PRACTICE PROBLEMS ON PROPORTIONS FOR SAT

Problem 1 :

The radius of a circle is increased by 25%. By what percent does the area of the circle increase ?

Solution

Problem 2 :

The length of a rectangle increased by 20%. The width is decreased by 20%. Which of the following accurately describes  the change in area of the following ?

(a)  Increases by 10%      (b)  Decreases by 10%

(c)  Decreases by 4%       (d)  Stays the same

Solution

Problem 3 :

F = 9q₁ q₂/r²

The force of attraction between two particles can be determined by the formula above, in which F is the force between them, r is the distance between them and q₁ and q₂ are charges of the two particles.

If the distance between two charged particles is doubled, the resulting force of attraction is what fraction of the original force ?

(a)  1/2    (b)  1/4   (c)  1/8       (d)  1/16

Solution

Problem 4 :

P = V²/R

Electric power P is related to the voltage V and resistance R by the formula above. If the voltage were halved, how would the electric power be affected ?

(a)  The electric power would be 4 times greater

(b) The elevtric power would be 2 times greater

(c)  The electric power would be halved

(d)  The electric power would be quarter of what it was.

Solution

Problem 5 :

Julie has a square fence that encloses her garden. She decides to expand her garden by making each side of the fence 10% longer. After this expansion, the area of Julie's garden will have increased by what percent ?

(a)  20%     (b)  21%     (c)  22%     (d) 25%

Solution

Problem 6 :

A right circular cone has a base radius of r and a height of h. If the radius is decreased by 20% and height is increased by 10%, which of the following is the resulting percent change in the volume of cone ?

(a)  10% decrease    (b)  12% decrease 

(c)  18.4% decrease     (d) 29.6% decrease

Solution

Problem 7 :

The area of the trapezoid above can be found using the formula (1/2)h(b₁+b₂). If lengths of BC and AD are halved and height is doubled, how would the area of the trapezoid change ?

(a)  The are would be increased by 50%

(b)  The area would stay the same

(c)  The area would be decreased by 25%

(d) The area would be decreased by 50%

Solution

Problem 8 :

Calvin has a sphere that is four times bigger than the one Kevin has in terms of volume. The radius of Calvin's sphere is how many times greater in length than the radius of Kevin's sphere (rounded to the nearest hundredth) 

(a)  1.44    (b)  1.59    (c)  1.67    (d) 2.00

Solution

Problem 9 :

If a number p increased by 120 percent equals a number q decreased by 20 percent, which of the following is true?

(a)  q = (5/2)p   (b)  q = (11/4)p   

(c)  q = (7/2)p    (d) q = (15/4)p

Solution