DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 219)

Problem 1 :

Triangle ABC above is isosceles with AB = BC, and the ratio of DE to DF is 3 : 2. If the area of triangle ABC is 78, what is the area of triangle ABD?

A)  46.8

B)  54

C)  60

D)  60.25

Solution :

Problem 2 :

P(x) = (x² + ax + 2) – 2(x – b)

In the polynomial P(x) defined above, a and b are constants. If P(x) is divisible by (x – 1) and (x – 3), what is the value of a?

A)  –4

B)  –2

C)  2

D)  4

Solution :

Problem 3 :

y = x² – 2x

y = x + k

In the system of equations defined above, k is a constant. If the system has no solution, which of the following could be the value of k?

A)  1

B)  0

C)  –2

D)  –3

Solution :

Problem 4 :

The distance between two parallel lines is defined as the length of the perpendicular segment between them. What is the distance between y = x and y = x – 4?

A)  √2

B)  2

C)  2√2

D)  4

Solution :

Problem 5 :

In the xy-plane above, the graph of a quadratic function y = f(x) intersects the x-axis at points O and Q, and has a vertex at point P. If line ℓ passes through points P and Q, what is the y-intercept of line ℓ?

A)  8

B)  10

C)  12

D)  15

Solution :

Problem 6 :

h = 3a + 28.6

A pediatrician uses the model above to estimate the  height h of a boy, in inches, in terms of the boy’s age a, in years, between the ages of 2 and 5. Based on the model, what is the estimated increase, in inches, of a boy’s height each year?

A)  3

B)  5.7

C)  9.5

D)  14.3

Solution :

Problem 7 :

The formula above gives the monthly payment m needed to pay off a loan of P dollars at r percent annual interest over N months. Which of the following gives P in terms of m, r, and N?

Solution :

Problem 8 :

If a/b = 2, what is the value of 4b/a?

A)  0

B)  1

C)  2

D)  4

Solution :

Problem 9 :

g(x) = ax² + 24

For the function g defined above, a is a constant and g(4) = 8. What is the value of g(-4)?

A)  8

B)  0

C)  -1

D)  -8

Solution :

Problem 10 :

b = 2.35 + 0.25x

c = 1.75 + 0.40x

In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?

A)  $2.60

B)  $2.85

C)  $2.95

D)  $3.35

Solution :

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