Answer to Q191:
What is the area of the shaded region?
Area of the shaded portion will be:
= area of the rectangle - area of the circle
= (L x B) - (πr²)
= (3 x 2) - (π x 1 x 1) . Diameter is 2 so radius is 1
= 6 - π
Answer: 6 - π
What is the area of the shaded region?
Area of the shaded portion will be:
= area of the rectangle - area of the circle
= (L x B) - (πr²)
= (3 x 2) - (π x 1 x 1) . Diameter is 2 so radius is 1
= 6 - π
Answer: 6 - π
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Answer to Q192:
From the diagram above, what is the length of AC?
You will agree with me that AC is the same length as BD, and BD is the same as the radius of the circle.
So,
AC = BD = radius of circle = 6" + 4" = 10"
Answer: 10"
From the diagram above, what is the length of AC?
You will agree with me that AC is the same length as BD, and BD is the same as the radius of the circle.
So,
AC = BD = radius of circle = 6" + 4" = 10"
Answer: 10"
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Answer to Q193:
If (A - A - A = 20), (B - B - B = 15) and (C - C - C = 25), then what is A + B + C?
A - A - A = 20:
that means -A = 20
A = -20
B - B - B = 15
-B = 15
B = -15
C - C - C = 25
-C = 25
C = -25
So A + B + C = -20 + -15 + -25
= -20 - 15 - 25
= -60
Answer: -60
If (A - A - A = 20), (B - B - B = 15) and (C - C - C = 25), then what is A + B + C?
A - A - A = 20:
that means -A = 20
A = -20
B - B - B = 15
-B = 15
B = -15
C - C - C = 25
-C = 25
C = -25
So A + B + C = -20 + -15 + -25
= -20 - 15 - 25
= -60
Answer: -60
Answer to Q194:
From the diagram above, find the area of the green triangle.
Area of the green triangle = ½ x BC x BD
But, BD² = AD² + BA²
BD² = 5² + 10²
BD = √(25 + 100) = √125
BD = 11.18
But also, ∠ DBA = ∠ BDF = δ
sin δ = ⁵⁄₁₁.₁₈
δ = sin⁻¹ (0.4472)
δ = 26.57°
So, ∠ BDF = 26.57°
that makes ∠ DCB = 90° - 26.57°
∠ DCB = 63.43°
and, DA = FB = 5
sin (DCB) = 5 ÷ BC
BC = 5 ÷ sin 63.43°
BC = 5.59
Area of the green triangle = ½ x BC x BD
= ½ x 5.59 x 11.18
= 31.25
Answer: 31.25 sq. unit
From the diagram above, find the area of the green triangle.
Area of the green triangle = ½ x BC x BD
But, BD² = AD² + BA²
BD² = 5² + 10²
BD = √(25 + 100) = √125
BD = 11.18
But also, ∠ DBA = ∠ BDF = δ
sin δ = ⁵⁄₁₁.₁₈
δ = sin⁻¹ (0.4472)
δ = 26.57°
So, ∠ BDF = 26.57°
that makes ∠ DCB = 90° - 26.57°
∠ DCB = 63.43°
and, DA = FB = 5
sin (DCB) = 5 ÷ BC
BC = 5 ÷ sin 63.43°
BC = 5.59
Area of the green triangle = ½ x BC x BD
= ½ x 5.59 x 11.18
= 31.25
Answer: 31.25 sq. unit
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Answer to Q195:
What is the area of the coloured square?
The first and important information is that the shaded area is a square so all we need to do is find the length of one side.
We can find the hypotenuse of the triangle of base 2 and height 6 using Pythagoras theorem.
hyp² = base² + height²
hyp² = 2² + 6²
hyp² = 4 + 36
hyp = √40
So one of the side is √40 and area of a square = L²
area of shaded square = (√40)²
= 40 sq. unit
Answer: 40 sq. unit
What is the area of the coloured square?
The first and important information is that the shaded area is a square so all we need to do is find the length of one side.
We can find the hypotenuse of the triangle of base 2 and height 6 using Pythagoras theorem.
hyp² = base² + height²
hyp² = 2² + 6²
hyp² = 4 + 36
hyp = √40
So one of the side is √40 and area of a square = L²
area of shaded square = (√40)²
= 40 sq. unit
Answer: 40 sq. unit
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Answer to Q196:
From the picture above, find the missing number.
