Digital SAT Math Questions and Answers (Part - 13)

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Question 1 :

The floor of a ballroom has an area of 600 square meters. An architect creates a scale model of the floor of the ballroom, where the length of each side of the model is 1/10 times the length of the corresponding side of the actual floor of the ballroom. What is the area, in square meters, of the scale model?

A) 6

B) 10

C) 60

D) 150

Answer :

Question 2 :

The result of increasing the quantity x by 1800% is 684. What is the value of x?

A) 12,996

B) 12,312

C) 38

D) 36

Answer :

Question 3 :

x(x + 1) - 56 = 4x(x − 7)

What is the sum of the solutions to the given equation?

Answer :

Question 4 :

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Question 5 :

A number consists of two digits the digit in the ten’s place is twice the digit in the unit’s place. If 18 be subtracted from the number the digits are reversed. Find the number.

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Question 6 :

How many gallons, to the nearest tenth, of cream that is 15% fat must be mixed with milk that is 4% fat to produce 20 gallons of cream that is 5% fat?

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Question 7 :

y = f(x) is a quadratic function, which has a factor of (x – a) and x = b is a positive zero of the function. If the minimum of the function is (78/2, k), what is the value of (a + b)?

Answer :

Question 8 :

∠X and ∠Y are acute angles and sin X = cos Y. The measures, in degrees, of ∠X and ∠Y are 15 – 2a and 3b + 26, respectively. If b is 3 more than 2 times of a, then what is the value of a?

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Question 9 :

An area of 46.00 square nautical miles is equivalent to k square kilometers. To the nearest tenth, what is the value of k? (1 nautical mile = 1.852 kilometers)

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Question 10 :

In triangle XYZ, the measure of angle X is 90°. Point W lies on segment YZ, and segment WX is perpendicular to segment YZ. The length of segment WY is 572, and the length of segment WX is 429. What is the value of tanZ?

A) 3/5

B) 3/4

C) 4/5

D) 4/3

Answer :

Question 11 :

25The histogram summarizes data set A, which represents the number of points per player earned by 50 players of a game. A new player earns 18 points playing the game, and this number of points is added to data set A to create data set B with 51 values. Which of the following must be true?

I. The median number of points per player for data set B is less than the median number of points per player for data set A.

II. The mean number of points per player for data set B is less than the mean number of points per player for data set A.

A) I only

B) II only

C) I and II

D) Neither I nor II

Answer :

Question 12 :

52(x³ + 64)(x⁴ - 81) = 0

How many distinct real solutions does the given equation have?

A) Exactly two

B) Exactly three

C) Exactly five

D) Exactly seven

Answer :

Question 13 :

In the figure shown, WZ and XY intersect at point Q, YQ = 21, WQ = 70, WX = 60, and XQ = 120. What is the length of YZ?

A) 18

B) 36

C) 120

D) 200

Answer :

Question 14 :

f(x) = -6x² + 60x - 126

The function f is defined by the given equation. Which of the following equivalent forms of the equation displays the maximum value of the function as a constant or coefficient?

A) f(x) = -6x² + 42x + 18x - 126

B) f(x) = -6x(x - 7) + 18(x - 7)

C) f(x) = -6(x - 7)² + 24

D) f(x) = -6(x - 7)(x - 3)

Answer :

Question 15 :

The number a is 55% less than the number b. The number b is 320% greater than 160. What is the value of a?

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Question 16 :

⁷√p4 = t^5/6

In the given equation, p > 1 and t > 1. If t = p^{2n – 1}, where n is a constant, what is the value of n?

Answer :

Question 17 :

A certain open star cluster contains M-type stars and K-type stars. The estimated total mass of M-type and K-type stars in this open star cluster is 127,882 quettagrams. The graph shown models the possible combinations of the number of M-type stars, x, and K-type stars, y, that could be in this open star cluster if all the M-type stars have the same estimated mass and all the K-type stars have the same estimated mass. Based on the graph, which of the following is closest to the estimated mass, in quettagrams, of each M-type star in this cluster?

A) 811

B) 938

C) 51,904

D) 75,978

Answer :

Question 18 :

For the quadratic function f , the table shows three values of x and their corresponding values of f(x). Which equation defines f ?

A) f(x) = (x - 8)(x - 32) + 32

B) f(x) = (x - 8)(x - 32) - 32

C) f(x) = (x - 24)(x - 30) + 4

D) f(x) = (x - 24)(x - 30) - 8

Answer :

Question 19 :

For the linear function g, the table shows four values of x and their corresponding values of g(x). The function can be written as g(x) = mx + b, where m and b are constants. What is the value of b?

A) 4

B) 16

C) 32

D) 36

Answer :

Question 20 :

For the polynomial function f, the graph of y = f(x) in the xy-plane passes through the points (-5, 0), (1, 0) and (4, 0). Which of the following must be a factor of f(x)?