DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 50)

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Problem 1 :

30x² + bx + 33

A factor of the expression above is (px + q), where p and q are positive integers. What is the value of b?

Solution :

Problem 2 :

Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch. If one side of his porch is 12 feet long, and each strand of his Christmas lights will wrap around a 70-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?

A) 6

B) 7

C) 8

D) 9

Solution :

Problem 3 :

The table shows x and y values for the function g(x). The function f(x) is an exponential function in the form of ab^x. What is the value of (a + b)?

Solution :

Problem 4 :

Kristen opens a bank account that earns 4% interest each year, compounded once every two years. If she opened the account with k dollars, which of the following expressions represents the total amount after t years?

Solution :

Problem 5 :

Circle F in the xy-plane is represented by the equation (x – 13)² + (y – 9)² = 196. Circle G is obtained by shifting circle F, 5 units to the left and 11 units up. An equation representing circle G is (2x + h)² + (2y + k)² = ℓ, where h, k and ℓ are constants. What is the value of h + k + ℓ?

Solution :

Problem 6 :

The quadratic equation above has got two values of x to staisfy the equation as

Solution :

Problem 7 :

One student is asked to divide a half of a number by 6 and other half by 4 and then to add the two quantities. Instead of doing so, the student divides the given number by 5. If the answer is 4 short of the correct answer then the number was

A) 320

B) 400

C) 480

D) 560

Solution :

Problem 8 :

The length of a side of equilateral triangle ABC above is 10. In the figure, ED||BC and DF||AB. If the ratio of DE to DF is 1 : 3, what is the perimeter of triangle CDF?

Solution :

Problem 9 :

The xy-plane above shows two points of intersection of the graphs of a linear function and a quadratic function. The vertex of the graph of the quadratic function is at (3, -4) and (r, s) is one of the points of intersection of the graphs. What is the value of r?

Solution :

Problem 10 :

Which of the following is equivalent to the expression shown above?

Solution :

Problem 11 :

There are red, green and blue marbles in a jar. 30% of the total marbles are blue and 20% of the blue marbles are green. If there are 32 red marbles, then find the number of green marbles.

A) 3

B) 5

C) 9

D) 10

Solution :

Problem 12 :

The perimeter and area of the parallelogram ABCD above are 30 cm. and 40 sq.cm respectively. If AB = 10 cm, then what is the length of AE?

A) 3 cm.

B) 4 cm.

C) 5 cm.

D) 6 cm.

Solution :

Problem 13 :

If 4m + 5n is equal to 250 percent of 4n, what is the value of (m + n)/(m - n)?

Solution :

Problem 14 :

In the parallelogram above, BM : MC = 2 : 3. if the area of triangle ABM is 20, what is the area of the shaded region?

Solution :

Problem 15 :

P(x) = 23,500 - 250x

The population of a certain town has been declining since the year 2,000. Scientists chose a linear decay model for the decline and arrived at the function above, where x is the number of years since 2,000. In how many years, will the population be decreased by 2,000?

Solution :

Problem 16 :

The figure above shows three squares with areas of 16, 64 and k respectively. If line ℓ passes through the vertex of each square, what is the value of k?

A) 81

B) 144

C) 196

D) 256

Solution :

Problem 17 :

In the figure above, two circles have a common center O, and two rays from the center intercept the circles at points P, Q, R and S. The measure of the angle POQ is 2π/5 and the area of the shaded region of sector OPQ is 20π. If OP : PR = 2 : 3, what is the lenth of the minor arc RS?

Solution :