Answer to Q24
A whole block is balance on a scale with ⅓kg weight plus ⅓ of another identical block. What is the weight of the whole block?
Let weight of whole block be x
Then we can rewrite the question as: x = ⅓ + ⅓x
Collecting like terms, x - ⅓x = ⅓
That can be rewritten as (3x -x) ÷ 3 = ⅓
Cross multiplying: 3(2x) = 3
6x = 3
Dividing through by 6
x = 3 ÷ 6
x = ½
Answer: ½
A whole block is balance on a scale with ⅓kg weight plus ⅓ of another identical block. What is the weight of the whole block?
Let weight of whole block be x
Then we can rewrite the question as: x = ⅓ + ⅓x
Collecting like terms, x - ⅓x = ⅓
That can be rewritten as (3x -x) ÷ 3 = ⅓
Cross multiplying: 3(2x) = 3
6x = 3
Dividing through by 6
x = 3 ÷ 6
x = ½
Answer: ½
Answer to Q25
A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sistes are there in the family?
This can actually be solved using mathematical equations. It's mosre or less like word problem!
Let the number of girls be x
Let the number of boys be y
A girl has as many brothers as sisters
So, x - 1 = y
each brother has only half as many brothers as sisters
So, y - 1 = x ÷ 2 we can rewrite this as 2(y - 1) = x
Putting x = 2(y - 1) into x - 1 = y
2y - 2 - 1 = y
Collecting like terms
2y - y = 2 + 1
y = 3
Putting y = 3 into x - 1 = y
x - 1 = 3
x = 3 + 1 = 4
So, x = 4; y = 3
Answer: 4 sisters, 3 brothers
A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sistes are there in the family?
This can actually be solved using mathematical equations. It's mosre or less like word problem!
Let the number of girls be x
Let the number of boys be y
A girl has as many brothers as sisters
So, x - 1 = y
each brother has only half as many brothers as sisters
So, y - 1 = x ÷ 2 we can rewrite this as 2(y - 1) = x
Putting x = 2(y - 1) into x - 1 = y
2y - 2 - 1 = y
Collecting like terms
2y - y = 2 + 1
y = 3
Putting y = 3 into x - 1 = y
x - 1 = 3
x = 3 + 1 = 4
So, x = 4; y = 3
Answer: 4 sisters, 3 brothers
Answer to Q26
If x is an integer and 2.134(10^x) is less than 210,000. What is the greatest possible value for x?
Remember the logarithm rule: if x^y = z then logz ÷ log x = y!
Our question says 2.134 x 10^x < 210,000
10^x < 210,000 ÷ 2.134
10^x < 98,406.748
So following our logarithm rule, x < log 98,406.748 ÷ log 10
x < 4.99
So flooring 4.99 = 4
Answer: 4
If x is an integer and 2.134(10^x) is less than 210,000. What is the greatest possible value for x?
Remember the logarithm rule: if x^y = z then logz ÷ log x = y!
Our question says 2.134 x 10^x < 210,000
10^x < 210,000 ÷ 2.134
10^x < 98,406.748
So following our logarithm rule, x < log 98,406.748 ÷ log 10
x < 4.99
So flooring 4.99 = 4
Answer: 4
Answer to Q27
John spent 40% of his earnings last month on rent and 30% less than what he spent on rent to purchase a new dishwasher. What percent of last month's earnings did John have left over?
Let John's salary be x
Rent = 40% of x = 40 ÷ 100 x = 0.4x
Dishwasher = 70% of rent (i.e. 30% less than) = 70 ÷ 100 (0.4x) = 0.7 x 0.4x = 0.28x
Total money spent = 0.4x + 0.28x = 0.68x
So John spent 0.68x100% of his salary = 68%
What is remaining = 100% - 68% = 32%
Answer: 32%
John spent 40% of his earnings last month on rent and 30% less than what he spent on rent to purchase a new dishwasher. What percent of last month's earnings did John have left over?
Let John's salary be x
Rent = 40% of x = 40 ÷ 100 x = 0.4x
Dishwasher = 70% of rent (i.e. 30% less than) = 70 ÷ 100 (0.4x) = 0.7 x 0.4x = 0.28x
Total money spent = 0.4x + 0.28x = 0.68x
So John spent 0.68x100% of his salary = 68%
What is remaining = 100% - 68% = 32%
Answer: 32%
Answer to Q28
What word in the English language does the following: the first two letters signify a male, the first three letters signify a female, the first four letters signify a great man, while the entire world signifies a great woman. What is the word?
