Problem 1 :
The original price of the suit is $1000. A sales man decides to discount it by 30%. Later on the manager decides to give a 15% discount off the salesman's price. What is the final price of the suit ?
a) 350 b) 485 c) 550 d) 595
Solution :
Original price of the suit = $1000
Discount = 30% of the original price
Which means, we dont have to pay 100% of the money and it is enough to pay (100 - 30)%, which is 70% of the original amount.
= 70% of 1000
= 0.70(1000)
= 700
Amount after manager's offer = (100 - 15)% of 700
= 85% of 700
= 0.85(700)
= 595
So, the final price of the suit is $595.
Problem 2 :
A large group of friends go out to dinner at a restaurant which charges them a service fee 12 percent of the original price of the meal. After this fee is factored in, the group uses the coupon to get 25% off the total. In the end, what percent discount did the group receive off the original price ?
a) 13% b) 16% c) 18% d) 20%
Solution :
Let x be the original price of the meal.
112% of x = amount paid after service fee
After using 25% of coupon, amount to be paid
= 75% of 112% of x
= 0.75 (1.12x)
= 0.84x
= 84% of x
After the discount = 100 - 84
= 16
So, the group will receive 16% discount.
Problem 3 :
The difference between two numbers is 30. One of the numbers x is 20% less than the other number, find the value of x?
Solution :
Let x and y be the two numbers.
One number x = 80% of y
y - x = 30
y - 0.80y = 30
0.20y = 30
y = 30/0.20
y = 150
x = 0.80y
x = 0.80(150)
x = 120
So, the required number is 120.
Problem 4 :
There are 50 tennis balls, 20 of which are blue in a container. After x blue tennis balls are removed, 25% of the tennis balls in the container are blue. What is the value of x ?
Solution :
Total number of balls = 50
Number of clue balls = 20
After removing x blue balls,
number of balls in total = 50 - x
number of blue balls = 20 - x
(20 - x) / (50 - x) = 25/100
(20 - x) / (50 - x) = 1/4
4(20 - x) = 1(50 - x)
80 - 4x = 50 - x
80 - 50 = -x + 4x
30 = 3x
x = 10
So, the value of x is 10.
Problem 5 :
During one season, a baseball player managed to hit 25% of the balls pitched at him. Of the balls he hit, 5 percent were home runs. Which of the following expresses the estimated number of home runs this player would hit if n balls were pitched at him ?
a) (0.25+0.05)n b) (0.25) (0.05)n
c) n/(0.25)(0.5) d) (1.25)(1.05n)
Solution :
Number of balls pitched at him = n
25% of n = the number of balls managed to hit
Number of home runs = 5% of (25% of n)
= 0.05 (0.25n)
So, option b is correct.
Problem 6 :
Gillian scored an 84 on her midterm and a 94 on her final. which of the following best approximates the percent increase in her score from her midterm to her final ?
a) 10.6% b) 11.9% c) 12.1% d) 15.5%
Solution :
Old score = 84
New score = 94
Since the new score is greater than the old score, percentage increase happened.
Percentage increase
= { (New value - old value) / old value } x 100%
= {(94 - 84) / 94} x 100%
= (10/94) x 100%
= 0.106 x 100%
= 10.6%
So, option a is correct.
Problem 7 :
A wine manufacturer produced x bottles of wine in its first production run. In its second run, it produced 35% less. If the manufacturer produced 3900 bottles in its second run, what is the value of x ?
a) 5265 b) 5750 c) 5830 d) 6000
Solution :
Number of bottles produced in the second run = 3900
Number of bottles produced in the first run = x
Number of bottles produced in the second run = 65% of x
3900 = 0.65 x
x = 3900 / 0.65
x = 6000
Number of bottles produced in the first run = 6000.
Problem 8 :
At the start of the semester, Andrew could swim a mile in 16 minutes. At the end of the semester he could swim a mile in 12 minutes. What is the percent decrease (to the nearest percent) in his time from the start to the end of the semester ?
a) 20% b) 25% c) 33% d) 40%
Solution :
Number of minutes taking last time = 16
Number of minutes he is taking at the end of the semester = 12
Percentage decrease happened.
Percentage decrease = {(16 - 12) / 16 } x 100%
= (4/16) x 100%
= (1/4) x 100%
= 25%
So, option b is the answer.
Problem 9 :
The table below shows the number of vowels and consonants in 4 different languages.
Based on the table, vowels make up approximately 38% of the alphabet in which language ?
a) Danish b) German c) Greek d) Portuguese
Solution :
Percentage of vowels in Danish = (32/52) x 100%
= 0.6153 x 100%
= 61.5%
Percentage of vowels in German = (17/42) x 100%
= 0.4047 x 100%
= 40.4%
Percentage of vowels in Greek = (5/23) x 100%
= 0.2173 x 100%
= 21.7%
Percentage of vowels in Portuguese = (14/37) x 100%
= 0.3783 x 100%
= 37.8%
Approximately 38%.
So, answer is option d.
Problem 10 :
From 2012 to 2013, the total budget for all four schools decreased by approximately what percent ?
Solution :
By observing the bar graph,
In 2012 = 35 + 60 + 80 + 75
= 250
In 2013 = 50 + 35 + 60 + 50
= 195
Percentage of decrease = { (250 - 195) / 250 } x 100%
= (55 / 250) x 100%
= 0.22 x 100%
= 22%
So, the percentage decrease is 22%.
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