Answer to Q122
15xy ÷ 3y can be rewritten as?
We are asked to simplify the above equation.
15 ÷ 3 = 5, so we can rewrite as 5xy ÷ y
xy ÷ y = x, so it becomes 5x
Answer: 5x
15xy ÷ 3y can be rewritten as?
We are asked to simplify the above equation.
15 ÷ 3 = 5, so we can rewrite as 5xy ÷ y
xy ÷ y = x, so it becomes 5x
Answer: 5x
Answer to Q123
Solve for y where 0.5y – 1.1 = 4.9
0.5y – 1.1 = 4.9
0.5y = 4.9 + 1.1 (sign changes when you move across your the equal)
0.5y = 6
Divide all through by 0.5
y = 6 ÷ 0.5
y = 6 ÷ ½
This can be rewritten as
y = 6 x 2 [a ÷ 1/b = a x b]
y = 12
Answer: 12
Solve for y where 0.5y – 1.1 = 4.9
0.5y – 1.1 = 4.9
0.5y = 4.9 + 1.1 (sign changes when you move across your the equal)
0.5y = 6
Divide all through by 0.5
y = 6 ÷ 0.5
y = 6 ÷ ½
This can be rewritten as
y = 6 x 2 [a ÷ 1/b = a x b]
y = 12
Answer: 12
Answer to Q124
Nine men went to a restaurant. Eight of them spent $6 each for their meals and the ninth man spent $4 more than the average expenditure of all nine men. What is the average expenditure?
Average simply is the sum of a set of data divided by the quantity of the data.
We know what 8 men spent which is $6 each
Let what the ninth man spent be = Y
Let the average of what the nine men spent be = Z
the ninth man spent $4 more than the average expenditure of all nine men
So, Y = Z + 4 (eqn 1)
average of what all nine men spent will then be
((6 x 8) + Y) ÷ 9 = Z
(48 + Y) ÷ 9 = Z
Multiply all through by 9
48 + Y = 9Z (eqn 2)
Put eqn 1 into eqn 2
48 + Z + 4 = 9Z
52 + Z = 9Z
52 = 9Z - Z
52 = 8Z
Z = 52 ÷ 8
Z = 6.5
So, average of the expenditure is $6.5
Answer: $6.5
Nine men went to a restaurant. Eight of them spent $6 each for their meals and the ninth man spent $4 more than the average expenditure of all nine men. What is the average expenditure?
Average simply is the sum of a set of data divided by the quantity of the data.
We know what 8 men spent which is $6 each
Let what the ninth man spent be = Y
Let the average of what the nine men spent be = Z
the ninth man spent $4 more than the average expenditure of all nine men
So, Y = Z + 4 (eqn 1)
average of what all nine men spent will then be
((6 x 8) + Y) ÷ 9 = Z
(48 + Y) ÷ 9 = Z
Multiply all through by 9
48 + Y = 9Z (eqn 2)
Put eqn 1 into eqn 2
48 + Z + 4 = 9Z
52 + Z = 9Z
52 = 9Z - Z
52 = 8Z
Z = 52 ÷ 8
Z = 6.5
So, average of the expenditure is $6.5
Answer: $6.5
Answer to Q125
The average age of a couple married four years ago was 25 years then. The average age of the family consisting of husband, wife and a child now is 20 years. What is the child’s present age?
Let the age of father 4 years ago be X
Let the age of mother 4 years ago be Y
The average age of a couple married four years ago was 25 years then.
So, (x + Y) ÷ 2 = 25
X + Y = 25 * 2
X + Y = 50 (eqn 1)
The average age of the family consisting of husband, wife and a child now is 20 years
Age of father after 4 years is then X + 4
Age of mother after 4 years is then Y + 4
Let age of child now be Z
So, ((X + 4) + (Y+4) + Z) ÷ 3 = 20
X + 4 + Y + 4 + Z = 20 * 3
X + Y + Z + 8 = 60
X + Y + Z = 60 - 8
X + Y + Z = 52 (eqn 2)
putting (eqn 1) into (eqn 2)
50 + Z = 52
Z = 52 - 50
Z = 2
Answer: 2 years
The average age of a couple married four years ago was 25 years then. The average age of the family consisting of husband, wife and a child now is 20 years. What is the child’s present age?
Let the age of father 4 years ago be X
Let the age of mother 4 years ago be Y
The average age of a couple married four years ago was 25 years then.
