Answer to Q211:
In a room of 100 people, 99% are left-handed.
How many people must leave the room to reduce the percentage of left-handed people to 98%?
Answer:
Step 1: Current numbers
Total people = 100
Left-handed = 99% of 100 = 99
Right-handed = 1
Step 2:
We cannot remove the only right handed people because that will get the left handed people to 100%, so we have to remove from left handed people instead.
Let y = number of left-handed people to remove.
Left-handed left = 99 − y
Total people left = 100 − y
We want:
(99−y) ÷ (100−y) = 0.98
99−y = 0.98(100−y)
99−y = 98−0.98y
99−98 = −0.98y+y
1 = 0.02y
y = 1 ÷ 0.02
y = 50
So, 50 people must leave the room (all left-handed) to reduce the left-handed percentage from 99% to 98%.
In a room of 100 people, 99% are left-handed.
How many people must leave the room to reduce the percentage of left-handed people to 98%?
Answer:
Step 1: Current numbers
Total people = 100
Left-handed = 99% of 100 = 99
Right-handed = 1
Step 2:
We cannot remove the only right handed people because that will get the left handed people to 100%, so we have to remove from left handed people instead.
Let y = number of left-handed people to remove.
Left-handed left = 99 − y
Total people left = 100 − y
We want:
(99−y) ÷ (100−y) = 0.98
99−y = 0.98(100−y)
99−y = 98−0.98y
99−98 = −0.98y+y
1 = 0.02y
y = 1 ÷ 0.02
y = 50
So, 50 people must leave the room (all left-handed) to reduce the left-handed percentage from 99% to 98%.
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Answer to Q212:
An item is discounted by 50%, then discounted again by 50% of the new price.
What percentage of the original price do you end up paying?
Answer:
Let’s assume the original price is £100 (just to make it easy).
First 50% discount:
50% of £100 = £50
New price = £50
Second 50% discount:
50% of £50 = £25
New price = £25
So, you end up paying £25 out of £100, which is:
25 ÷ 100 = 0.25 = 25%
So, you pay 25% of the original price.
An item is discounted by 50%, then discounted again by 50% of the new price.
What percentage of the original price do you end up paying?
Answer:
Let’s assume the original price is £100 (just to make it easy).
First 50% discount:
50% of £100 = £50
New price = £50
Second 50% discount:
50% of £50 = £25
New price = £25
So, you end up paying £25 out of £100, which is:
25 ÷ 100 = 0.25 = 25%
So, you pay 25% of the original price.
Answer to Q213:
A number is increased by 20%, then decreased by 20%.
What is the final result compared to the original number?
Answer:
Let’s assume the original number is 100 (for simplicity).
Step 1: Increase by 20%
20% of 100 = 20
New number = 120
Step 2: Decrease by 20%
20% of 120 = 24
120 − 24 = 96
You end up with 96, compared to the original 100.
That means the final result is:
96 ÷ 100 = 0.96 = 96%
The number ends up 4% less than the original.
A number is increased by 20%, then decreased by 20%.
What is the final result compared to the original number?
Answer:
Let’s assume the original number is 100 (for simplicity).
Step 1: Increase by 20%
20% of 100 = 20
New number = 120
Step 2: Decrease by 20%
20% of 120 = 24
120 − 24 = 96
You end up with 96, compared to the original 100.
That means the final result is:
96 ÷ 100 = 0.96 = 96%
The number ends up 4% less than the original.
Answer to Q214:
A clock strikes once at 1 o’clock, twice at 2 o’clock, three times at 3 o’clock, and so on, striking twelve times at 12 o’clock.
How many times does the clock strike in one full day?
Answer:
First, count how many strikes happen in 12 hours:
1 + 2 + 3 + ... + 12
The sum of the first 12 numbers is:
(12×13) ÷ 2 = 78
So in 12 hours, the clock strikes 78 times.
Since a full day has two 12-hour cycles (AM and PM):
78 × 2 = 156
The clock strikes 156 times in one full day.
A clock strikes once at 1 o’clock, twice at 2 o’clock, three times at 3 o’clock, and so on, striking twelve times at 12 o’clock.
How many times does the clock strike in one full day?
Answer:
First, count how many strikes happen in 12 hours:
1 + 2 + 3 + ... + 12
The sum of the first 12 numbers is:
(12×13) ÷ 2 = 78
So in 12 hours, the clock strikes 78 times.
