# The Dech Maths Challenge

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• 1.

• 2.

• 3.

### An airplane takes off from Murtala Muhammed International airport at 10am on Feb 7th, 2015. Given that the average speed of the airplane throughout the journey is 800 km/hr, and it travels a distance of 4800 km. At what time does the plane reach its destination?

• A.

4pm

• B.

4am

• C.

10pm

• D.

6pm

A. 4pm
Explanation
The airplane travels a distance of 4800 km at an average speed of 800 km/hr. To find the time it takes to reach the destination, we divide the distance by the speed: 4800 km / 800 km/hr = 6 hours. Since the plane takes off at 10am, it will reach its destination 6 hours later at 4pm.

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• 4.

### A vehicle has a 100 litre fuel tank capacity. If the vehicle consumes 10 litres per 100km, what is the maximum distance that can be covered by the vehicle on a full tank?

• A.

400 km

• B.

1,000 km

• C.

100 km

• D.

250 km

B. 1,000 km
Explanation
The maximum distance that can be covered by the vehicle on a full tank is 1,000 km. This is calculated by dividing the fuel tank capacity of 100 litres by the fuel consumption rate of 10 litres per 100 km. So, for every 100 km, the vehicle consumes 10 litres of fuel. Therefore, it can cover 1,000 km on a full tank of 100 litres.

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• 5.

### A company makes a pre-tax profit of \$10,000,000. If the corporate tax rate is 25%, how much tax will the company pay?

• A.

\$12,500,000

• B.

\$7,500,000

• C.

\$2,500,000

• D.

\$75,000

C. \$2,500,000
Explanation
The correct answer is \$2,500,000. To calculate the tax amount, we need to multiply the pre-tax profit by the tax rate. In this case, the pre-tax profit is \$10,000,000 and the tax rate is 25%. Multiplying these two values gives us \$2,500,000, which is the amount of tax the company will pay.

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• 6.

### A company makes a pre-tax profit of \$10,000,000. If the corporate tax rate is 25%, what is the company’s profit after tax?(This question tests your understanding of percentages)

• A.

\$2,500,000

• B.

\$12,500,000

• C.

\$100,000

• D.

\$7,500,000

D. \$7,500,000
Explanation
The corporate tax rate is 25%, which means that the company will pay 25% of its pre-tax profit as taxes. To calculate the profit after tax, we need to subtract the tax amount from the pre-tax profit. In this case, 25% of \$10,000,000 is \$2,500,000. Subtracting this amount from the pre-tax profit gives us \$7,500,000 as the company's profit after tax.

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• 7.

### A bag contains 40 balls. 11 red balls, 9 blue balls, 12 green balls and 8 yellow balls. If a single ball is selected at random from the bag, it will most likely be

• A.

A red ball

• B.

A blue ball

• C.

A yellow ball

• D.

A green ball

D. A green ball
Explanation
The bag contains the highest number of green balls (12) compared to any other color. Therefore, if a single ball is selected at random from the bag, it is most likely to be a green ball.

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• 8.

### A mobile app (application) is being downloaded onto a smartphone, if it takes 1 second to download 10% of the mobile application. Estimate the total time it takes to download the complete app?

• A.

10 seconds

• B.

100,000 seconds

• C.

1,000 seconds

• D.

10,000 seconds

A. 10 seconds
Explanation
If it takes 1 second to download 10% of the mobile application, it means that each 10% can be downloaded in 1 second. Since there are 10 parts of 10% in the complete app, it will take 1 second for each part. Therefore, it will take a total of 10 seconds to download the complete app.

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• 9.

### If Linda and Megan shared 8 pancakes in the ratio 1:3 respectively, how many pancakes did Megan receive?

• A.

6

• B.

1

• C.

3

• D.

4

A. 6
Explanation
Linda and Megan shared the pancakes in a ratio of 1:3. This means that for every 1 pancake Linda received, Megan received 3 pancakes. Since they shared a total of 8 pancakes, we can calculate Megan's share by dividing 8 by the sum of the parts in the ratio, which is 1+3=4. Therefore, Megan received 8/4=2 portions of the ratio. And since each portion represents 3 pancakes, Megan received a total of 2*3=6 pancakes.

