10 Hard SAT Math Questions (Part - 6)

Question 1 :

If 4k – x is a factor of x³ – 72nk³, where n and k are constants and k > 0, what is the value of n?

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Question 2 :

The numbers a, b, c, p and w are positive constants, where b > c. The number a is 1,150% more than the positive difference between b and c, and c is 50% of b. If a is p% greater than c, and c is w% of a, what is the value of pw?

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Question 3 :

(10b + 6a)x² + (9a² – 25b²)x – 12ab = 0

The equation above has two real solutions, where a and b are constants. The sum of the solutions to the given equation is k(21a – 35b), where k is a constant. What is the value of k?

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Question 4 :

Ramachandran invented a new temperature scale he called the Onlinemath4all scale. The function T gives the temperature, in degree Torte, that corresponds to a temperature of x degrees Celsius. If a temperature increased by 3.3 degree Torte, by how much did the temperature increase, in degrees Celsius? Round your answer to the nearest hundredth.

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Question 5 :

A circle has center A, and points B and C lie on the circle. Line segments BD and CD are tangent to the circle at points B and C, respectively. The measure of angle BDC is 120°. The length of line segment CD is 12 inches. What is the area of the region that is both inside the quadrilateral ABCD and outside the circle, in square inches? (Round your answer to the nearest hundredth of a square inch)

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Question 6 :

In the figure shown, point C is the center of both circles. The ratio of AB to CD is 6 to 5. If the area of the larger circle is 242, what is the area of the shaded region?

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Question 7 :

a(x – 5) + 4b = 7(b – 5x)

The equation above has no solution, where a and b are constants. The number b CANNOT be equal to the number m. What is the value of m? Round your answer to the nearest hundredth.

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Question 8 :

A fruit orchard has 8 rows of apple trees and 4 rows of orange trees. Each row of apple trees has 15 trees that are healthy and 6 trees that are unhealthy. Each row of orange trees has 10 trees that are healthy and 2 trees that are unhealthy. The probability of selecting an apple tree, given that that the tree is unhealthy, is equal to w. The probability of selecting an unhealthy tree , given that the tree is an orange tree, is equal to z. Note that w and z are positive constants. What is the positive difference between w and z? Round your answer to the nearest hundredth.

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Question 9 :

(3x – 7p)(5x² + 8x – 4p)(x³ + 3x² – 16x – 48) = 0

In the given equation, p is a positive constant. The product of the solutions to the equation is –560/9. What is the value of p?

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Question 10 :

In triangles ABC and JKL, angles B and K each have a measure of 44°. The length of side BC and the length of side KL are both equal to 25. Which additional piece of information is sufficient to prove that triangle ABC is congruent to triangle JKL?

A) The length of side AC is 13 and the length of side JL is 13.

B) The measure of angle A is 58° and the measure of angle L is 58°.

C) The measure of angle A is 37° and the measure of angle J is 37°.

D) No additional information is necessary.

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