DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 218)

Problem 1 :

√x/2 + √y = 5

√x - √y/2 = -1/2

If (a, b) is the solution to the system of equations above, what is the value of a?

A)  8/5

B)  9/5

C)  64/25

D)  81/25

Solution :

Problem 2 :

The graph above displays the total cost C, in dollars, of renting a car for d days. If Nigel rents a car for 21 days for his summer trip, what is the total rental cost?

A)  $600

B)  $650

C)  $700

D)  $750

Solution :

Problem 3 :

In the figure above, the area of square AFIE is 9 times the area of square HIGC. What percent of square ABCD is shaded?

A) 56.25%

B)  62.5%

C)  67.5%

D)  70.5%

Solution :

Problem 4 :

A survey of 700 randomly selected people aged 15 through 20 in a certain tows was conducted to gather data on how they prefer to see movies. The data are shown in the table below.

If a person is chosen at random from those under 18 years old, which of the following is closest to the probability that the person preferred smartphone downloads?

A)  0.49

B)  0.52

C)  0.54

D)  0.56

Solution :

Problem 5 :

If the graph of y = x² is translated up 3 units and right 5 units, what is the equation of the new graph?

A)  y = x² – 3x + 5

B)  y = x² – 6x + 14

C)  y = x² + 10x + 5

D)  y = x² – 10x + 28

Solution :

Problem 6 :

If (x - 1)/3 = k and k = 3, what is the value of x?

A)  2

B)  4

C)  9

D)  10

Solution :

Problem 7 :

On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?

A)  9mp

B)  20mp

C)  5m + 4p

D)  4m + 5p

Solution :

Problem 8 :

Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation

P = 108 - 23d,

where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation?

A)  Kathy will complete the repairs within 108 days.

B)  Kathy starts each week with 108 phones to fix.

C)  Kathy repairs phones at a rate of 108 per hour.

D)  Kathy repairs phones at a rate of 108 per day.

Solution :

Problem 9 :

(x²y - 3y² + 5xy²) - (-xy² + 3xy² - 3y²)

Which of the following is equivalent to the expression above?

A)  4x²y²

B)  8xy² - 6y²

C)  2x²y + 2xy²

D)  2x²y + 8xy² -6y²

Solution :

Problem 10 :

Solve for x :

Solution :

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