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• 10.

### Bawo and Amole share sweets in a certain ratio. After sharing the sweets, Bawo has 10 sweets and Amole has 2 sweets. What is the ratio of the number of sweets received by Bawo to the number of sweets received by Amole?

• A.

5:1

• B.

2:3

• C.

9:8

• D.

4:1

A. 5:1
Explanation
Bawo received 10 sweets and Amole received 2 sweets. To find the ratio, we divide the number of sweets received by Bawo (10) by the number of sweets received by Amole (2). This gives us a ratio of 5:1, which means that Bawo received 5 times the number of sweets that Amole received.

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• 11.

### The locations of 3 houses in a neighbourhood are shown below. The shortest distance between house A & house B is 300 metres while the shortest distance between house B and house C is 500 metres, what is the shortest distance between house A & C? (Houses A, B & C lie on the vertices of the given right angle triangle below)

• A.

800 metres

• B.

350 metres

• C.

400 metres

• D.

200 metres

C. 400 metres
Explanation
The shortest distance between house A and house C can be found by adding the shortest distances between house A and house B (300 meters) and between house B and house C (500 meters). Therefore, the shortest distance between house A and house C is 300 meters + 500 meters = 800 meters.

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• 12.

### What percentage of 10 days is 24 hours?

• A.

10%

• B.

24%

• C.

15%

• D.

9%

A. 10%
Explanation
The question asks for the percentage of 24 hours in 10 days. To find this, we need to calculate the ratio of 24 hours to 10 days and then convert it to a percentage. Since there are 24 hours in a day, we can calculate the total number of hours in 10 days by multiplying 24 hours by 10 days, which equals 240 hours. Therefore, the percentage of 24 hours in 10 days is 10% (24 hours is 10% of 240 hours).

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• 13.

### The sum of two numbers is 12 and their product is 20. The two numbers are

• A.

5 & 7

• B.

6 & 8

• C.

4 & 8

• D.

2 & 10

D. 2 & 10
Explanation
The sum of two numbers is 12 and their product is 20. To find the two numbers, we can use a system of equations. Let's call the two numbers x and y. We know that x + y = 12 and xy = 20. From the first equation, we can solve for x in terms of y by subtracting y from both sides: x = 12 - y. Substituting this into the second equation, we get (12 - y)y = 20. Simplifying, we have 12y - y^2 = 20. Rearranging and factoring, we have y^2 - 12y + 20 = 0. Factoring further, we get (y - 10)(y - 2) = 0. Therefore, the two numbers are 2 and 10.

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• 14.

### What is the next number in the following sequence?2,5,8,11,....

• A.

14

• B.

12

• C.

13

• D.

15

A. 14
Explanation
The given sequence is increasing by 3 each time. Starting from 2, the next number would be 2 + 3 = 5. Then, 5 + 3 = 8, 8 + 3 = 11, and so on. Therefore, the next number in the sequence would be 11 + 3 = 14.

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• 15.

### What is the next number in the following sequence?1,5,13,29,......

• A.

42

• B.

45

• C.

61

• D.

69

C. 61
Explanation
The sequence follows a pattern where each number is obtained by multiplying the previous number by 2 and adding 3. Starting with 1, we have 1*2+3=5, 5*2+3=13, 13*2+3=29, and so on. Therefore, the next number in the sequence would be 29*2+3=61.

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• 16.

### What is the product of the numbers below?-1,-1 & -1

• A.

-1

• B.

-5

• C.

1

• D.

5

A. -1
Explanation
The product of the numbers -1, -1, and -1 is -1. When multiplying three negative numbers together, the result is negative. Since all three numbers are the same (-1), the product will also be -1.

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• 17.

### A pack of chocolate contains 50 individual chocolate bars. A basket contains 3 packs of chocolate. What is the total number of individual chocolate bars in 10 baskets?

• A.

150

• B.

500

• C.

1,500

• D.

5,000

C. 1,500
Explanation
There are 3 packs of chocolate in each basket, and each pack contains 50 individual chocolate bars. Therefore, the total number of individual chocolate bars in one basket is 3 packs x 50 bars = 150 bars. Since there are 10 baskets, the total number of individual chocolate bars in all 10 baskets is 10 baskets x 150 bars = 1,500 bars.