So, (x + Y) ÷ 2 = 25
X + Y = 25 * 2
X + Y = 50 (eqn 1)
The average age of the family consisting of husband, wife and a child now is 20 years
Age of father after 4 years is then X + 4
Age of mother after 4 years is then Y + 4
Let age of child now be Z
So, ((X + 4) + (Y+4) + Z) ÷ 3 = 20
X + 4 + Y + 4 + Z = 20 * 3
X + Y + Z + 8 = 60
X + Y + Z = 60 - 8
X + Y + Z = 52 (eqn 2)
putting (eqn 1) into (eqn 2)
50 + Z = 52
Z = 52 - 50
Z = 2
Answer: 2 years
Answer to Q126
A person sells a TV set at 35% loss. Had he sold it for $135 more, his loss would have been reduced by 15%. How much did he buy the TV?
Let the price of the TV = X
Let the amount he sold the TV = Y
A person sells a TV set at 35% loss
Y = (100% - 35%) of X
Y = (1 - 0.35) of X
Y = 0.65X (eqn 1)
Had he sold it for $135 more, his loss would have been reduced by 15%.
Y + 135 = ((100% - 35%) + 15%) of X
Y + 135 = (0.65 + 0.15) of X
Y + 135 = 0.8X (eqn 2)
How much did he buy the TV?
In short, what is X (A.K.A: find X 😂)
Put (eqn 1) into (eqn 2)
0.65X + 135 = 0.8X
135 = 0.8X - 0.65X
135 = 0.15X
X = 135 ÷ 0.15
X = 900
Answer: $900
A person sells a TV set at 35% loss. Had he sold it for $135 more, his loss would have been reduced by 15%. How much did he buy the TV?
Let the price of the TV = X
Let the amount he sold the TV = Y
A person sells a TV set at 35% loss
Y = (100% - 35%) of X
Y = (1 - 0.35) of X
Y = 0.65X (eqn 1)
Had he sold it for $135 more, his loss would have been reduced by 15%.
Y + 135 = ((100% - 35%) + 15%) of X
Y + 135 = (0.65 + 0.15) of X
Y + 135 = 0.8X (eqn 2)
How much did he buy the TV?
In short, what is X (A.K.A: find X 😂)
Put (eqn 1) into (eqn 2)
0.65X + 135 = 0.8X
135 = 0.8X - 0.65X
135 = 0.15X
X = 135 ÷ 0.15
X = 900
Answer: $900
Answer to Q127
If the sum of money is divided among ‘n’ children, each child will receive $60. If another child is added to the group and the amount is distributed again each child will receive $50. What is the sum of money to be distributed?
Let the money be = Y
If the sum of money is divided among ‘n’ children, each child will receive $60
Y ÷ n = 60
Y = 60n (eqn 1)
If another child is added to the group and the amount is distributed again each child will receive $50
Y ÷ (n+1) = 50
Y = 50 * (n+1)
Y = 50n + 50 (eqn 2)
putting (eqn 1) into (eqn 2)
60n = 50n + 50
60n - 50n = 50
10n = 50
n = 50 ÷ 10
n = 5
Remember "n" is the number of children, but the question says What is the sum of money to be distributed?. So what will are looking for is Y, not "n".
From (eqn 1)
Y = 60n
Y = 60 * 5
Y = 300
Answer: $300
If the sum of money is divided among ‘n’ children, each child will receive $60. If another child is added to the group and the amount is distributed again each child will receive $50. What is the sum of money to be distributed?
Let the money be = Y
If the sum of money is divided among ‘n’ children, each child will receive $60
Y ÷ n = 60
Y = 60n (eqn 1)
If another child is added to the group and the amount is distributed again each child will receive $50
Y ÷ (n+1) = 50
Y = 50 * (n+1)
Y = 50n + 50 (eqn 2)
putting (eqn 1) into (eqn 2)
60n = 50n + 50
60n - 50n = 50
10n = 50
n = 50 ÷ 10
n = 5
Remember "n" is the number of children, but the question says What is the sum of money to be distributed?. So what will are looking for is Y, not "n".
From (eqn 1)
Y = 60n
Y = 60 * 5
Y = 300
Answer: $300
Answer to Q128
Raul can do a piece of work in 20 days and Kate in 25 days. They work together for 5 days and then Kate leaves. In how many more days would Raul finish the work?
