DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 5)

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

Problem 1 :

A) 3

B) 6

C) 8

D) 150

Solution :

Problem 2 :

James must drive 100 miles before he can take his driver’s license test. He knows that when he drives around town running errands, he drives at an average speed of 20 miles per hour. If James maintains this average speed, how many hours must he drive to meet the requirement for his driver’s license test?

A) 5

B) 20

C) 80

D) 100

Solution :

Problem 3 :

The production cost p(x), in dollars, to produce x units of an item when materials cost $2 per item is given by p(x) = 2x + 150. What is the total cost to produce 2,000 units of this item?

A) $1,850

B) $2,300

C) $3,850

D) $4,150

Solution :

Problem 4 :

In the figure above, what is the value of d if line a is parallel to line b?

Solution :

Problem 5 :

Stella had 211 invitations to send for an event. She has already sent 43 invitations and will send them all if she sends 24 each day for the next d days. Which of the following equations represents this situation?

A) 24d - 43 = 211

B) 24d + 43 = 211

C) 43d - 24 = 211

D) 43d + 24 = 211

Solution :

Problem 6 :

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 7 :

In triangle ABC, the sum of the measures of angle A and angle B is 90 degrees. The value of sin (A) = 2√7/8. What is the value oif cos (B) ?

A) 2√7/8

B) 2√7/6

C) 6√2/14

D) 8/23√2

Solution :

Problem 8 :

A quadratic function models the height, in feet, of an object above the ground in terms of time, in seconds, after the object was launched. According to the model, the object was launched from a height of 8 feet and reached its maximum height of 1800 feet 16 seconds after it was launched. Based on the model, what was the height in feet, of the object 24 seconds after it was launched?

Solution :

Problem 9 :

The median of seven consecutive positive integers is 5. If one of the integers is selected at random, what is the probability that the selected integer is a multiple of 3?

Solution :

Problem 10 :

In triangle ABC, the sum of the measures of angle A and angle B is 90 degrees. The value of sin (A) = 2√7/8. What is the value oif cos (B) ?

A) 2√7/8

B) 2√7/6

C) 6√2/14

D) 8/23√2

Solution :

Problem 11 :

C = (10 + 0.1m)(1 + r)

The Sunny Information and Telephone Company (SITC) calculates a customer’s total monthly cell phone charge using the formula above, where C is the total cell phone charge, r is the tax rate and m is the number of minutes the customer used that month. Last month a customer used 6 hours 40 minutes and paid $54. If the customer uses 8 hours this month, which of the following will be the customer’s cost this month?

A) $56.25

B) $62.64

C) $70.56

D) $85.25

Solution :

Problem 12 :

If 5x² – 5y² = 13 and x = y + 7, what is the value of x + y?

A) 8

B) 2

C) 23/33

D) 13/35

Solution :

Problem 13 :

Members of a reading club want to buy a science fiction books for their sponsors. If each member of the club contributes $4.00 towards the purchase of the book, they will still be short $7.00. If each member contributes $6.00, they will have a surplus of $9.00 after the purchase of the book. What is the price of the book in dollars?

A) 8

B) 24

C) 39

D) 48

Solution :

Problem 14 :

A group of men agreed to share equally the cost of a hunting trip which they estimated to be $720. At the last minute, two of the men were unable to go, with the result that each of the others had to pay an additional $12. How many men actually went on the hunting trip?

A) 10

B) 12

C) 13

D) 14

Solution :

Problem 15 :

The average of m numbers is a and the average of n numbers is b. If the average of all the (m + n) numbers is k, what is the value of m?

Solution :

Problem 16 :

A scientist counts 80 cells in a petri dish and finds that each one splits into two new cells every hour. How many cells are in the petri dish after 5 hours?

Solution :

Problem 17 :

f(x) = ax³ + b

In the function defined above, a and b are constants. If f(-1) = 4 and f(1) = 10, what is the value of b?

Solution :

Problem 18 :

If (x, y) is the solution to the system of equations above, what is the value of x ?

Solution :

Problem 19 :

The original price of a suit is $1000. A salesman decides to discount it by 30%. Later on, the manager decides to give a 15% discount off the salesman's price. What is the final price of the suit?

A) $350

B) $485

C) $550

D) $595

Solution :