DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 35)

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Problem 1 :

If a is 2403% of b + c, and b is 89% of c, what percent of b is a?

Solution :

Problem 2 :

A number x is at most 2 less than 3 times the value of y. If the value of y is -4, what is the greatest possible value of x?

Solution :

Problem 3 :

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If a triangle has side lengths of 6 and 12, which inequality represents the possible lengths x, of the third side of the triangle?

A) x < 18

B) x > 18

C) 6 < x < 18

D) x < 6 or x > 18

Solution :

Problem 4 :

Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?

A) 3

B) 7

C) 8

D) 12.

Solution :

Problem 5 :

A salesperson’s total earnings consists of a base salary of x dollars per year, plus earnings of 11% of the total sales the salesperson makes during the year. This year, the salesperson has a goal for the total earnings to be at least 3 times and at most 4 times the base salary. Which of the following inequalities represents all possible values of total sales s, in dollars the salesperson can make this year in order to meet that goal?

Solution :

Problem 6 :

Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles m, he should drive each week?

Solution :

Problem 7 :

Which of the following expressions has a factor of x + 2b, where b is a positive integer constant?

A) 3x² + 7x + 14b

B) 3x² + 28x + 14b

C) 3x² + 42x + 14b

D) 3x² + 49x + 14b

Solution :

Problem 8 :

The graph of y = 2x² + bx + c is shown, where b and c are constants. What is the value of bc?

Solution :

Problem 9 :

f(x) = (1.84)^x/4

The function f is defined by the given equation. The equation can be written as f(x) = (1 + p/100)^x, where p is a constant. Which of the following is closest to the value of p?

A) 16

B) 21

C) 46

D) 96

Solution :

Problem 10 :

The graph of a circle shown in the xy-plane above, intersects the x-axis and y-axis at three points. What is the radius of the circle?

A) 4

B) 5

C) 6

D) 7

Solution :

Problem 11 :

Claire has $40 in her own savings jar and puts in $10 every week. David has $80 in his own savings jar and puts in $8 every week. Each of the graphs below shows the amount in the jar over time.

If the graphs intersect at the point (a, b), what is the value of b?

A) 200

B) 220

C) 240

D) 260

Solution :

Problem 12 :

57x² + (57 + a)x + ab = 0

In the given equation, a and b are constants. The product of the solutions to the given equation is kab, where k is a constant. What is the value of k?

A) 1/57

B) 1/19

C) 1

D) 57

Solution :

Problem 13 :

If the graph of the function f(x) = a^x – b passes through the points (c, 9) and (2c, 219), Which of the following could be a value of b?

A) 6

B) -21

C) 10

D) -6

Solution :

Problem 14 :

(x + 4)² + (y – 19)² = 121

The graph of the given equation is a circle in the xy-plane. The point (a, b) lies on the circle. Which of the following is the possible value for a ?

A) -16

B) -14

C) 11

D) 19

Solution :

Problem 15 :

In the xy-plane, a circle has center C with coordinates (h, k). Points A and B lie on the circle. Point A has coordinates (h + 1, k + √102) and ∠ACB is a right angle. What is the length of AB?