10 Hard SAT Math Questions (Part - 32)

Question 1 :

At a movie theater, there are a total of 350 customers. Each customer is located in either theater A, theater B, or theater C. If one of these customers is selected at random, the probability of selecting a customer who is located in theater A is 0.48, and the probability of selecting a customer who is located in theater B is 0.24. How many customers are located in theater C?

A) 28

B) 40

C) 84

D) 98

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Question 2 :

3 consecutive even integers are ordered from smallest to largest. 5 times the first integer is at least 9 more than the sum of the second and third integers. What is the minimum possible value for the second integer?

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Question 3 :

In triangle ABC, the measure of angle B is 90°, AB is a leg with a length of 12, and segment AC contains the point D. Which of the following must be true?

I. BC = 12tan(∠CAB)

II. cos(∠ABD) – sin(∠DBC) = 0

III. m∠ABD = m∠BDC

A) I and II only

B) II and III only

C) I and III only

D) I, II and III

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Question 4 :

In the xy-plane, the graph of x² + 6x + y² + 2y = 15 is a circle. Line k is a tangent to this circle at the point (a, b) and has a slope of 3/4. What is a possible of b?

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Question 5 :

A square pyramid has a volume of 400 cubic inches and a slant height of 13 inches. If each side of the square base and height are integers in inches, what is the surface area of the pyramid in square inches?

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Question 6 :

The frequency table above summarizes data set A. Data set B is created by multiplying all of the values in data set A by 2. Which of the following must be true?

I. The difference between the mean and median of data set B is 0.

II. The standard deviation of data set B is equal to the standard deviation of data set A.

III. The range of data set B is double the range of data set A.

A) I and II only

B) II and III only

C) I and III only

D) I, II and III

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Question 7 :

In triangle ABC, the measure of angle B is 90°, BD is an altitude of the triangle. The length of BC is 10 and m∠ABD = 60°. What is the length of AD?

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Question 8 :

The function h(x) is defined by h(x) = a^x + b, where a and b are positive constants. The graph of y = h(x) in the xy-plane passes through the points (0, 4) and (2, 12). What is the value of ab?

A) 8

B) 9

C) 12

D) 15

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Question 9 :

The perimeter of a right isosceles triangle is 52 + 52√2. What is the length of hypotenuse?

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Question 10 :

Rectangle ABCD is similar to rectangle WXYZ. The area of rectangle ABCD is 486 square units, and the area of rectangle WXYZ is 54 square units. The length of the longest side of rectangle ABCD is 27 units. What is the length, in units, of the longest side of rectangle WXYZ?

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