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• 18.

### In a certain women’s sports league, the current standings of the top 3 teams are shown below.Matches in the sport are such that, a win is rewarded with 5 points, a draw is rewarded with 2 points and a loss is rewarded with 0 points. At the conclusion of the league every team would have played 10 matches.What is the maximum possible points tally that team B can finish the league with?

• A.

42

• B.

45

• C.

50

• D.

48

B. 45
Explanation
Team B can finish the league with a maximum of 45 points. This can be achieved if they win all 10 matches, as each win is rewarded with 5 points. Since a win is the highest reward, maximizing the number of wins will result in the maximum possible points tally for Team B.

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• 19.

### In a certain women’s sports league, the current standings of the top 3 teams are shown below.Matches in the sport are such that, a win is rewarded with 5 points, a draw is rewarded with 2 points and a loss is rewarded with 0 points. By the end of the league every team would have played 10 matches.What is the maximum possible points tally that team C can finish the league with?

• A.

47

• B.

42

• C.

44

• D.

37

A. 47
Explanation
Team C can finish the league with a maximum possible points tally of 47. This can be achieved if they win all 10 matches, as each win is rewarded with 5 points. Since a win is the highest point reward, winning all matches would result in the maximum possible points tally for Team C.

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• 20.

### £50,000 is invested for 2 years. At the end of each year, the investor makes a 10% profit of the investment's value at the start of that year. How much does the investor have at the start of year 3?(Assume the £50,000 is invested at the start of year one)

• A.

£60,000

• B.

£50,000

• C.

£55,000

• D.

£60,500

D. £60,500
Explanation
At the end of year one, the investor makes a 10% profit on the initial investment of £50,000, resulting in a total of £55,000. At the end of year two, the investor again makes a 10% profit on the investment's value at the start of that year, which is £55,000. This adds £5,500 to the total, resulting in a final amount of £60,500 at the start of year three.

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• 21.

### In a certain women’s sports league, the current standings of the top 3 teams are shown below.Matches in the sport are such that, a win is rewarded with 5 points, a draw is rewarded with 2 points and a loss is rewarded with 0 points. By the end of the league every team would have played 10 matches. Team C has 2 matches left. 2 sample unique outcomes are shown below:Outcome 1: Win then DrawOutcome 2: Draw then WinHow many sets of unique outcomes will result in team C having the most points at the end?( Assume that team B will win its last game)

• A.

9

• B.

1

• C.

7

• D.

3

B. 1
Explanation
In both Outcome 1 and Outcome 2, Team C will have a total of 7 points by the end of the league. However, since Team B is assumed to win its last game, Team B will have a total of 8 points. Therefore, there is only one set of unique outcomes (Outcome 2) that will result in Team C having the most points at the end.

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• 22.

• A.

9

• B.

7

• C.

8

• D.

5

C. 8
• 23.

### Consider the statement below.y>2x+1The above statement means that the value of y must be greater than the value of (2 multiplied by x, plus 1)For which values of x & y is the statement above false?

• A.

x=3 & y=10

• B.

x=-12 & y=0

• C.

x=-10 & y=1

• D.

x=4 & y=8

D. x=4 & y=8
Explanation
The given statement y > 2x + 1 means that the value of y must be greater than 2 times the value of x, plus 1. In the case of x = 4 and y = 8, when we substitute these values into the statement, we get 8 > 2(4) + 1, which simplifies to 8 > 9. However, this is false because 8 is not greater than 9. Therefore, the statement is false for x = 4 and y = 8.

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• 24.

### A heavy metallic ball and a light feather are dropped from the top of a building at the same time, from the same height and with the same initial speed. The speed of both the ball and the feather are the same throughout the downward journey. For the described scenario which one of the following statements is true?

• A.

The metallic ball gets to the ground before the feather

• B.

The feather gets to the ground before the ball

• C.

The ball and feather get to the ground at the same instant

• D.

