DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 242)

Problem 1 :

If a/2b = 5, what is the value of 15b/2a?

A)  2/3

B)  3/4

C)  7/2

D)  15/2

Solution :

Problem 2 :

Which of the following is equal to a^1/2/a^-1/3?

A)  ⁶√a

B)  √6⁵

C)  ⁶√a⁵

D)  ⁵√a⁶

Solution :

Problem 3 :

The equation 3x³ – 5x + 5 = (3x² + 3x – 2)(x – 1) + a is true for all values of x, where a is a constant. What is the value of a?

A)  3

B)  5

C)  7

D)  8

Solution :

Problem 4 :

A pharmaceutical company receives a monthly salary of $3000 plus a commission of k percent of his sales. If the salesperson's monthly wage is $7200, what are his sales in terms of k?

A)  7200k

B)  4200k

C)  4200/k

D)  420000/k

Solution :

Problem 5 :

On a trip downtown, Peter drove his car at an average speed of 50 miles per hour. On the return trip due to bad weather, he drove his car at an average rate of 30 miles per hour and the return trip took 1 hour longer. How much time did he spend on the returning trip?

A)  1.5 hours

B)  2 hours

3)  2.5 hours

D)  3 hours

Solution :

Problem 6 :

If a = x² - 5x + 2 and b = 3x³ + 4x² - 6, what is (3a - b) in terms of x? 

A)  4x² - 15x + 12

B)  -3x³ - x² - 15x + 12

C)  -3x³ - x² - 15x

D)  -3x³ + 7x² - 15x + 12

Solution :

Problem 7 :

In the xy-plane above, line l has slope -5/4. What is the area of the triangle bounded by line l, the x-axis and the y-axis?

A)  5

B)  8

C)  10

D)  16

Solution :

Problem 8 :

The price of a textbook this year is 20% greater than the price last year. If this year's price is p, what was last year's price in terms of p?

Solution :

Problem 9 :

y = x² - 2x - 3

A parabola in the xy-plane is given by the equation above. Which of the following equivalent forms of the equation displays the coordinates of the vertex of the parabola as constants or coefficients?

A)  y = (x - 1)² - 4

B)  y = (x - 1)² - 2

C)  y = (x - 3)(x + 1)

D)  y + 3 = x(x + 2)

Solution :

Problem 10 :

The number of dandelions in a large park is recorded over the course of five months, as shown the table below.

Which of the following best describes the relationship between time and the number of dandelions during five months?

A)  Increasing linear

B)  Decreasing linear

C)  Exponential growth

D)  Exponential decay

Solution :

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