Question 1 :
In a cricket team of 11 players, the average age of 4 players is 17, the average of 3 players is 18 and the average of 2 players is 19. The average age of the whole team is 18. One of the players is aged 22. Find the age of the last player.
Solution :
Average of 11 players = 18 years
Total age of 11 players = 18 x 11
= 198
Average of 4 players = 17 years
Total age of 4 players = 4 x 17
= 68
Average of 3 players = 18 years
Total age of 3 players = 3 x 18
= 54
Average of 2 players = 19 years
Total age of 2 players = 2 x 19
= 38
Age of another player = 22 years
Total age of 10 players = 68 + 54 + 38 + 22
= 182 years
Age of last player = 198 - 182
= 16 years
Therefore the required age = 16 years.
Question 2 :
A fruit merchant bought 1200 mangoes for $1000.300 fruits went bad. He sold fruits at $18 per dozen, and the bad fruits at $9 per dozen. Find his total gain or loss per cent in the transaction.
Solution :
Cost price of the mangoes = $1000
Number of good fruits = 900
Number of dozens of good fruit = 900/12
= 75 dozens
Selling price of 1 dozen = $18
Selling price of 75 dozens = 75 x 18
= 1350
Number of bad fruits = 300
Number of dozens of bad fruits = 300/12
= 25
Selling price of 1 dozen bad fruit = $9
Selling price of 25 dozens of bad fruits = 9 x 25
= $225
Total selling price = 1350 + 225
= $1575
Profit = Selling price - Cost price
= 1575 - 1000
= $575
Profit percent = (profit amount/cost price) x 100
= (575/1000) x 100
= 57.5 %
Question 3 :
Walking at a constant rate of 8 kilometers per hour, Juan can cross a bridge in 6 minutes. What is the length of the bridge in meters? (1 kilometer = 1000 meters)
A. 480 B. 600 C. 720 D. 750 E. 800
Solution :
Speed = 8 kilometer per hour
1 kilometer = 1000 meters
Converting speed into minutes
= 8 x (1000/60)
= 400/3
Time taken by Juan = 6 minutes
Length of bridge :
Time = distance / speed
Distance = time x speed
= 6 x (400/3)
= 2(400)
= 800 meters
Question 4 :
In order to qualify for the year-end tennis tournament, Sam must win at least 60 percent of his matches this year. To date, Sam has won 14 of his 18 matches. Of Sam’s 13 matches remaining in the year, what is the least number that he must win in order to qualify for the year-end tournament?
A. 4 B. 5 C. 6 D. 7 E. 8
Solution :
Total number of matches she plays in the year = 18 + 13
= 31 matches
In this she should win 60% of the matches
= 60% of 31
= (60/100) x 31
= 18.6
Number of matches she should win is 18.
So far, she won 14 matches. Then the number of matches yet to be played = 18 - 14
= 4 matches
So, option A is correct.
Question 5 :
Five years from now, Tatiana will be two years older than Frederico is now. If Frederico is currently thirteen, how old is Tatiana now?
A. 8 B. 10 C. 13 D. 15 E. 18
Solution :
Let x be Frederico's present age.
Five years from now, age of Tatiana = x + 2
Applying x = 13, then x + 2 will be 15.
So, option D is correct.
Question 6 :
In the Antares Corporation, 3/7 of the managers are female. If there are 42 female managers, how many managers in total are there?
A. 18 B. 24 C. 60 D. 66 E. 98
Solution :
Let x be the total number of managers.
3/7 of x = 42
3x/7 = 42
x = 42 (7/3)
x = 98
So, the total number of managers are 98.
Question 7 :
A company has 40 executives and 120 customer service representatives. If these are the only employees, what percentage of the employees are executives?
A. 20% B. 25% C. 33% D. 40% E. 80%
Solution :
Number if executives = 40
Number of customer service representatives = 120
Total number of employess = 40 + 120
= 160
percentage of executives = (40/160) x 100%
= (1/4) x 100%
= 25%
Question 8 :
If R = 10b2 and b = 5, then R =
A. 25 B. 50 C. 100 D. 250 E. 500
Solution :
R = 10b2
Applying b = 5
R = 10(5)2
R = 10(25)
R = 250
So, option D is correct.
Question 9 :
A prism with dimensions given in centimeters is shown below. If the volume of a prism is the area of a triangular base times the length of a rectangular base, what is the volume of this prism, in cubic cm?
A. 30 B. 40 C. 50 D. 60 E. 120
Solution :
Volume of prism = base area x height
base area = 1/2 x base x height
= 1/2 x 3 x 4
= 6 cm2
height of prism = 10 cm
volume of prism = 6 x 10
= 60 cm2
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