None of the above

C. The ball and feather get to the ground at the same instant
Explanation
The ball and feather experience the same acceleration due to gravity, regardless of their mass. Therefore, they both fall at the same rate and reach the ground at the same time. This is known as the equivalence principle and is demonstrated by Galileo's famous experiment at the Leaning Tower of Pisa.

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• 25.

### If the perimeter of a square is 8cm, what is the area of the square?

• A.

8 square centimeters

• B.

4 square centimeters

• C.

2 square centimeters

• D.

16 square centimeters

B. 4 square centimeters
Explanation
The perimeter of a square is the sum of all its sides. In this case, the perimeter is given as 8 cm. Since a square has all sides equal in length, each side of the square would be 8 cm divided by 4, which is 2 cm. The area of a square is calculated by multiplying the length of one side by itself. Therefore, the area of the square would be 2 cm multiplied by 2 cm, which equals 4 square centimeters.

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• 26.

### The perimeter of a rectangle is 30 cm. If the length of the rectangle is 10cm what is the area of the rectangle?

• A.

50 centimeters

• B.

300 square centimeters

• C.

3 square centimeters

• D.

50 square centimeters

D. 50 square centimeters
Explanation
If the perimeter of a rectangle is 30 cm and the length of the rectangle is 10 cm, we can find the width by dividing the perimeter by 2 and subtracting the length. In this case, the width would be (30/2) - 10 = 5 cm. To find the area of the rectangle, we multiply the length by the width, which is 10 cm * 5 cm = 50 square centimeters.

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• 27.

### The product of a positive number and a negative number is always negative?

• A.

True

• B.

False

A. True
Explanation
When multiplying a positive number by a negative number, the result will always be negative. This can be understood by considering the concept of multiplication as repeated addition. When we multiply a positive number by a negative number, we are essentially adding the positive number a certain number of times indicated by the magnitude of the negative number. Since we are adding a positive number a negative number of times, the result will be a negative number. Therefore, the statement "The product of a positive number and a negative number is always negative" is true.

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• 28.

### The sum of two negative numbers is not always negative?

• A.

True

• B.

False

B. False
Explanation
The sum of two negative numbers is always negative. When two negative numbers are added, the negative signs are combined, resulting in a larger negative value. Therefore, the statement "The sum of two negative numbers is not always negative" is incorrect.

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• 29.

### X is a positive integer e.g. 1,2,3,4 etcy is a positive integer greater than 1 e.g. 2,3,4,5 etc                                                  The result of x divided by 2y is greater than x?

• A.

True

• B.

False

B. False
Explanation
The statement is asking whether the result of x divided by 2y is greater than x. To determine if this is true or false, we can simplify the expression. Since y is a positive integer greater than 1, 2y will always be greater than y. Therefore, x divided by 2y will always be less than x. Hence, the answer is false.

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• 30.

### X is a positive integer e.g. 1,2,3,4,5 etcy is a positive integer greater than 1 e.g. 2,3,4,5 etcThe result of x multiplied by y is greater than x?

• A.

True

• B.

False

A. True
Explanation
The statement is true because when you multiply a positive integer (x) by a positive integer greater than 1 (y), the result will always be greater than x. This is because multiplying x by y essentially adds x to itself y times, resulting in a larger value.

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• 31.

### The profit after tax of a company is €85 million, if the corporate tax rate is 15%, what is the pre-tax profit of the company?

• A.

€ 100,000,000

• B.

€ 90,000,000

• C.

€ 195,000,000

• D.

€ 95,000,000

A. € 100,000,000
Explanation
The pre-tax profit of the company is €100,000,000. This can be calculated by dividing the after-tax profit by (1 - tax rate). In this case, the after-tax profit is €85,000,000 and the tax rate is 15%. So, €85,000,000 / (1 - 0.15) = €100,000,000.

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• 32.

### Imagine you buy groceries worth £30, at the checkout till you hand the attendant £40. Subsequently the attendant asks you to hand over an extra £10 so that he/she can give you your change exactly. How much change are you owed?

• A.

£20

• B.

£10

• C.

£30

• D.

£50

A. £20
Explanation
If you buy groceries worth £30 and hand the attendant £40, you initially have given £10 more than the cost of the groceries. The attendant asks for an extra £10 so that they can give you your change exactly. Therefore, you are owed £20 in change.

