Tricky SAT Math Problems Solved Easily

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Problem 1 :

The length x, and width y, of a rectangle can be related by the following system of equations. If both the length and width are integers, what is the area of the rectangle?

Problem 2 :

If (a – 3)² + (b – 4)² + (c + 5)² = 0, what is the value of a + b + c?

Problem 3 :

⁷√p4 = t^5/6

In the given equation, p > 1 and t > 1. If t = p^{2n – 1}, where n is a constant, what is the value of n?

Problem 4 :

If (px + 5)(qx + 3) = 8x² + rx + 15 for all values of x, and p + q = 6, what are two possible values for r?

A) 2 and 4

B) 7 and 12

C) 22 and 26

D) 29 and 39

Problem 5 :

The graph of a circle intersects the x-axis and y-axis at four distinct points, one of which lies on the negative x-axis at (k, 0). If k is a constant, what is its value?

A) –4

B) –6

C) –8

D) –10

Answers (1-5)

Problem 6 :

If x ≠ 0 and y ≠ 0, which of the following is equivalent to the above expression?

A) 2xy^-2

B) 4x^-2y²

C) 4x^-1y^-2

D) 4xy²

Problem 7 :

(ax + 3)(5x² – bx + 4) = 20x³ – 9x² – 2x + 12

The equation above is true for all real values of x, where a and b are constants. What is the value of ab?

A) 18

B) 20

C) 24

D) 40

Problem 8 :

For a certain rectangular region, the ratio of its length to its width is 35 to 10. If the width of the rectangular region increases by 7 units, how must the length change to maintain this ratio?

A) It must decrease by 24.5 units.

B) It must increase by 24.5 units.

C) It must decrease by 7 units.

D) It must increase by 7 units.

Problem 9 :

In the xy-plane above, O is the center of the circle and the measure of ∠POQ is a°. What is the cosine of a°?

Problem 10 :

In the given equation, r and s are constants. The equation has no solution. What is the value of r?

Answers (6-10)

Problem 11 :

James’ present age is 120% of Henry’s present age, Liam’s present age is 80% of Henry’s present age. If the sum of James’ present age and Liam’s present age is 80 years, then what is Henry’s present age in years?

Problem 12 :

If a = x² + 10x + 6, b = –2x + 5 and a + b = 5, then what is the value of (x² + 8x + 8)⁵?

Problem 13 :

x-axis, y-axis and a line 4x + 3y = 12 form a right triangle. What is the length of the perpendicular line segment drawn from the origin to the hypotenuse?

A) 3.5 units

B) 5.3 units

C) 2.4 units

D) 4.2 units

Problem 14 :

5x² + 13x + k = 0

In the quadratic equation above, k is a constant. If one root of the equation is the reciprocal of the other, then which of the following is the value of k?

A) –5

B) 5

C) 1/5

D) – 1/5

Problem 15 :

The average of the present ages of 3 persons is 50 years. 10 years ago their ages were in the ratio 7 : 8 : 9. Which of the following represents the present ages of 3 persons in years?

A) (45, 50, 55)

B) (40, 60, 50)

C) (35, 45, 70)

D) (30, 50, 70)