Digital SAT Math Questions and Answers (Part - 8)

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Question 1 :

If (ax + 2)(bx + 3) = 14x²+ cx + 6 for all values of x and

a + b = 9, what are the two possible values of c?

A) 2 and 7

B) 4 and 14

C) 6 and 21

D) 20 and 25

Answer :

Question 2 :

In a xy-plane, the line determined by the points (5a, 3) and (15, a) passes through the origin. Which of the following could be the value of a?

A) -3

B) 0

C) 2

D) 6

Answer :

Question 3 :

The County Reception Hall charges a rental fee of $1,000 and at least $3,000 for food. Olivia is planning a class reunion. If she has chosen a buffet that costs $38.56 per person, what is the minimum possible number of people who must attend to support the expense?

Answer :

Question 4 :

The graph of a linear function f is shown in the xy-plane above. If f(k) = 1, what is the value of f(-2k)?

Answer :

Question 5 :

The average of 2a and b is equal to 50 percent of 4b, what is the value of a/b?

Answer :

Question 6 :

Two cylinders shown above have the same volume. If the radius of cylinder II is twice the radius of cylinder I and the height of cylinder I is 10, what is the height h of cylinder II?

Answer :

Question 7 :

One of the factors of the function f(x) is x + k. Given that k is a positive integer, what is the value of k?

Answer :

Question 8 :

g(x) = px² – 8x + q

The function g is defined above, where p and q are constants. The graph of y = g(x) is parabola that has a vertex at the point (m, n), where m and n are constants. If g(-6) = g(-1) and q > 0, which of the following must be true?

I. p < -2/3

II. n > 12

A) I only

B) II only

C) I and II

D) Neither I nor II

Answer :

Question 9 :

(2x - 6k)(2x² + 5x - k)(3x² + 4x - 4k) = 0

In the given equation, k is a positive constant. The product of the solutions of the equation is 54/125. What is the value of r?

A) 3/5

B) 9/10

C) 6/5

D) 5/3

Answer :

Question 10 :

If 5m – x is a factor of x³ – 45rm³, where r and m are constants and m > 0, what is the value of r?

A) 3/5

B) 4/5

C) 17/9

D) 25/9

Answer :

Question 11 :

y = 3(2x – a)² + 1

y = 6x – 5

If (x, y) is the only solution to the above system of equations, what is the value of x?

Answer :

Question 12 :

Pat delivers packages for the post office. The graph above shows his distance from the post office during his delivery route. Which portion of the graph represents the times when Pat is driving along a circular road around the post office?

A) The portion from 0 hours to 1 hour

B) The portion from 1 hour to 3 hours

C) The portion from 3 hours to 5 hours

D) The portion from 5 hours to 6 hours

Answer :

Question 13 :

A bakery standardizes muffins to weigh between 1¾ and 2½ ounces. If m is the weight of a muffin from this bakery, which of the following inequalities expresses the possible values of m?

A) |m - 1¾| < ¼

B) |m - 2| < ¼

C) |m - 2| < ½

D) |m - 1¾| < ½

Answer :

Question 14 :

On vacation, Jill spends ¼ of her money the first day. Then she spends ¼ of the money she has left on the second day. She starts the third day with $180 left to spend. How many dollars did she have at the start of the vacation?

A) 280

B) 320

C) 360

D) 400

Answer :

Question 15 :

If 3n – 8 < x < n, which of the following must be true?

I. n – x < 0

II. n < 4

III. 2x < 4n – 8

A) I and II only

B) II only

C) II and III only

D) I, II and III

Answer :

Question 16 :

For x > 0, the function f is defined as follows :

f(x) is obtained by halving each value of x.

Which of the following could describe this function?

A. Decreasing exponential

B. Decreasing linear

C. Increasing exponential

D. Increasing linear

Answer :

Question 17 :

2x + 6y = 5

ax + by = 7

If the system of equations above has only one solution, which of the following could be the values of a and b?

A) a = 1 and b = 3

B) a = 2 and b = 6

C) a = 3 and b = 8

D) a = 4 and b = 12

Answer :

Question 18 :

A smart phone company plans to produce and sell p smart phones. The company spends $265,000 for technical information and $150 for producing each phone. The company receives $400 on the sale of each phone. For what value of p is the revenue equal to the total cost?

A) 500

B) 840

C) 1060

D) 1200

Answer :