10 Hard SAT Math Questions (Part - 15)

Question 1 :

A circle in the xy-plane has its center at (3, -7) and has a radius of 12. An equation of this circle is

x² + y² + ax + by + c = 0,

where a, b and c are constants. What is the value of c?

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Question 2 :

Sphere A has a radius of 7x and sphere B has a radius of 91x. The volume of sphere B is how many times the volume of sphere A?

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Question 3 :

One gallon of resin costs $79 and will cover 48 square feet of a countertop. The countertops in a given room have a total surface area of k square feet. Which equation represents the cost c, in dollars, of resin needed to cover the countertops twice?

A) c = 48k/79

B) c = 96k/79

C) c = 79(k/24)

D) c = 79(k/96)

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Question 4 :

For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system?

10x + 8y = 15

25x + 20y = 37.5

A) (2r/5 + 10, -2r/5 + 25)

B) (r, 5r/4 + 4/5)

C) (-4r/5 + 3/8, r)

D) (r, -4r/5 + 15/8)

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Question 5 :

A researcher selected 2 random samples of employees in a large company to estimate the percentage of employees that planned to vote in favor of a new division. Based on the first sample, the researcher estimated that 68% of the employees would vote in favor, with an associated margin of error of 9.7%. Based on the second sample, the researcher estimated that 84% of the employees would vote in favor, with an associated margin of error of 6.7%. Assuming the margins of error were calculated in the same way, which of the following best explains why the second sample obtained a smaller margin of error than the first sample?

A) The first sample contained fewer employees than the second sample.

B) The first sample contained more employees than the second sample.

C) The first sample contained a lower percentage of residents that planned to vote in favor of a new division.

D) The first sample contained a higher percentage of residents that planned to vote in favor of a new division.

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Question 6 :

The function f is defined by f(x) = a^x + b, where a and b are constants. In the xy-plane, the graph of y = f(x) has an x-intercept at (3, 0) and a y-intercept at (0, -342). What is the value of a + b?

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Question 7 :

684 is p% greater than 9. What is the value of p?

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Question 8 :

Two numbers a and b, are each greater than zero, and the fifth root of a is equal to the cube root of b. For what value of x is a^{8x - 4} equal to b?

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Question 9 :

For the given system of equations, what is the value of 7(j - k)?

(j - k) - 16(m + l) = 689

(j - k) + 12(m + l) = 1235

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Question 10 :

A model initially estimates that there are 24,000 bacteria on a petri dish. 14 days later, the model estimates that there are 96,000 bacteria on the petri dish. Assuming exponential growth, the formula B = a(2)^xdgives the estimated number of bacteria on a petri dish, where a and x are constants and B is the number of bacteria on the petri dish d days after the initial measurement. What is the value of x?

A) 1/14

B) 1/7

C) 7

D) 14

Answer :