10 Hard SAT Math Questions (Part - 45)

Question 1 :

If (5.678)^x = (0.5678)^y = 10^z, then, which of the following is true?

A)  1/x - 1/y + 1/z = 0

B)  1/x + 1/y - 1/z = 0

C)  1/x + 1/y + 1/z = 0

D)  1/x - 1/y - 1/z = 0

Answer :

Question 2 :

The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively and a right triangle is formed. What is the length of each side of the equilateral triangle?

Answer :

Question 3 :

The number p is 125% greater than the number q, the number q is 85% less than the number r and the number r is 15% greater than 60. What is the value of p?

Answer :

Question 4 :

A line is passing through the points (–8, 4) and (4, 1) and the equation of the line can be written as y = f(x) + 14. Which equation defines function f?

A)  f(x) = –0.25x – 12

B)  f(x) = –0.25x + 16

C)  f(x) = –0.25x + 2

D)  f(x) = –0.25x – 14

Answer :

Question 5 :

The expression (⅓)x² – 2 can be rewritten as (⅓)(x – k)(x + k), where k is a positive constant. What is the value of k?

A)  2

B)  6

C)  √2

D)  √6

Answer :

Question 6 :

There are two circles X and Y, where the radius of circle X is 125k and that of circle Y is 25k, where k is a positive constant. The area of circle X is how many times the area of circle Y?

Answer :

Question 7 :

An equilateral triangle has a perimeter of 42√3 inches. What is the height, in inches, of this triangle?

Answer :

Question 8 :

In the figure, AC is parallel to GD, and BF is parallel to CE. What is the value of x?

Answer :

Question 9 :

The circle shown has center O and diameter AC. Point B lies on the circle. If AC = 1, which of the following represents the area of triangle ABC?

Answer :

Question 10 :

A positive integer less than or equal to 125 is to be selected at random. What is the probability of selecting a two-digit number that is a multiple of 3? (Express your answer as a decimal or fraction, not as a percent.)

Answer :

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