DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 227)

Problem 1 :

Friday, Peter drives from home to his office in 24 minutes. Saturday, there is no traffic, so he can drive to his office 15 miles per hour faster and gets to the office in 15 minutes. How far, in miles, is it from home to his office?

A)  10

B)  12

C)  20

D)  25

Solution :

Problem 2 :

In the xy-plane above, the graph of the equation y = a(x + 4)(x – 2) has a vertex at point P. if the graph intersects the x-axis at points R and S, what is the area of ΔRPS?

A)  -54a

B)  -27a

C)  27a

D)  54a

Solution :

Problem 3 :

When 2x² – 5x + 4 is divided by (x – 1)(x + 1), the resulting remainder is ax + b, where a and b are constants. What is the value of a + b?

Solution :

Problem 4 :

In the figure above, ∠XAB and ∠XYA are inscribed in the circle. If AB is the diameter of the circle, and the measure of ∠XAB is 65°, what is the value of x?

Solution :

Problem 5 :

x² – 8x – 3 + y² – 6y = k²

The graph of the equation above in the xy-plane is a circle, where k is a positive real number. If the radius of the circle is 8, what is the value of k?

Solution :

Problem 6 :

A faulty register records only $5 for every $8 deposit. If the register shows a total balance of $40, what is the actual balance?

(A)  $25

(B)  $64

(C)  $72

(D)  $80

Solution :

Problem 7 :

If (x - 2)² + (y - 3)² + (z + 4)² = 0, what is the value of

(x + y + z)?

(A)  -4

(B)  0

(C)  1

(D)  2

Solution :

Problem 8 :

If 3^{x - 3} = 27, what is the value of x?

(A)  -4

(B)  0

(C)  1

(D)  2

Solution :

Problem 9 :

The triangle above is isosceles and b > a. Which of the following must be FALSE?

(A)  AB = BC

(B)  AB = AC

(C)  AC = BC

(D)  a = c

Solution :

Problem 10 :

The graph opf a parabola has x-intercepts at ⅗ and -½. Which of the following could be the equation of the parabola?

(A)  y = (5x - 1)(2x + 3)

(B)  y = (5x + 1)(2x - 3)

(C)  y = (5x - 3)(2x + 1)

(D)  y = (5x + 3)(2x - 1)

Solution :

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