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• 33.

### On a certain day James drives to work at an average speed of 40 miles per hour, and drives back home from work at an average speed of 20 miles per hour. Given that James uses the same route to and from work, and that James spends a total of 3 hours commuting to and from work.How many miles did James cover whilst driving to work?

• A.

50 miles

• B.

40 miles

• C.

10 miles

• D.

60 miles

B. 40 miles
Explanation
James spends a total of 3 hours commuting to and from work. Since the average speed is given, we can use the formula Distance = Speed x Time. Let's assume the distance James drives to work is x miles. Therefore, the distance James drives back home is also x miles.

Using the formula, we can set up the equation x/40 + x/20 = 3.

To solve for x, we can multiply both sides of the equation by 40 to get rid of the denominators. This gives us x + 2x = 120.

Combining like terms, we have 3x = 120. Dividing both sides by 3, we find that x = 40.

Therefore, James covers 40 miles while driving to work.

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• 34.

### On a certain day James drives to work at an average speed of 40 miles per hour, and drives back home from work at an average speed of 20 miles per hour. Given that James uses the same route to and from work, and that James spends a total of 3 hours commuting to and from work.How much time did James spend driving back from work?

• A.

1 hour

• B.

30 minutes

• C.

45 minutes

• D.

2 hours

D. 2 hours
Explanation
James spends a total of 3 hours commuting to and from work, and since he drives at an average speed of 40 miles per hour on the way to work and 20 miles per hour on the way back, it means that the distance from his home to work is twice the distance from work to his home. Therefore, James spends 2 hours driving back from work.

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• 35.

### Using an exchange rate of 180 Naira per US dollar. How much Naira can one get with  \$10,000?

• A.

NGN 1,800,000

• B.

NGN 180,000

• C.

NGN 555.6

• D.

NGN 55.6

A. NGN 1,800,000
Explanation
With an exchange rate of 180 Naira per US dollar, one can get 1,800,000 Naira with \$10,000.

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• 36.

### If £1 is worth \$2, and \$1 is worth 100 Naira (NGN). How much Naira would one get for £500?

• A.

NGN 100,000

• B.

NGN 1,000,000

• C.

NGN 50,000

• D.

NGN 25,000

A. NGN 100,000
Explanation
If £1 is worth \$2 and \$1 is worth 100 Naira, then £500 would be worth 500 * 2 = \$1000. And since \$1 is worth 100 Naira, \$1000 would be worth 100 * 100 = NGN 100,000. Therefore, one would get NGN 100,000 for £500.

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• 37.

### If a barrel of oil costs \$100, how many barrels of oil can be bought with \$1,000,000?

• A.

10 barrels

• B.

10,000 barrels

• C.

1,000 barrels

• D.

100,000 barrels

B. 10,000 barrels
Explanation
If a barrel of oil costs \$100, then to find out how many barrels of oil can be bought with \$1,000,000, we divide \$1,000,000 by \$100. This gives us 10,000 barrels. Therefore, the correct answer is 10,000 barrels.

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• 38.

### If x is increased by 28% to give y, decreasing y by 28% will give x.(Where x & y are positive integers e.g. 1,2,3,4...)

• A.

True

• B.

False

B. False
Explanation
This statement is false because increasing x by 28% and then decreasing y by 28% will not necessarily give us back the original value of x. This is because the percentage increase and decrease do not cancel each other out. The final value of y after decreasing by 28% will be less than the original value of x.

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• 39.

### If the product of two numbers is a positive number, and the sum of the two numbers is a negative number. Which of the following is/are true?I)    Both numbers have opposite signs II)    Both numbers are negative numbersIII)    Both numbers are positive numbersIV)    Cannot say

• A.

II only

• B.

I only

• C.

III only

• D.

II & III

• E.

IV

A. II only
Explanation
If the product of two numbers is positive, it means that both numbers have the same sign (either both positive or both negative). If the sum of the two numbers is negative, it means that both numbers have opposite signs (one positive and one negative). Therefore, the only true statement is II only, which states that both numbers are negative.

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