

(E)

3.A florist buys roses at apiece and sells them for apiece. If there are no other expenses, how many roses must be sold in order to make a profit of ?

Answer Choices

(A)

(B)

(C)

(D)

(E)

4.If two sides of the triangle above have lengths and , the perimeter of the triangle could be which of the following?

. 　　. 　　.

Answer Choices

(A) only

(B) only

(C) only

(D) and only

(E) , , and

5.The function , defined for, is graphed above. For how many different values of is ?

Answer Choices

(A) None

(B) One

(C) Two

(D) Three

(E) Four

Explanation

1.The correct answer is E

If , and , then . Therefore, .

2.The correct answer is C

Since can be written as and can be written as , the left side of the equation is . Since , the value of is .

3.The correct answer is E

Each rose brings a profit of minus , or . The number of roses that need to be sold to make a profit of is . This is roses.

4.The correct answer is B

In questions of this type, statements , , and should each be considered independently of the others. You must determine which of those statements could be true.

Statement cannot be true. The perimeter of the triangle cannot be , since the sum of the two given sides is without even considering the third side of the triangle.

Continuing to work the problem, you see that in , if the perimeter were , then the third side of the triangle would be , or . A triangle can have side lengths of , , and . So the perimeter of the triangle could be .

Finally, consider whether it is possible for the triangle to have a perimeter of . In this case, the third side of the triangle would be . The third side of this triangle cannot be , since the sum of the other two sides is not greater than . By the Triangle Inequality, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the correct answer is only.

5.The correct answer is E

when the point is on the graph of . Drawing the line , as in the graph below, shows that the is equal to for four values of between and .

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