10 Hard SAT Math Questions (Part - 24)

Question 1 :

The function f is defined by f(x) = a√(x + b), where a and b are constants and a ≠ 0. In the xy-plane, the graph of y = f(x) passes through the point (–24, 0), and f(24) is less than 0. Which of the following must be true?

A)  a > 0

B)  b < 0

C)  a > b

D)  a < b

Answer :

Question 2 :

A 100 gram metal alloy is 40% silver. It contains a metal alloy that is 65% silver and a second metal alloy made up of 25% silver. What is the mass of the first metal alloy?

Answer :

Question 3 :

Joshua Tree National Park has an area of 1,242 square miles. What is the area, in square yards, of Joshua Tree National Park? ( 1 mile = 1,760 yards).

A)  1,242/1,760

B)  1,242/(1,760)²

C)  1,242(1,760)

D)  1,242(1,760)²

Answer :

Question 4 :

There are two ranches. Ranch A and ranch B. The ratio of male horses to female horses is 1: 15 for the total number of horses on ranch A and B. The ratio of female horses on ranch A to ranch B. is 7: 17. There are 168 horses on ranch A and 344 horses on Ranch B. How many more male horses are there on ranch A than on ranch B?

Answer :

Question 5 :

A certain bacterial colony currently has 5,000 spores. If the number of spores in this colony quadruples every 33 hours, which of the following functions p gives the number of spores in the colony d days from now?

A)  N(d) = 5,000(4)^11d/8

B)  N(d) = 5,000(4)^8d/11

C)  N(d) = 5,000(4)^5d/4

D)  N(d) = 5,000(4)^4d/5

Answer :

Question 6 :

In the given equations, a and b are constants, a is greater than 1 and b is greater than 1. What is the value of x?

⁷√a⁵ = √b⁵

a^{3x - 3} = b³

Answer :

Question 7 :

a is 3700% greater than b. a is also 5% less than c. What percent greater than c is b?

Answer :

Question 8 :

The proposal for a development project was included on a city’s election ballots. A local tv station reported that 6 times as many people voted in favor of the proposal as people who voted against it. If 1,770 more people voted in favor of the proposal than those who voted against the proposal. How many people voted against the proposal?

Answer :

Question 9 :

The table gives the volume and surface area of two similar rectangular prisms A and B, where k is a constant. What is the value of k?

A)  5,346

B)  12,474

C)  87,318

D)  611,226

Answer :

Question 10 :

In the given system of equations, c is a constant. The system has two distinct real solutions. Which of the following could be the value of c?

y = x - c

y = -6(x - 5)²

A)  2

B)  4

C)  119/24

D)  7

Answer :

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