A Tricky 'n' Easy Maths Quiz! (4)

Answer: 3.33%

There is a formula for such questions which is:

Percentage Error = Actual Error/True Value * 100

The actual error is 62 - 60 or 2 degrees. Plug in the numbers and we get:

Percentage error = 2/60 * 100 = 3.33% (correct to 3 sig. fig.)

Answer: 45

Such questions are logical problems and are called group questions which involve Venn Diagrams. There is a formula for such questions which is (in this case):
Total Number of Children = Number of children who like Maths + Number of Children who like English - Number of children who like both subjects + Number of children who like neither or x = Number of children who like only Maths + Number of children who like only English + Number of children who like both subjects + Number of children who like neither subject We know that 7 like both subjects and 17 like neither, but we do not know how many like ONLY Maths and how many like ONLY English. It's apparent that the number of students who like only Maths is the number of students who like both English and Maths subtracted from the number of students who like Maths. Similarly, the number of students who like only English is the number of students who like both subtracted from the number of students who like English. So, Number of students who like only Maths = 10 - 7 = 3, and Number of students who like only English = 25 - 7 = 18. Therefore, x = 3 + 18 + 7 + 17 = 45.
Plug in the numbers and we get:

10 + 25 - 7 + 17 = 45.

Answer: £48.12

The dividend on £1 is 15 p. Therefore, the dividend on £320.80 or 32080 pence (320.80 * 100) will be (32080*15)pence or 4812 pence, which is £48.12 (4812/100).

Answer: 14

Let the number of mangoes be m and let the number of grapes be g. The problem reads: "There are 8 more mangoes than grapes". Therefore, m can also be written as 8 + g, because the number of grapes plus eight is equal to the number of mangoes. Now we can form an equation and solve:

m + g = 20

8 + g + g = 20

8 + 2g = 20

2g = 20 - 8

2g = 12

g = 12/2

g = 6.

Therefore, m = 8 + 6 = 14.

There are 14 mangoes in the box.

Answer: 20/52 = 5/13

There are 12 face cards. Aces are not considered as face cards. There are 26 black cards, but half of the face cards are black and we have already included them, therefore, the probability of drawing a card which is neither a face card nor a black card is:
(52 - [12 + 20])/52 = (52 - 32)/52 = 20/52 = 5/13.

Answer: 93

Let the tens digit be x and let the unit digit be y. Then, the value of the number is 10x + y because (for example) 23 is equal to 2 * 10 + 3 where 2 is the tens digit and 3 is the unit digit (Aha! That's why I gave that hint!). When the digits are interchanged (reversed), the value of the number is 10y + x.
Therefore:

(10x+y) - (10y+x) = 54

10x + y - 10y - x = 54

9x - 9y = 54.

If you divide the equation throughout by 9, we get

x - y = 6.

We know that the tens digit is three times the unit digit, therefore

x = 3y.

3y - y = 6

2y = 6

y = 6/2

y = 3.

Since x = 3y and y = 3, x = 9.

The number is 93.

The number with the digits reversed is 39 (93 - 39 = 54).

Notice that the ten digit in 93 (9) is three times the unit digit (3).

Answer: 16

64^(2/3) means sixty-four to the power of two-thirds. q^(m/n) means the 'n'th root of q raised to the power m. Similarly, 64^(2/3) means the cube root of 64 (namely 4) raised to the power of 2, which yields 16.

Answer: 200 mm

The depth of one box will be:
3/15 m = 1/5 m = 0.2 m = 20 cm (1 m = 100 cm, therefore 0.2 m is equal to 0.2*100 cm) = 200 mm (1 cm = 10 mm, therefore 20 cm is equal to 20*10 mm). 0.2 m = 0.0002 km (1 km = 1000 m, therefore 1 m is 1/1000 of a kilometre).

Answer: 729

A cube has six faces which are all squares. The formula for finding the area of a square is l^2 (or length squared). Therefore:
Area = l^2

81 = l^2
l = sq. rt. of 81
l = 9 cm.

Now we know that the cube measures 9 cm on an edge. The formula for finding the volume of a cube is l^3 (or length cubed). Therefore its volume will be:

Volume = l^3

Volume = 9^3

Volume = 729 cm^3.

Answer: 21.0 m^3

296 cm = 2.96 m (1 m = 100 cm, therefore 1 cm is equal to 1/100 of a metre).

If the diameter is 2.96 m, the radius will be 2.96/2 m or 1.48 m (This is because the radius of a circle is half the diameter of the circle).

The formula for calculating the volume of a cylinder is:

pi r^2 h.

Therefore:

3.14 * 1.48 * 1.48 * 3.054 = 21.0 m^3 (correct to 3 sig. fig.)

cm^2 is a unit of area, and 2100 cm^3 is equal to 0.0021 m^3 (1 m = 100 cm, therefore 1 m^3 = 100 * 100 * 100 cm or 1000000 cm. 1 cm^3 = 1/1000000 of a cubic metre.)

Answer: 49/50

2y metres = 200y centimetres (1 metre = 100 cm, therefore 2y metres is equal to 2y*100 cm).

If I cut a piece of length 4y centimetres from a stick measuring 200y centimetres long, 196y centimetres of stick is left.

If we express this as a fraction we get:

196y/200y = 196 * y/200 * y = 196/200 = 49/50

Answer: 28 degrees

([dozen sixes] + 80) degrees = ([12*6] + 80) degrees = (72 + 80) degrees = 152 degrees.

Supplementary angles are two angles on a straight line which add up to 180 degrees. If one of them is 152 degrees, the other one is 180 degrees - 152 degrees or 28 degrees.

Notice that 'dozen sixes' can also be written as 'twelve sixes'.

Answer: 330

We know that:

Percentage profit = Actual profit/Original price * 100.

Using this formula, we can solve the problem:

10% = x/300 * 100
10 = x/3
x = 10*3
x = £30.
Now we know that the man has to sell the cuckoo clock to make a profit of £30. Therefore, he has to sell it for £300 + £30 or £330.

Answer: 900

There are several ways of solving this problem. If 5/8 of the children in a school are boys, then 3/8 of the children in that school are girls. (5/8 + 3/8 = 1)
3/8 of 2400 = 3/8 * 2400 = 900
Therefore, there are 900 girls and 1500 boys (2400 - 900) in the school.

Answer: 9

We know that the average is equal to the sum of all values divided by the number of values. His total mark after 8 subjects was:
average = sum of all values / number of values
54 = x / 8
x = 54*8 = 432
Therefore, his total mark after 8 subjects was 432.
His total mark after 9 subjects was:
Average = Sum of all values / Number of values
49 = x / 9
x = 49*9 = 441
Therefore, his total mark after 9 subjects was 441.
Score in 9th subject = Total mark after 9 subjects - Total mark after 8 subjects
Score in 9th subject = 441 - 432
Score in 9th subject = 9.
Therefore, he scored 9 marks in Maths.
This was a nice question to end with, wasn't it? Maths is my favourite subject and if you have any trouble with the above questions, do not hesitate to ask me. I will appreciate all your corrections, suggestions and ratings. Every subject has its own difficulties and I hope you know what the difficulties of Maths are like, and I hope you have learnt something new. Bye bye till next time to face more Maths questions! ;)