DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 44)

Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.

Problem 1 :

Albert is 7 years older than Henry. In 5 years, Albert will be twice as old as Henry. How many years is Albert old now?

Solution :

Problem 2 :

A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the packages can be at most 1,100 pounds. What is the maximum number of 120-pound packages that the helicopter can carry per trip?

A) 2

B) 4

C) 5

D) 6

Solution :

Problem 3 :

A window repair specialist charges $220 for the first two hours of repair plus an hour fee for each additional hour. The total cost for 5 hours of repair is $400. Which function f gives the total cost, in dollars for x hours of repair, where x ≥ 2?

A) f(x) = 60x + 100

B) f(x) = 60x + 220

C) f(x) = 80x

D) 80x + 220

Solution :

Problem 4 :

An economist modeled the demad Q for a certain product as a linear function of the selling price P. The demand was 20,000 units when the selling price was $40 per unit, and the demand was 15,000 units, when the selling price was $60 per unit. Based on the model, what is the demand, in units, when the selling price is $55 per unit?

A) 16,250

B) 16,500

C) 16,750

D) 17,500

Solution :

Problem 5 :

A certain apprentice has enrolled in 85 hours of training courses. The equation 10x + 15y = 85 represents this situation, where x is the number of on-site training courses and y is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?

Solution :

Problem 6 :

What is the value of the following expression, if x – y = 20?

2x² + 10x – 4xy – 10y + 2y²

Solution :

Problem 7 :

The circle above has center O, the length of arc ADC is 5π and x = 100. What is the length of arc ABC?

A) 9π

B) 13π

C) 18π

D) 13π/2

Solution :

Problem 8 :

Matt earns a bonus based on the total sales made each day. Matt made sales on Monday and Wednesday.

⋅ The bonus is 15% of the total sales made.

⋅ The sales made on Monday totaled $1,225.

⋅ The bonus Matt earned for sale made on Monday and Wednesday was $510.

What was the total value, in dollars, of the sales made by Matt on Wednesday?

Solution :

Problem 9 :

The math club had $200 to buy supplies for t-shirt decorating.

⋅ They spent $10 for the first t-shirt and $8 for each additional t-shirt.

⋅ They purchased y t-shirts.

Which inequality best represents this situation?

A) 10(y - 1) + 8 ≥ 200

B) 10 + 8(y - 1) ≥ 200

C) 10(y - 1) + 8 ≤ 200

D) 10 + 8(y - 1) ≤ 200

Solution :

Problem 10 :

Stella has some colored cards that are the same size and shape.

⋅ The probability of randomly selecting a blue card is 20%.

⋅ The probability of randomly selecting a red card is 30%.

What is the probability Stella will randomly select a card that is NOT blue, replave it, then randomly select a card that is red?

A) 6%

B) 14%

C) 24%

D) 50%

Solution :

Problem 11 :

In the equation above, a > 0. What is the value of x?

Solution :

Problem 12 :

In the xy-plane above, the graphs of line ℓ and line m intersect at point P. If line ℓ is perpendicular to line m, what is the length of OP?

Solution :

Problem 13 :

In the xy-plane above, the graphs of functions f and g intersect at points B and C. What is the area of the quadrilateral ABCD?

Solution :

Problem 14 :

g(x) = 2f(x) + k

In the equation above, f(x) is a linear function and k is a constant. If g(2) = 10 and g(5) = 18, what is the slope of the function f(x)?

Solution :

Problem 15 :

15x + 9y = b

ax + by = 1

In the system of equations above, a and b are constants, where b > 0. If the system has infinitely many solutions, what is the value of a?

Solution :

Problem 16 :

f(x) = a^x – b

The exponential function given above passes through the points (c, 8) and (2c, 350). What is a possible value of b?

Solution :

Problem 17 :

In the xy-plane, a unit circle with center at the origin O contains point A with coordinates (1, 0) and point B with coordinates (3/√34, -5/√34). If the measure of angle AOB is p radians, what is the value of cos p/sin p?

Solution :

Problem 18 :

The circle x² + x√t + y² – y – 69 = 0 has a radius of √86. What is the value of t?

Solution :

Problem 19 :

The function f is defined by f(x) = ax² + bx + c, where a, b and c are constants. The graph of y = f(x) in the xy-plane passes through the points (7, 0) and (-3, 0). If a is an integer greater than 1, which of the following could be the value of a + b?

A) -6

B) -3

C) 4

D) 5

Solution :

Problem 20 :

Jack appeared in three tests of full marks 20, 50 and 30 marks respectively. He obtained 75% marks in the first and 60% marks in the second test. What should be his percentage of marks in the third test if the overall score is 60%?

Solution :