10 Hard SAT Math Questions (Part - 11)

Question 1 :

If a, b and c are positive constants such that 53% of a equals 27% of b and a equals 34% of c, then what percent of b is equal to c? Round your answer to the nearest tenth. Exclude the percent sign from your answer.

Answer :

IQuestion 2 :

If 8^{x + 1} - 2^3x = k(16^3x/4), what is the value of k?

A) 3

B) 5

C) 7

D) 8

Answer :

Question 3 :

The ratio of the speeds of two trains is 7 : 8. If the second train runs 400 miles in 5 hours, what is the speed of the first train?

A) 10 miles/hr

B) 50 miles/hr

C) 70 miles/hr

D) 80 miles/hr

Answer :

Question 4 :

Triangle ABC and PQR are similar and have the following properties.

• ∠A is the smallest angle and ∠C is the largest.

• The measure of ∠P is equal to k times the measure of ∠A, and the measure of ∠Q is equal to k times the measure ∠B.

• The perimeter of ΔPQR is 2 times the perimeter of ΔABC.

• k > 1 and PQ = 54.

Which of the following must be true?

A) k = 2

B) PQ/AB = 2

C) BC = 27

D) k = 27

Answer :

Question 5 :

If x = ²ⁿ√(4xⁿ + 21), where n is an odd positive integer constant, what is the value of xⁿ?

Answer :

Question 6 :

nx – 7k = –7x + 2n

In the equation above, n and k are constants. If the equation has no solution, what cannot be the value of n + k?

Answer :

Question 7 :

3(w – a)(w + 5) = w + 5

In the equation above, a is a conatnt. If the sum of the solutions to the equation is 34/3, what is the value of a?

Answer :

Question 8 :

The edge length, in centimeters, of cube A is 4/27 the edge length, in centimeters, of cube B. The surface area, in square centimeters, of cube B is k times the surface area, in square centimeters, of cube A. What is the value of k?

A) 64/19,683

B) 16/729

C) 729/16

D) 19,683/64

Answer :

Question 9 :

4x² + bx – 90 = (cx + m)(x – p)

Given that c, m and p are integers, which of the following must be true?

A) m is a factor of b

B) c is a factor of 90

C) c is a factor of b

D) p is a factor of 90

Answer :

Question 10 :

The results of two random samples of votes for a population are given in the table. The samples were selected from the same population, and the margins of error were calculated using the same method. Which of the following is the most appropriate reason that the margin of error for sample A is greater than the margin of error for sample B?