DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 43)

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Problem 1 :

In the given figure, AC = CD. The measure of angle EBC is 45° and the measure of angle ACD is 104°. What is the value of x?

Solution :

Problem 2 :

In the figure shown, points Q, R, S and T lie on line segment PV, and line segment RU intersects line segment SX at point W. The measure of ∠SQX is 48°, the measure ∠SXQ is 86°, the measure of ∠SWU is 85°, and the measure of ∠VTU is 162°. What is the measure, in degrees, of ∠TUR?

Solution :

Problem 3 :

A scientist initially measures 12,000 bacteria in a growth medium. 4 hours later, the scientist measures 24,000 bacteria. Assuming exponential growth, the formula P = C(2)^rt gives the number of bacteria in the growth medium, where r and C are constants and P is the number of bacteria t hours after the initial measurement. What is the value of r?

Solution :

Problem 4 :

A rectangle was altered by increasing its length by 10 percent and decreasing its width by p percent. If these alterations decreased the area of the rectangle by 12 percent, what is the value of p?

Solution :

Problem 5 :

Suppose an online store has an item on sale for 10% off the original price. By what percent does the store have to increase the price of the item in order to sell it for the original amount? (Round your answer to the nearest hundredth).

Solution :

Problem 6 :

The function g is defined by the given equation. For which of the following values of a does g(a) = a?

A) -180

B) 27/2

C) 45/2

D) 360/2

Solution :

Problem 7 :

(x + 1)(x – 1) = x(x – 1)

How many solutions does the above equation have ?

A) Zero

B) One

C) Two

D) Infinitely many

Solution :

Problem 8 :

For the function f, a and b are constants and f(16) = 0. If f(9) > 0, which of the following could be the value of a + b?

A) -3

B) 7

C) 9

D) 15

Solution :

Problem 9 :

2x + by = 10

ax + 4y = 15

In the system of equations above, a and b are constants and a = 2b. If the system has no solution, which of the following could be a possible value of a?

A) -2

B) ½

C) 4

D) 8

Solution :

Problem 10 :

The graph of a quadratic function f(x) = ax² + bx + c is shown in the xy-plane above. Which of the following must be true?

I. a > 0

II. b > 0

III. c > 0

A) I only

B) I and II only

C) II and III only

D) I, II and III

Solution :

Problem 11 :

In the rectangle above, the length of AE is of the length of AC. If the area of ΔAED is 18, what is the area of ΔCED?

Solution :

Problem 12 :

In the figure above, the value of sin x is 0.6 and the length of AB is 12. What is the area of ΔABC?

Solution :

Problem 13 :

The graphs of f(x) = ax³ and g(x) = x are shown in the xy-plane above, where a is a constant. If the area of ΔAOB is 1/8, what is the value of a?

Solution :

Problem 14 :

In the equation above, a and b are constants. If the equation is true for all values of x except 5 and -2. What is the value of a?

Solution :

Problem 15 :

The average weekly salary paid to all employees in a certain company was $600. The average weekly salary paid to the male and female employees were $620 and $520 respectively. What is the ratio of the number of male and female employees?

A) 3 : 2

B) 4 : 5

C) 5 : 7

D) 4 : 1

Solution :