DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 30)

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Problem 1 :

The graph of f(x) is shown above for -5 ≤ x ≤ 5. How many real solutions does f(x) = 2 have?

A) None

B) 1

C) 2

D) 3

Solution :

Problem 2 :

3x² + 10x - 8 = 0

If r and s are two solutions of the equatioon above, which of the following is the value of r + s?

Solution :

Problem 3 :

The price of a backpack is b dollars, to which t percent of sales tax is added at the counter. What is the price of the backpack after tax in terms of b and t?

A) b(1 + 0.01t) dollars

B) b(1 + t) dollars

C) (b + 0.01t) dollars

D) (b + t) dollars

Solution :

Problem 4 :

The scatter plot above shows the perimeters and areas of 10 rectangles. What is the perimeter, in centimeters, of the rectangle represented by the data point that is farthest from the line of best fit (not shown)?

A) 12

B) 17

C) 20

D) 23

Solution :

Problem 5 :

If (2x - 3)(x - p) = 2x² - qx + 12 for all values of x, what is the value of p + q?

A) 13

B) 15

C) 17

D) 19

Solution :

Problem 6 :

Yellow Cab of Charleston charges $5.00 for the first two miles and 50 cents for each additional 1/5 of a mile. If Peter paid Yellow Cab $25.00 for his trip, how many miles did he travel for the trip?

A) 6 miles

B) 8 miles

C) 10 miles

D) 12 miles

Solution :

Problem 7 :

In the rectangle ABCD above, AB = 8, BE = 4, FD = 6, and BC = 20. If BD and EF intersect at point G, What is the area of the shaded region?

A) 18.4

B) 20.8

C) 36.8

D) 41.6

Solution :

Problem 8 :

A) 27

B) 39.2

C) 42

D) 45

Solution :

Problem 9 :

In the xy-plane above, vertices of triangle ABC are lying on the graph of y = -x² + k, where k is a constant. If the area of triangle ABC is 27, what is the value of k?

A) 3

B) 9

C) 18

D) 27

Solution :

Problem 10 :

The sum of four numbers is 2,835. One of the numbers, a, is 25% more than the sum of the other three numbers. What is the average of the other three numbers?

A) 365

B) 420

C) 475

D) 600

Solution :

Problem 11 :

If Claire paid k dollars for a computer that was only 20 dollars more than half the original price, what was the original price, in dollars?

A) k + 20

B) k - 40

C) 2k - 20

D) 2k - 40

Solution :

Problem 12 :

Jenny is in school swim team and has swim practice m hours in the morning and p hours in the evening each day. The schedule is the same each day. If she swims k hours for five days, which of the following is the expression for m?

A) ⁽ᵏ ⁻ ᵖ⁾⁄₅

B) ⁽ᵏ ⁻ ⁵ᵖ⁾⁄₅

C) k - 5p

D) 5(k - p)

Solution :

Problem 13 :

In the figure above, each of two circles has the same center O. If OP : OQ = 3 : 5 and the area of the shaded region is 40, what is the area of the larger circle?

Solution :

Problem 14 :

f(x) = ax² + bx + c

In the function f above, f(0) = 10 and f(-1) = 18. What is the value of (a - b)?

Solution :

Problem 15 :

In the figure above, D and E are the midpoints of AB and BC respectively. If the area of the shaded is 42, what is the area of triangle ABC?

Solution :

Problem 16 :

In the xy-plane, the graphs of y = –x² + 12 and line ℓ intersect at points P(p, 3) and Q(q, -4). What is the greatest possible value of the slope of line ℓ?

Solution :

Problem 17 :

A salesman’s commission is k percent of the selling price of a car. This week, Peter, a salesman sold 10 cars for $20,000 each. Which of the following represents the commission this week?

A) 200k

B) 2,000k

C) 20,000/k

D) 20,000k/(100 + k)

Solution :

Problem 18 :

Emily is walking a trail. After walking k percent of the length of the trail, she has 10 km left to go. Which of the following represents the length of the trail?

A) 10(100 - k)

B) (100 - k)/10

C) 10k/(100 - k)

D) 1000/(100 - k)

Solution :

Problem 19 :

Which of the following equations has the same solution as 2x² + 12x + 32 = 0?

A) 2(x + 3)² = 32

B) 2(x + 3)² = 32

C) 2(x + 3)² = 32

D) 2(x + 3)² = 32

Solution :

Problem 20 :

The graph of y = a(x + 1)(x – 5) is shown in the xy-plane above, where a is a constant. If the graph with vertex (h, k) intersects the y-axis at point (0, 5), which of the following is equal to k?

A) 7

B) 8

C) 9

D) 10

Solution :