Clue 1: first two words signify a male (HE)
Clue 2: first three words signify a female (HER)
Clue 3: first four words signify a great male (HERO)
Clue 4: whole word signify a great woman (HEROINE)
Not heroin, heroin is a drug!
Answer: HEROINE
What word in the English language does the following: the first two letters signify a male, the first three letters signify a female, the first four letters signify a great man, while the entire world signifies a great woman. What is the word?
Clue 1: first two words signify a male (HE)
Clue 2: first three words signify a female (HER)
Clue 3: first four words signify a great male (HERO)
Clue 4: whole word signify a great woman (HEROINE)
Not heroin, heroin is a drug!
Answer: HEROINE
Answer to Q29
It is possible for an English word to have three consecutive double letters? If it's possible, what is that word?
Yes it is possible and there are several words that fit this e.g. Bookkeeper, Bookkeeping, Tattooee, Balloonning, etc
Committee is however not one as the m and t are not consecutive.
It is possible for an English word to have three consecutive double letters? If it's possible, what is that word?
Yes it is possible and there are several words that fit this e.g. Bookkeeper, Bookkeeping, Tattooee, Balloonning, etc
Committee is however not one as the m and t are not consecutive.
Answer to Q30
How can four be twice of five?
Answer: The number of their digits when written in Roman Numerals
Four - IV (2 digits)
Five - V (1 digit)
How can four be twice of five?
Answer: The number of their digits when written in Roman Numerals
Four - IV (2 digits)
Five - V (1 digit)
Answer to Q31
How can you get 30 by placing the balls into the boxes in the following equation?
Answer: 13 + 11 + 6 (that is not a 9 ball but a 6 ball facing up side down)
How can you get 30 by placing the balls into the boxes in the following equation?
Answer: 13 + 11 + 6 (that is not a 9 ball but a 6 ball facing up side down)
Answer to Q32
Please use all the numbers and equation marks only once and do the correct equation.
2345+=
Answer: 5 + 4 = 3²
Please use all the numbers and equation marks only once and do the correct equation.
2345+=
Answer: 5 + 4 = 3²
Answer to Q33
It's dark. You have ten grey boxes and ten blue boxes and you want a pair of the same colour. All boxes are exactly the same except for their colour. How many boxes would you need to take with you to ensure you had at least a pair?
To ensure you select a pair of boxes of the same colour, the total number of boxes you need to select is 3 because with 3 boxes you get 3 grey boxes or 3 blue boxes or 2 grey boxes and 1 blue box or 1 grey box and 2 blue boxes. Either ways, you have atleast 2 boxes of same colour
Answer: 3
It's dark. You have ten grey boxes and ten blue boxes and you want a pair of the same colour. All boxes are exactly the same except for their colour. How many boxes would you need to take with you to ensure you had at least a pair?
To ensure you select a pair of boxes of the same colour, the total number of boxes you need to select is 3 because with 3 boxes you get 3 grey boxes or 3 blue boxes or 2 grey boxes and 1 blue box or 1 grey box and 2 blue boxes. Either ways, you have atleast 2 boxes of same colour
Answer: 3
Answer to Q34
At a party, everyone shook hands with everybody else. There were 4005 handshakes. How many people were at the party?
The number of handshakes between people is always the sum of 1+2+3+...+(n-1). n = number of people. Say there are 5 people, handshake between them will be 1+2+3+4 = 10 (try that with your friends 😀)
The sum of 1 to n of any number is (n(n+1))÷2. For example 1+2+3+4+5 = 15 and (5(5+1))÷2 = (5*6)÷2 = 15
So, to find the number of people at the party
(n(n+1))÷2 = 4005
Cross multiplying:
n(n+1) = 4005x2 = 8010
Expanding the bracket:
n² + n = 8010
n² + n - 8010 = 0
Solving that using the Almighty Formula (I don't think I need to go into that details)
n = 90 and -89
Ofcourse there can be negative people at the party so answer is 90 people
Answer: 90
At a party, everyone shook hands with everybody else. There were 4005 handshakes. How many people were at the party?
