DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 131)

Problem 1 :

Given :

(a - b)³ = a³ - 3ab(a - b) - b³ 

x = p^1/3 - p^-1/3

What is the value of x³ + 3x ?

Solution :

Problem 2 :

Tickets to a concert are $40 for reserved seats and $15 for general admission seats. If a total of 1,200 tickets have been sold and x of them are for reserved seats, which of the following gives all possible values of x for which total ticket sales are at least $30,000?

A)  x ≤ 480

B)  x ≥ 480

C)  x ≤ 520

D)  x ≥ 520

Solution :

Problem 3 :

A cable company surveyed a random sample of 400 subscribers to determine their favorite sport to watch. The results of the survey are shown in the table below.

The cable company has 2 million subscribers. Based on the survey data, which of the following is most likely to be accurate statement?

A) Baseball is the favorite sport to watch for about 200,000 subscribers.

B) Baseball is the favorite sport to watch for about 450,000 subscribers.

C) Football is the favorite sport to watch for about 600,000 subscribers.

D) Football is the favorite sport to watch for about 750,000 subscribers.   

Solution :

Problem 4 :

In the xy-plane above, the line y = (4/3)x + 8 crosses the x and y axes at points A and B respectively. What is the length of AB?

A)  6

B)  8

C)  10

D)  12

Solution :

Problem 5 :

The complete function f is shown in the xy-plane above. If f(x) = k has two solutions, which of the following could be the value of k?

I. -3

II. 0

III. 2.5

A) I and II only

B) III only

C) I and III only

D) I, II and III

Solution :

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