Since a full day has two 12-hour cycles (AM and PM):
78 × 2 = 156
The clock strikes 156 times in one full day.
Answer to Q215:
You flip 2 fair coins once.
What’s the probability of getting at least one head?
Answer:
When you flip 2 fair coins, the possible outcomes are:
HH
HT
TH
TT
We want the probability of at least one head.
The only outcome with no heads is: TT
All the other 3 outcomes (of 4 total) has at least one head = 3/4
You flip 2 fair coins once.
What’s the probability of getting at least one head?
Answer:
When you flip 2 fair coins, the possible outcomes are:
HH
HT
TH
TT
We want the probability of at least one head.
The only outcome with no heads is: TT
All the other 3 outcomes (of 4 total) has at least one head = 3/4
Answer to Q216:
Three friends check into a hotel room costing £30. They each pay £10.
Later, the hotel realises there was a discount. The room should have cost £25, so the clerk gives £5 to the bellboy to return.
The bellboy, being sneaky, keeps £2 and gives each friend £1 back.
So now:
Each friend paid £9 (since they got £1 back)
£9 × 3 = £27
Bellboy kept £2
£27 + £2 = £29
Where did the missing £1 go since we had £30 to start with?
Answer:
There is no missing £1, the trick in the question is in the way the numbers are added, so let’s track the money properly.
Step 1: Original payment
3 friends pay £10 each → £30
Step 2: Correct room cost
Actual cost = £25
Bellboy keeps £2
Friends get £3 back (£1 each)
25 + 2 + 3 = 30
Step 3: What did the friends actually pay?
Each paid £10 but got £1 back →
Each paid £9
Total paid:
9 × 3 = 27 (that £27 already includes the £2 the bellboy kept, that's where the question tries to confuse you)
Because: £25 (hotel) + £2 (bellboy) = £27 (paid by the three friends)
So the 27 + 2 = 29 in the question is adding the £2 twice because the £2 is already part of the £27!
The correct calculation is 25 + 2 + 3 = 30 so there is no missing £1.
Three friends check into a hotel room costing £30. They each pay £10.
Later, the hotel realises there was a discount. The room should have cost £25, so the clerk gives £5 to the bellboy to return.
The bellboy, being sneaky, keeps £2 and gives each friend £1 back.
So now:
Each friend paid £9 (since they got £1 back)
£9 × 3 = £27
Bellboy kept £2
£27 + £2 = £29
Where did the missing £1 go since we had £30 to start with?
Answer:
There is no missing £1, the trick in the question is in the way the numbers are added, so let’s track the money properly.
Step 1: Original payment
3 friends pay £10 each → £30
Step 2: Correct room cost
Actual cost = £25
Bellboy keeps £2
Friends get £3 back (£1 each)
25 + 2 + 3 = 30
Step 3: What did the friends actually pay?
Each paid £10 but got £1 back →
Each paid £9
Total paid:
9 × 3 = 27 (that £27 already includes the £2 the bellboy kept, that's where the question tries to confuse you)
Because: £25 (hotel) + £2 (bellboy) = £27 (paid by the three friends)
So the 27 + 2 = 29 in the question is adding the £2 twice because the £2 is already part of the £27!
The correct calculation is 25 + 2 + 3 = 30 so there is no missing £1.
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Answer to Q217:
A father says to his son:
“I am twice as old as you were when I was as old as you are now.”
If the father is 40 years old, how old is the son?
Answer:
This question is deliberately tricky. The option 20 is placed as bait. Many people see “40 years old” and “twice as old” and immediately think:
But that ignores the tense in the statement. The words “is” and “were” are very important. The father is referring to a time in the past.
Let’s break it down properly.
Step 1: Let's define our variables
Let:
Father’s current age = F(now)
Son’s current age = S(now)
The father refers to a past time:
Father’s age in the past = F(past)
Son’s age in the past = S(past)
One key fact:
The age difference between father and son is constant so you will agree with me that F(now) − S(now) will always be equal to F(past) − S(past)
So, F(now) − S(now) = F(past) − S(past) ∴ call this Equation (1).
Step 2: Translate the statement carefully
The father says: “I am twice as old as you were when I was as old as you are now.”
