A Lion’s Share of Luck It’s the beginning of February, and as they do every year, thousands of people line H Street, the heart of Chinatown in Washington, DC. The crowd has gathered to celebrate Lunar New Year. The street is a sea of **red. Red is** the traditional Chinese color of luck and happiness. Which choice most effectively combines the sentences at the portion surrounded by astericks (**)? A) red, B) red; in addition, red is C) red; in other words, red is D) red, the color; that is

The correct answer is A. Although B and C are grammatically correct, B and C do not effectively combine the two sentences because they are too wordy. Keep in mind that the ACT likes the wording to be as concise as possible. D is not grammatically correct because it is not a full sentence. A is grammatically correct and concise.

How many irrational numbers are there between 1 and 6 ? a) 1 b) 3 c) 4 d) 10 e) infinitely many

The correct answer is e. An irrational number is any number that cannot be expressed as a ratio between two numbers. Therefore, 7 is a rational number because it can be expressed as 7/1, while square root of 2 is an irrational number because the numbers in the decimal go on forever (1.41421...). a,b,c,d are incorrect because between any two integers, there are infinitely many irrational numbers.

What is the solution of the equation (x+2)/2 =4/x?

First, get the x's on one side and the numbers on the other.: x (x+2)/2= 4 x (x+2) = 8 Then, you will find that this equation can be rearranged to make a quadratic equation: x^2 + 2x -8=0 Then, solve for the quadratic equation: (x+4)(x-2)=0 x= - 4, x=2