Raul can do a piece of work in 20 days
So, this means Raul works at the rate of = 1 ÷ 20 = 0.05 per day (equivalent of 5% per day)
and Kate in 25 days
and Kate works at the rate of = 1 ÷ 25 = 0.04 per day (equivalent of 4% per day)
They work together for 5 days and then Kate leaves
The percentage of work completed in that 5 days is (5% * 5) + (4% * 5) = 45% (or 0.45)
Remaining work = 100% - 45% = 55%
So, Raul does 5% of work per day and has 55% of work to complete, that will take him: 55% ÷ 5% = 11 days to complete
Answer: 11 days
Raul can do a piece of work in 20 days and Kate in 25 days. They work together for 5 days and then Kate leaves. In how many more days would Raul finish the work?
Raul can do a piece of work in 20 days
So, this means Raul works at the rate of = 1 ÷ 20 = 0.05 per day (equivalent of 5% per day)
and Kate in 25 days
and Kate works at the rate of = 1 ÷ 25 = 0.04 per day (equivalent of 4% per day)
They work together for 5 days and then Kate leaves
The percentage of work completed in that 5 days is (5% * 5) + (4% * 5) = 45% (or 0.45)
Remaining work = 100% - 45% = 55%
So, Raul does 5% of work per day and has 55% of work to complete, that will take him: 55% ÷ 5% = 11 days to complete
Answer: 11 days
Answer to Q129
A fort has a provision for 900 men for 40 days. After 20 days, 300 men join them. For how many days more will the provision last for?
A fort has a provision for 900 men for 40 days
Let the total provision be Y
Y = 900 men * 40 days = 36,000 provisions
After 20 days,
Let consumed provision be Z
Z = 900 men * 20 days = 18,000 provisions
So, remaining provision = 36,000 - 18,000 = 18,000 provisions
300 men join them
Total number of men increased to 900 + 300 = 1,200
For how many days more will the provision last for?
In other words how many days will it take 1,200 men to finish 18,000 provisions
= 18,000 ÷ 1,200
= 15
Answer: 15 days
A fort has a provision for 900 men for 40 days. After 20 days, 300 men join them. For how many days more will the provision last for?
A fort has a provision for 900 men for 40 days
Let the total provision be Y
Y = 900 men * 40 days = 36,000 provisions
After 20 days,
Let consumed provision be Z
Z = 900 men * 20 days = 18,000 provisions
So, remaining provision = 36,000 - 18,000 = 18,000 provisions
300 men join them
Total number of men increased to 900 + 300 = 1,200
For how many days more will the provision last for?
In other words how many days will it take 1,200 men to finish 18,000 provisions
= 18,000 ÷ 1,200
= 15
Answer: 15 days
Answer to Q130
If A gets 25% more than B and B gets 20% more than C, how much does C get out of $740?
If A gets 25% more than B
A = 125% of B
A = 1.25B (eqn 1)
B gets 20% more than C
B = 120% of C
B = 1.2C (eqn 2)
how much does C get out of $740?
So, A + B + C = 740 (eqn 3)
From eqn 1 and eqn 2,
A = 1.25 (1.2C)
A = 1.5C (eqn 4)
From eqn 3,
1.5C + 1.2C + C = 740
3.7C = 720
C = 720 ÷ 3.7
C = 200
Answer: $200
If A gets 25% more than B and B gets 20% more than C, how much does C get out of $740?
If A gets 25% more than B
A = 125% of B
A = 1.25B (eqn 1)
B gets 20% more than C
B = 120% of C
B = 1.2C (eqn 2)
how much does C get out of $740?
So, A + B + C = 740 (eqn 3)
From eqn 1 and eqn 2,
A = 1.25 (1.2C)
A = 1.5C (eqn 4)
From eqn 3,
1.5C + 1.2C + C = 740
3.7C = 720
C = 720 ÷ 3.7
C = 200
Answer: $200
Answer to Q131
You walk up to a mountain that has two paths. One leads to the other side of the mountain, and the other will get you lost forever. Two twins know the path that leads to the other side. You can ask them only one question each. Except, one lies and one tells the truth, and you don't know which is which.
So, what would you ask?
There are several ways to get the correct answer from the twins. One of the simplest way:
1. Ask both twins "If I ask your brother for the right path, where will he point to?"
2. Both twins will point to the same path, because the lying twin will want to lie to you and he knows his brother would point to the right path so he point to the wrong path and the truth-telling twins knows his brother will lie so he points to the wrong path too.
3. The path they both point to is the wrong path, take the other path.
You walk up to a mountain that has two paths. One leads to the other side of the mountain, and the other will get you lost forever. Two twins know the path that leads to the other side. You can ask them only one question each. Except, one lies and one tells the truth, and you don't know which is which.
