PROBLEMS ON PERCENTAGE INCREASE AND DECREASE FOR SAT

Problem 1 :

The sum of three numbers is 1133. One of the numbers, k, is 20% greater than the sum of the other two numbers. What is the value of k?

A) 453     B) 515     C) 618     D) 906

Solution :

Sum of three numbers = 1133

Let k, x and y are three numbers.

k + x + y = 1133

x + y = 1133 - k

k = 120% of (x + y)

Applying the value of x + y above, we get

k = 120% of (1133 - k)

k = 1.20(1133 - k)

k = 1360 - 1.20k

k + 1.20k = 1360

2.2k = 1360

k = 1360/2.2

k = 618.18

So, option B is correct.

Problem 2 :

A rectangle was altered by increasing its length by 20% and decreasing its width by p percent. If these changes decreased the area of the rectangle by 40%, what is the value of p?

A) 10      B) 15      C) 25     D) 50

Solution :

Let l be the length and w be the width of the rectangle.

New length = 0.80 of l

width = (100 - p)% of w

Area of the rectangle = l x w

0.80 l x (100 - p)% of w = 60% of lw

0.80 l x (100 - p)% of w = 0.60  lw

(100 - p)% of w = 0.60  lw / 0.80 l

((100 - p) / 100) w = 0.75 w 

(100 - p) w = 0.75w (100)

(100 - p)w = 75w

100 w - pw = 75 w

pw = 25w

p = 25

So, option C is correct.

Problem 3 :

A city planner estimates that the population of a certain small town will increase by 5% every 10 years. If the current population of the town is 10,000, which of the following expressions represents the population y years from now?

A) 10000(1.05)^ (𝑦/10)     B) 10000(.05)^(10𝑦)

C) 10000(0.95)^ (𝑦/10)       D) 10000(1.05)^(10𝑦)

Solution :

Population growth = P(1+r)^nt

= 10000 (1 + 0.05)^ (𝑦/10) 

Problem 4 :

A high school administrator is giving a civics quiz to all the juniors in her school to prepare them for an upcoming election. There are 420 juniors in the school, and she gives them the quiz over two days. On the first day, she gives the quiz to 210 juniors, and 160 of them answer the first question correctly. On the second day, she gives the quiz to the remainder of the students, and j answer the first question correctly. If more than 80% of all the juniors answered the first question correctly, which of the following inequalities best describes the possible values of j?

A) 𝑗 > 0.8(420−160),𝑤ℎ𝑒𝑟𝑒 𝑗 ≤ 210

B) 𝑗 > 0.8(420+160),𝑤ℎ𝑒𝑟𝑒 𝑗 ≤ 210

C) 𝑗 −160 >0.8(420),𝑤ℎ𝑒𝑟𝑒 𝑗 ≤ 210

D) 𝑗 +160 >0.8(420),𝑤ℎ𝑒𝑟𝑒 𝑗 ≤ 210

Solution :

Total number of juniors in the school = 420

Number of juniors attending = 210

Number of juniors answered correctly = 160

Remaining number of questions = 420 - 210

= 210

out of 210, j answered correctly.

j > 0.80(420 - 160)

Where 160 students answered correctly, so the difference will be answering correctly on the second day.

So, option A is correct.

Problem 5 :

Cam opened a bank account that earns 2 percent interest compounded annually. His initial deposit was $1500, and he uses the expression $1500(𝑟)^𝑥 to find the value of the account after x years.

i)  What is the value of r in the expression?

Solution :

Initial deposit = $1500

Formula for compound interest = a(1+r)^nt

Rate of interest = 2%

r = 1 + 2%

= 1 + 0.02

= 1.02

So, the value of r is 1.02.

Problem 6 :

The population of Greenville increased by 7% from 2015 to 2016. If the 2016 population is k times the 2015 population, what is the value of k ?

A) 0.07    B) 0.7    C) 1.07    D) 1.7

Solution :

Let x be the population in 2016.

In 2016, the population is = 107% of x

kx = 107% of x

kx = 1.07 x

k = 1.07

So, the value of k is 1.07.