DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 244)

Problem 1 :

In the xy-plane above, ABCDEF is a regular hexagon with a side of 2. What is the x-coordinate of E?

A)  5

B)  6

C)  7

D)  8

Solution :

Problem 2 :

sin (2x - π/12) = cos (x + π/12)

In the equation above, the angle measures are in radians. Which of the following could be the value of x?

A)  π/12

B)  π/8

C)  π/6

D)  π/4

Solution :

Problem 3 :

For a polynomial p(x), the value of p(2) and p(-1) is 0. Which of the following could not be true about p(x)?

A)  x - 2 is a factor of p(x).

B)  x + 1 is a factor of p(x).

C)  x² - x - 2 is a factor of p(x).

D)  (x - 2) + (x + 1) is a factor of p(x).

Solution :

Problem 4 :

The graph of f(x) = (x - a)(x - 3), where a is a constant, is shown in the xy-plane above. If the y-intercept of the graph is 3, what is the minimum value of f?

A)  -1

B)  -1.5

C)  -2

D)  -2.5

Solution :

Problem 5 :

In the xy-plane above, the base of a rectangle is on the x-axis and the upper vertices are on the parabola y = 10 - 2x². Which of the following represents the area of the rectangle?

A)  10a - 2a³

B)  2a³ - 10a

C)  20a - 4a³

D)  4a³ - 20a

Solution :

Problem 6 :

A food manufacturer fills containers of seasoning with various spices, pepper and salt. The amount of pepper p, in milligrams, used in the seasoning can be modeled by the equation

where s is the amount of salt, in milligrams, in the seasoning. According to the model, how many milligrams of pepper are added for every 1 milligram increase in the amount of salt?

Solution :

Problem 7 :

The incomplete table above shows the results of a survey that asked a group of doctors and lawyers how many vacations they take each year. If a doctor from the surveyed group is chosen at random, the probability that the doctor takes at least 1 vacation each year is 4/5. How many people from the surveyed group take at least 2 vacations each year?

Solution :

Problem 8 :

A boutique shop is selling handmade necklaces. The cost per necklace C can be determined by the equation above, where n is the number of necklaces made.

(a) What is the cost of making 6 necklaces now?

(b) If the shop sells each necklace for $150, how many necklaces should be made so that the shop makes a total profit of $564 after all of them are sold?

Solution :

Problem 9 :

0 < |5/x| < 1

Which of the following values of x satisfies the inequality above?

A)  -8

B)  -3

C)  2

D)  3

Solution :

Problem 10 :

If c = ab/d and d ≠ 0, 1/ab =

A)  c + d

B)  cd

C)  1/cd

D)  c/d

Solution :

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