The number of handshakes between people is always the sum of 1+2+3+...+(n-1). n = number of people. Say there are 5 people, handshake between them will be 1+2+3+4 = 10 (try that with your friends 😀)
The sum of 1 to n of any number is (n(n+1))÷2. For example 1+2+3+4+5 = 15 and (5(5+1))÷2 = (5*6)÷2 = 15
So, to find the number of people at the party
(n(n+1))÷2 = 4005
Cross multiplying:
n(n+1) = 4005x2 = 8010
Expanding the bracket:
n² + n = 8010
n² + n - 8010 = 0
Solving that using the Almighty Formula (I don't think I need to go into that details)
n = 90 and -89
Ofcourse there can be negative people at the party so answer is 90 people
Answer: 90
Answer to Q35
You can only amend once and it can be any of the digits or operators to correct this equation
5 + 5 + 5 + 5 = 555
Answer: Change one of the + to 4 e.g 5 + 5 + 545 = 555
You can only amend once and it can be any of the digits or operators to correct this equation
5 + 5 + 5 + 5 = 555
Answer: Change one of the + to 4 e.g 5 + 5 + 545 = 555
Answer to Q36
A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
Using common sense, you can answer this correctly. If he sent more of large boxes and 8 large boxes can be placed in a carton. If he sent 96 boxes, the number of boxes he sent will be lesser than 96 ÷ 8 = 12. The only option given that is less that 12 is 11
Answer: 11
A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
Using common sense, you can answer this correctly. If he sent more of large boxes and 8 large boxes can be placed in a carton. If he sent 96 boxes, the number of boxes he sent will be lesser than 96 ÷ 8 = 12. The only option given that is less that 12 is 11
Answer: 11
Answer to Q38
If 2 squares are 8, then 1 square is 4
If 2 circles plus 1 square are 14, then 2 circles are 14 - 4 = 10. Then 1 circle is 5
If 1 triangle and 1 circle are 11, then 1 triangle is 11 - 5 = 6
Answer: 6
If 2 squares are 8, then 1 square is 4
If 2 circles plus 1 square are 14, then 2 circles are 14 - 4 = 10. Then 1 circle is 5
If 1 triangle and 1 circle are 11, then 1 triangle is 11 - 5 = 6
Answer: 6
Answer to Q39
The clue is the number of squares in the main square. In the first diagram there are 4 smaller squares and the 4 squares makes one big square making 5 squares
In the second diagram, there are 9 small squares, these 9 squares makes 1 big square, making 10 altogether.
But if you pick 4 of this 9 squares, they also make 1 square and you can count additional 4 squares this way.
Answer: 9 + 1 + 4 = 14
The clue is the number of squares in the main square. In the first diagram there are 4 smaller squares and the 4 squares makes one big square making 5 squares
In the second diagram, there are 9 small squares, these 9 squares makes 1 big square, making 10 altogether.
But if you pick 4 of this 9 squares, they also make 1 square and you can count additional 4 squares this way.
Answer: 9 + 1 + 4 = 14
Answer to Q40
If A + B = 60 and A - B = 40, then what is A ÷ B?
A + B = 60 so, B = 60 - A
A - B = 40 so, A - (60 - A) = 40
A - 60 + A = 40
2A = 40 + 60 = 100
A = 100 ÷ 2 = 50
And, B = 60 - A = 60 - 50 = 10
So, A ÷ B = 50 ÷ 10 = 5
Answer: 5
If A + B = 60 and A - B = 40, then what is A ÷ B?
A + B = 60 so, B = 60 - A
A - B = 40 so, A - (60 - A) = 40
A - 60 + A = 40
2A = 40 + 60 = 100
A = 100 ÷ 2 = 50
And, B = 60 - A = 60 - 50 = 10
So, A ÷ B = 50 ÷ 10 = 5
Answer: 5
Answer to Q41
If 13, 18 = 31 and 7, 25 = 32 and 12, 30 = 42. What is 26, 13?
Simple, the comma represents addition. 13 + 18 = 31, etc
Answer: 26, 13 = 26 + 13 = 39
If 13, 18 = 31 and 7, 25 = 32 and 12, 30 = 42. What is 26, 13?
Simple, the comma represents addition. 13 + 18 = 31, etc
Answer: 26, 13 = 26 + 13 = 39
Answer to Q42
8 - 8 ÷ 4 x 3
Questions like this are always to test your understanding of BODMAS rule (Bracket, Order, Division, Multiplication, Addition, Substraction). If you don't follow the BODMAS rule, you will arrive at the wrong answer.
Bracket: we don't have any bracket
Order: we don't have any order
Division: we have 8 ÷ 4 = 2
so our equation becomes 8 - 2 x 3
Multiplication: we now have 2 x 3 = 6
so our equation becomes 8 - 6 = 2
Answer: 2
8 - 8 ÷ 4 x 3
Questions like this are always to test your understanding of BODMAS rule (Bracket, Order, Division, Multiplication, Addition, Substraction). If you don't follow the BODMAS rule, you will arrive at the wrong answer.
Bracket: we don't have any bracket
Order: we don't have any order
Division: we have 8 ÷ 4 = 2
so our equation becomes 8 - 2 x 3
Multiplication: we now have 2 x 3 = 6
so our equation becomes 8 - 6 = 2
Answer: 2