So, what would you ask?
There are several ways to get the correct answer from the twins. One of the simplest way:
1. Ask both twins "If I ask your brother for the right path, where will he point to?"
2. Both twins will point to the same path, because the lying twin will want to lie to you and he knows his brother would point to the right path so he point to the wrong path and the truth-telling twins knows his brother will lie so he points to the wrong path too.
3. The path they both point to is the wrong path, take the other path.
Answer to Q132
Apple and Orange cost $250. The apple is $200 more than the orange. How much is the orange?
I could see a lot of people fell for the $50 for the orange but read the question again, it didn't say the cost of Apple is $200. If the cost of Apple is $200 then obviously that of orange will be 250 - 200 = $50, but like I said cost of Apple is not $200. The question said Apple is $200 more than Orange.
In fact, that is another way to prove $50 is not the correct answer, if Orange is $50 which makes Apple $200, then Apple is (200 - 50 = $150) more that Orange but the question said it should be $200.
Ok, enough of that, let's solve the question.
Apple and Orange cost $250
Let Apple = A
Let Orange = O
A + O = $250 (eqn 1)
The apple is $200 more than the orange
A = O + 200 (eqn 2)
How much is the orange? (AKA, find O)
putting eqn 1 and eqn 2 together
"O" + 200 + "O" = 250
2"O" = 250 - 200 (did 2"O" so you don't mistake that for twenty)
2"O" = 50
O = 50 ÷ 2
O = 25
So, Orange is $25 and that makes Apple $225
To check our answer, $225 - $25 = $200 (The apple is $200 more than the orange).
Answer: 25
Apple and Orange cost $250. The apple is $200 more than the orange. How much is the orange?
I could see a lot of people fell for the $50 for the orange but read the question again, it didn't say the cost of Apple is $200. If the cost of Apple is $200 then obviously that of orange will be 250 - 200 = $50, but like I said cost of Apple is not $200. The question said Apple is $200 more than Orange.
In fact, that is another way to prove $50 is not the correct answer, if Orange is $50 which makes Apple $200, then Apple is (200 - 50 = $150) more that Orange but the question said it should be $200.
Ok, enough of that, let's solve the question.
Apple and Orange cost $250
Let Apple = A
Let Orange = O
A + O = $250 (eqn 1)
The apple is $200 more than the orange
A = O + 200 (eqn 2)
How much is the orange? (AKA, find O)
putting eqn 1 and eqn 2 together
"O" + 200 + "O" = 250
2"O" = 250 - 200 (did 2"O" so you don't mistake that for twenty)
2"O" = 50
O = 50 ÷ 2
O = 25
So, Orange is $25 and that makes Apple $225
To check our answer, $225 - $25 = $200 (The apple is $200 more than the orange).
Answer: 25
Answer to Q135
Three types of drinks each worth $6.00/ltr, $7.50/ltr and $x/ltr are mixed in proportion of 1 : 2 : 3 to form a cocktail worth $8.50/ltr. What is the value of x in $/ltr?
Three types of drinks each worth $6.00/ltr, $7.50/ltr and $x/ltr
A = $6.00/ltr
B = $7.50/ltr
C = $x/ltr
are mixed in proportion of 1 : 2 : 3 to form a cocktail worth $8.50/ltr
1+2+3 = 6
so,
[(1÷6)*A] + [(2÷6)*B] + [(3÷6)*C] = $8.50/ltr
[(1÷6)*6] + [(2÷6)*7.5] + [(3÷6)*C] = 8.50
1 + 2.5 + 0.5C = 8.50
3.5 + 0.5C = 8.50
0.5C = 8.50 - 3.50
0.5C = 5
C = 5 ÷ 0.5
C = 10
Answer: 10.00
Three types of drinks each worth $6.00/ltr, $7.50/ltr and $x/ltr are mixed in proportion of 1 : 2 : 3 to form a cocktail worth $8.50/ltr. What is the value of x in $/ltr?