Let's break this into parts:
“When I was as old as you are now”
This means: F(past) = S(now) ∴ call this Equation (2).
“I am twice as old as you were”
F(now) = 2 × S(past)
We are told: If the father is 40 years old
F(now) = 40
So:
40 = 2 × S(past)
S(past) = 20
So we now know
F(now) = 40
S(past) = 20
But we were told to find S(now) not S(past) "how old is the son?"
Step 3: Use the constant age difference
Now return to Equation (1):
F(now) − S(now) = F(past) − S(past)
Substitute what we know:
40 − S(now) = F(past) − 20
From Equation (2), we know:
F(past) = S(now)
So:
40 − S(now) = S(now) − 20
Now solve:
40 + 20 = S(now) + S(now)
60 = 2S(now)
S(now) = 30
The son is 30 years old.
A father says to his son:
“I am twice as old as you were when I was as old as you are now.”
If the father is 40 years old, how old is the son?
Answer:
This question is deliberately tricky. The option 20 is placed as bait. Many people see “40 years old” and “twice as old” and immediately think:
40 ÷ 2 = 20
But that ignores the tense in the statement. The words “is” and “were” are very important. The father is referring to a time in the past.
Let’s break it down properly.
Step 1: Let's define our variables
Let:
Father’s current age = F(now)
Son’s current age = S(now)
The father refers to a past time:
Father’s age in the past = F(past)
Son’s age in the past = S(past)
One key fact:
The age difference between father and son is constant so you will agree with me that F(now) − S(now) will always be equal to F(past) − S(past)
So, F(now) − S(now) = F(past) − S(past) ∴ call this Equation (1).
Step 2: Translate the statement carefully
The father says: “I am twice as old as you were when I was as old as you are now.”
Let's break this into parts:
“When I was as old as you are now”
This means: F(past) = S(now) ∴ call this Equation (2).
“I am twice as old as you were”
F(now) = 2 × S(past)
We are told: If the father is 40 years old
F(now) = 40
So:
40 = 2 × S(past)
S(past) = 20
So we now know
F(now) = 40
S(past) = 20
But we were told to find S(now) not S(past) "how old is the son?"
Step 3: Use the constant age difference
Now return to Equation (1):
F(now) − S(now) = F(past) − S(past)
Substitute what we know:
40 − S(now) = F(past) − 20
From Equation (2), we know:
F(past) = S(now)
So:
40 − S(now) = S(now) − 20
Now solve:
40 + 20 = S(now) + S(now)
60 = 2S(now)
S(now) = 30
The son is 30 years old.
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Answer to Q218:
Five people need to cross a river at night:
Each person takes the following minutes to cross
Person A: 1 min
Person B: 2 min
Person C: 5 min
Person D: 10 min
Person E: 15 min
Rules:
1. The boat can carry at most 2 people.
2. They must carry a torch to cross. There’s only 1 torch, and someone must bring it back each time.
3. When two people cross, they move at the slower person’s speed.
Question:
What is the minimum total time for all five to cross?
Answer:
Many people fall for the “35 minutes” trap. They assume the fastest person can just ferry everyone one by one, calculating something like:
15 + 1 + 10 + 1 + 5 + 1 + 2 = 35
It seems logical at first, make the fastest person do all the work. But the problem is when two people cross together, they move at the slower person’s speed, which that method doesn’t fully account for.
Step 1: Optimising strategy
Instead of sending the slowest people individually, we can pair the two slowest people together and have a faster person bring the boat back. This reduces wasted time.
Step 2: Step-by-step plan
A + B cross first → 2 minutes
A returns with the boat → 1 minute
D + E cross together → 15 minutes (that's massively reduce time)
B returns with the boat → 2 minutes
A + C cross → 5 minutes
A returns → 1 minute
A + B cross again → 2 minutes
Step 3: Total time
2 + 1 + 15 + 2 + 5 + 1 + 2 = 28 minutes
The minimum total time for all five to cross is 28 minutes.
Five people need to cross a river at night:
Each person takes the following minutes to cross
Person A: 1 min
Person B: 2 min
Person C: 5 min
Person D: 10 min
Person E: 15 min
Rules:
1. The boat can carry at most 2 people.
2. They must carry a torch to cross. There’s only 1 torch, and someone must bring it back each time.
3. When two people cross, they move at the slower person’s speed.
Question:
What is the minimum total time for all five to cross?
