DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 236)

Problem 1 :

In the xy-plane, the line with equation ax – by = 5, where a and b are constants, is perpendicular to the line with equation 11x – 4y = 5. Which of the following equations represents a line that is perpendicular to the line with equation 11x + 12y = 5?

A)  ax – 3by = 5

B)  ax + 3by = 5

C)  3ax – by = 5

D)  3ax + by = 5

Solution :

Problem 2 :

In the xy-plane, the graph of the linear function f has a negative slope and a y-intercept at (0, k), where k is a positive constant. Which of the following must be true?

I.  If a > b, then f(a) < f(b).

II.  If a < 0, then f(a) > k.

III.  If a > 0, then f(a) > 0.

A)  I and II only

B)  I and III only

C)  II and III only

D)  I, II and III

Solution :

Problem 3 :

If 2^{x + 3} – 2^x = k(2^x), what is the value of k?

A)  3

B)  5

C)  7

D)  8

Solution :

Problem 4 :

If √(x√x) = x^a, what is the value of a?

A)  1/2

B)  3/4

C)  1

D)  4/3

Solution :

Problem 5 :

The manufacturer wants to create a new alloy by mixing two metals. One metal is 35% copper and the other is 75% copper. How many kilograms of eah metal must be used to produce 80 kilograms of an alloy that is 50% copper?

Solution :

Problem 6 :

ax + 4y = 14

5x + 7y = 8

In the system of equations above, a is a constant and x and y are variables. If the system has no solution, what is the value of a?

A)  20/7

B)  35/4

C)  -35/4

D)  -20/7

Solution :

Problem 7 :

The graph of line l is shown in the xy-plane above. The equation of line n (not shown) is y = mx + b, where m and b are constants. If line l is perpendicular to line n, which of the following must be true?

A)  m < 0

B)  m > 0

C)  b > 0

D)  b < 0

Solution :

Problem 8 :

On Friday, Janice read x pages every 30 minutes for 4 hours and Kim read y pages for every 15 minutes for 5 hours. Which of the following represents the total number of pages read by Janice and Kim on Friday?

A)  4x + 5y

B)  8x + 20y

C)  20x + 8y

D)  120x + 75y

Solution :

Problem 9 :

Victor wants to sell 3 watches, each at the same price. After negotiating with customers, however, he ends up selling one at a 30% discount, one at a 20% discount and one at a 10% discount. If Victor sold the watches for a total of $240, how much money did he lose by giving the discounts?

(A)  $45

(B)  $60

(C)  $75

(D)  $90

Solution :

Problem 10 :

x² + kx + 9 = (x + a)²

In the equation above, k and a are positive constants. If the equation is true for all values of x, what is the value of k?

A)  0

B)  3

C)  6

D)  9

Solution :

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