Three types of drinks each worth $6.00/ltr, $7.50/ltr and $x/ltr
A = $6.00/ltr
B = $7.50/ltr
C = $x/ltr
are mixed in proportion of 1 : 2 : 3 to form a cocktail worth $8.50/ltr
1+2+3 = 6
so,
[(1÷6)*A] + [(2÷6)*B] + [(3÷6)*C] = $8.50/ltr
[(1÷6)*6] + [(2÷6)*7.5] + [(3÷6)*C] = 8.50
1 + 2.5 + 0.5C = 8.50
3.5 + 0.5C = 8.50
0.5C = 8.50 - 3.50
0.5C = 5
C = 5 ÷ 0.5
C = 10
Answer: 10.00
Answer to Q136
Find a, b and x
From Pythagorean theorem,
(9+16)² = a² + b² (i)
b² = 16² + x² (ii)
a² = 9² + x² (iii)
from (i)
625 = a² + b² (iv)
put (ii) into (iv)
625 = a² + 16² + x²
625 = a² +256 + x² (v)
put (iii) into (v)
625 = 9² + x² + 256 + x²
625 = 81 + x² + 256 + x²
625 = 2x² + 337
2x² + 337 - 625 = 0
2x² - 288 = 0
2x² = 288
x² = 288 ÷ 2
x² = 144
x = √144
x = 12
put x into (v)
625 = a² +256 + x²
625 = a² + 256 + 144
625 = a² + 400
a² = 625 - 400
a² = 225
a = √225
a = 15
From (ii)
b² = 16² + x²
b² = 256 + 144
b² = 400
b = √400
b = 20
So, x = 12, a = 15, b = 20
Find a, b and x
From Pythagorean theorem,
(9+16)² = a² + b² (i)
b² = 16² + x² (ii)
a² = 9² + x² (iii)
from (i)
625 = a² + b² (iv)
put (ii) into (iv)
625 = a² + 16² + x²
625 = a² +256 + x² (v)
put (iii) into (v)
625 = 9² + x² + 256 + x²
625 = 81 + x² + 256 + x²
625 = 2x² + 337
2x² + 337 - 625 = 0
2x² - 288 = 0
2x² = 288
x² = 288 ÷ 2
x² = 144
x = √144
x = 12
put x into (v)
625 = a² +256 + x²
625 = a² + 256 + 144
625 = a² + 400
a² = 625 - 400
a² = 225
a = √225
a = 15
From (ii)
b² = 16² + x²
b² = 256 + 144
b² = 400
b = √400
b = 20
So, x = 12, a = 15, b = 20
Answer to Q136:
A woman steals $100 from a shop. Then she buys items worth $70 from the shop using the same $100 and gets $30 change. How much did the shop lose?
A woman steals $100 from a shop - at this point the shop is losing $100
Then she buys items worth $70 - at this point the shop is losing $100 + $70 = $170
using the same $100 - at the point where she hands over the $100 to the cashier, the shop is only losing the goods in her possession, $70
and gets $30 change. - now the shop is losing $70 (goods) + $30 (change) = $100
Answer: $100
A woman steals $100 from a shop. Then she buys items worth $70 from the shop using the same $100 and gets $30 change. How much did the shop lose?
A woman steals $100 from a shop - at this point the shop is losing $100
Then she buys items worth $70 - at this point the shop is losing $100 + $70 = $170
using the same $100 - at the point where she hands over the $100 to the cashier, the shop is only losing the goods in her possession, $70
and gets $30 change. - now the shop is losing $70 (goods) + $30 (change) = $100
Answer: $100
Answer to Q137
What is the value of "?"
I am not going to lie, this question threw me off at first but it's actually one of the simplest question I have come across:
The answer is 9, how? No need for any calculation, just check the graph paper.
The value 8 is in entirely 8 boxes, the value 6 is in entirely 6 boxes, and ? is in 9 boxes
Answer: 9
What is the value of "?"
I am not going to lie, this question threw me off at first but it's actually one of the simplest question I have come across:
The answer is 9, how? No need for any calculation, just check the graph paper.
The value 8 is in entirely 8 boxes, the value 6 is in entirely 6 boxes, and ? is in 9 boxes
Answer: 9
Answer to Q138
Let small cup = S
Let big cup = B
Let handle-less paper coffee cup = H
S + B = 5
S + H = 7
B + H = 8
S + B + H = ?
It, can be written as:
S + B + 0 = 5
S + 0 + H = 7
0+ B + H = 8
Adding all together gives:
2S + 2B + 2H = 20
Divide all through by 2
s + B + H = 10
Answer: 10
Let small cup = S
Let big cup = B
Let handle-less paper coffee cup = H
S + B = 5
S + H = 7
B + H = 8
S + B + H = ?
It, can be written as:
S + B + 0 = 5
S + 0 + H = 7
0+ B + H = 8
Adding all together gives:
2S + 2B + 2H = 20
Divide all through by 2
s + B + H = 10
Answer: 10