Answer:
Many people fall for the “35 minutes” trap. They assume the fastest person can just ferry everyone one by one, calculating something like:
15 + 1 + 10 + 1 + 5 + 1 + 2 = 35
It seems logical at first, make the fastest person do all the work. But the problem is when two people cross together, they move at the slower person’s speed, which that method doesn’t fully account for.
Step 1: Optimising strategy
Instead of sending the slowest people individually, we can pair the two slowest people together and have a faster person bring the boat back. This reduces wasted time.
Step 2: Step-by-step plan
A + B cross first → 2 minutes
A returns with the boat → 1 minute
D + E cross together → 15 minutes (that's massively reduce time)
B returns with the boat → 2 minutes
A + C cross → 5 minutes
A returns → 1 minute
A + B cross again → 2 minutes
Step 3: Total time
2 + 1 + 15 + 2 + 5 + 1 + 2 = 28 minutes
The minimum total time for all five to cross is 28 minutes.
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Answer to Q219:
Three painters, A, B, and C, are painting a house.
Painter A can finish the house in 6 hours
Painter B can finish it in 8 hours
Painter C can finish it in 12 hours
If:
A and B start working together, but after 2 hours, A leaves.
Then B and C continue working together until the house is finished.
Question:
How long in total does it take to finish the house?
Answer:
Step 1: Work rates (per hour)
Painter A finishes in 6 hours → rate = 1/6 of the house per hour
Painter B finishes in 8 hours → rate = 1/8 per hour
Painter C finishes in 12 hours → rate = 1/12 per hour
Step 2: First 2 hours (A and B together)
Combined rate of A and B:
1/6 + 1/8
Common denominator = 24
4/24 + 3/24 = 7/24
So together they complete 7/24 of the house per hour.
In 2 hours:
2 × (7/24) = 14/24 = 7/12
After 2 hours, 7/12 of the house is finished.
Step 3: Work remaining
1 − (7/12) = 5/12
So 5/12 of the house is left.
Step 4: B and C work together
Combined rate of B and C:
1/8 + 1/12
Common denominator = 24
3/24 + 2/24 = 5/24
So B and C complete 5/24 of the house per hour.
Step 5: Time to finish remaining 5/12
We divide remaining work by that rate:
5/12 ÷ 5/24
Flip and multiply:
5/12 × 24/5
5 cancels out:
24/12 = 2
So it takes 2 more hours.
So, total time = 2+2 = 4 hours
Three painters, A, B, and C, are painting a house.
Painter A can finish the house in 6 hours
Painter B can finish it in 8 hours
Painter C can finish it in 12 hours
If:
A and B start working together, but after 2 hours, A leaves.
Then B and C continue working together until the house is finished.
Question:
How long in total does it take to finish the house?
Answer:
Step 1: Work rates (per hour)
Painter A finishes in 6 hours → rate = 1/6 of the house per hour
Painter B finishes in 8 hours → rate = 1/8 per hour
Painter C finishes in 12 hours → rate = 1/12 per hour
Step 2: First 2 hours (A and B together)
Combined rate of A and B:
1/6 + 1/8
Common denominator = 24
4/24 + 3/24 = 7/24
So together they complete 7/24 of the house per hour.
In 2 hours:
2 × (7/24) = 14/24 = 7/12
After 2 hours, 7/12 of the house is finished.
Step 3: Work remaining
1 − (7/12) = 5/12
So 5/12 of the house is left.
Step 4: B and C work together
Combined rate of B and C:
1/8 + 1/12
Common denominator = 24
3/24 + 2/24 = 5/24
So B and C complete 5/24 of the house per hour.
Step 5: Time to finish remaining 5/12
We divide remaining work by that rate:
5/12 ÷ 5/24
Flip and multiply:
5/12 × 24/5
5 cancels out:
24/12 = 2
So it takes 2 more hours.
So, total time = 2+2 = 4 hours
Answer to Q200:
What is 8÷2(2+2)
Answer:
Many people get this question wrong because they misunderstand BODMAS.
What is BODMAS?
BODMAS stands for:
B – Brackets
O – Orders (powers/roots)
D – Division
M – Multiplication
A – Addition
S – Subtraction
But here’s the part people forget: Division and multiplication are equal in priority. Addition and subtraction are also equal in priority so when operations have equal priority, you must work from left to right. This simple rule is what many always forget to apply.
Applying BODMAS correctly to the question:
8 ÷ 2(2 + 2)
Step 1: Brackets first
2 + 2 = 4
Now it becomes:
8 ÷ 2(4)
Which is same thing as 8 ÷ 2 × 4
Step 2: Division and multiplication (left to right, very important)
8 ÷ 2 = 4
4 × 4 = 16
Answer: 16
What is 8÷2(2+2)
Answer:
Many people get this question wrong because they misunderstand BODMAS.
What is BODMAS?
BODMAS stands for:
B – Brackets
O – Orders (powers/roots)
D – Division
M – Multiplication
A – Addition
S – Subtraction
But here’s the part people forget: Division and multiplication are equal in priority. Addition and subtraction are also equal in priority so when operations have equal priority, you must work from left to right. This simple rule is what many always forget to apply.
Applying BODMAS correctly to the question:
8 ÷ 2(2 + 2)
Step 1: Brackets first
2 + 2 = 4
Now it becomes:
8 ÷ 2(4)
Which is same thing as 8 ÷ 2 × 4
Step 2: Division and multiplication (left to right, very important)
8 ÷ 2 = 4
4 × 4 = 16
Answer: 16
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Answer to Q221:
What is (⁵⁄₄)⁻¹ + ½ ÷ ¾ ?
Answer:
Given:
(⁵⁄₄)⁻¹ + ½ ÷ ¾
Step 1: Solve the negative exponent
(⁵⁄₄)⁻¹
A power of ⁻¹ means take the reciprocal:
(⁵⁄₄)⁻¹ = ⅘
Step 2: Solve the division
½ ÷ ¾
Dividing by a fraction means multiply by its reciprocal:
½ ÷ ¾ = ½ × ⁴⁄₃
½ × ⁴⁄₃ = ⁴⁄₆ = ⅔
Step 3: Add the results
⅘ + ⅔
Find a common denominator (15):
(12 + 10) / 15 = ²²⁄₁₅ = 1⁷⁄₁₅
Answer = 1⁷⁄₁₅
What is (⁵⁄₄)⁻¹ + ½ ÷ ¾ ?
Answer:
Given:
(⁵⁄₄)⁻¹ + ½ ÷ ¾
Step 1: Solve the negative exponent
(⁵⁄₄)⁻¹
A power of ⁻¹ means take the reciprocal:
(⁵⁄₄)⁻¹ = ⅘
Step 2: Solve the division
½ ÷ ¾
Dividing by a fraction means multiply by its reciprocal:
½ ÷ ¾ = ½ × ⁴⁄₃
½ × ⁴⁄₃ = ⁴⁄₆ = ⅔
Step 3: Add the results
⅘ + ⅔
Find a common denominator (15):
(12 + 10) / 15 = ²²⁄₁₅ = 1⁷⁄₁₅
Answer = 1⁷⁄₁₅
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Answer to Q222:
Solve for x: √(x+9) = x - 3
Answer:
Given √(x+9) = x - 3
Step 1: Square both sides
(√(𝑥 + 9))² = (𝑥 − 3)²
(𝑥 + 9) = (𝑥 − 3)²
Expand:
𝑥 + 9 = 𝑥² − 6𝑥 + 9
Step 2: Rearrange
Move everything to one side:
0 = 𝑥² − 6𝑥 + 9 − 𝑥 − 9
0 = 𝑥² − 7𝑥
Factor:
0 = 𝑥(𝑥 − 7)
Step 3: Solve
𝑥 = 0 or 𝑥 = 7
Answer: 0, 7
Solve for x: √(x+9) = x - 3
Answer:
Given √(x+9) = x - 3
Step 1: Square both sides
(√(𝑥 + 9))² = (𝑥 − 3)²
(𝑥 + 9) = (𝑥 − 3)²
Expand:
𝑥 + 9 = 𝑥² − 6𝑥 + 9
Step 2: Rearrange
Move everything to one side:
0 = 𝑥² − 6𝑥 + 9 − 𝑥 − 9
0 = 𝑥² − 7𝑥
Factor:
0 = 𝑥(𝑥 − 7)
Step 3: Solve
𝑥 = 0 or 𝑥 = 7
Answer: 0, 7
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