The pattern is n²+1 of prime numbers (2, 3, 5, 7, 11, etc)
For 2: n²+1 = 2²+1 = 5
For 3: n²+1 = 3²+1 = 10
For 5: n²+1 = 5²+1 = 26
For 7: n²+1 = 7²+1 = 50
For 11: n²+1 = 11²+1 = 122
Answer: 26
From the picture above, find the missing number.
The pattern is n²+1 of prime numbers (2, 3, 5, 7, 11, etc)
For 2: n²+1 = 2²+1 = 5
For 3: n²+1 = 3²+1 = 10
For 5: n²+1 = 5²+1 = 26
For 7: n²+1 = 7²+1 = 50
For 11: n²+1 = 11²+1 = 122
Answer: 26
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Answer to Q197:
Which of the trucks is moving in the direction as shown?
Answer C: because as the truck accelerates towards the right, there is an equal and opposite reaction on the water which pushes it to the left. Same thing happens to humans in a car when it accelerates or breaks, you move towards the opposite direction.
Which of the trucks is moving in the direction as shown?
Answer C: because as the truck accelerates towards the right, there is an equal and opposite reaction on the water which pushes it to the left. Same thing happens to humans in a car when it accelerates or breaks, you move towards the opposite direction.
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Answer to Q198:
I am not alive, but I can grow.
I don't have lungs, but I need air.
I don't have a mouth, but I need water to survive.
What am I?
Can you guess what it is?
The answer is Rust
Not alive ✅
Needs air (oxygen) to form and grow ✅
Needs water (moisture) to form and continue growing ✅
I am not alive, but I can grow.
I don't have lungs, but I need air.
I don't have a mouth, but I need water to survive.
What am I?
Can you guess what it is?
The answer is Rust
Not alive ✅
Needs air (oxygen) to form and grow ✅
Needs water (moisture) to form and continue growing ✅
Answer to Q199:
Which festival comes first?
Christmas or New Year
The answer is New Year, it is the very first day of the year!
Which festival comes first?
Christmas or New Year
The answer is New Year, it is the very first day of the year!
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Answer to Q200:
I have 5 apples today and ate 3 apples last week. How many apples do I have today?
The answer is 5 as the question says "I have 5 apples today... How many apples do I have today?"
I have 5 apples today and ate 3 apples last week. How many apples do I have today?
The answer is 5 as the question says "I have 5 apples today... How many apples do I have today?"
Answer to Q201:
All roses are flowers. Some flowers fade quickly. That means all roses fades quickly! True or False
The answer is False
All roses are flowers. ✅
(Roses belong to the group “flowers.”)
Some flowers fade quickly. ✅
(Only some, not all.)
The key word is “some.”
“Some flowers fade quickly” does not mean all flowers fade quickly.
All roses are flowers. Some flowers fade quickly. That means all roses fades quickly! True or False
The answer is False
All roses are flowers. ✅
(Roses belong to the group “flowers.”)
Some flowers fade quickly. ✅
(Only some, not all.)
The key word is “some.”
“Some flowers fade quickly” does not mean all flowers fade quickly.
Answer to Q202:
Guess the name:
🚖 + 🧻 + _______
Hint:it is the name of a female human
The answer is Caroline
🚖 = Car
🧻 = Roll (toilet paper roll)
_______ = Line
So:
Car + roll + line
Guess the name:
🚖 + 🧻 + _______
Hint:
The answer is Caroline
🚖 = Car
🧻 = Roll (toilet paper roll)
_______ = Line
So:
Car + roll + line
Answer to Q203:
You have three switches, but they are not labelled. Each switch corresponds to one of three light bulbs in a room. Each bulb is either on or off. You can turn the switches on and off as many times as you want, but you can only enter the room once to observe the bulbs. How can you figure out which switch controls which light bulb?
Answer:
Turn on Switch 1 and leave it on for about 5–10 minutes.
Then turn Switch 1 off.
Turn on Switch 2.
Leave Switch 3 off the whole time.
Now enter the room once.
What you’ll observe:
The bulb that is on → controlled by Switch 2.
The bulb that is off but warm → controlled by Switch 1 (it was on long enough to heat up).
The bulb that is off and cold → controlled by Switch 3.
You have three switches, but they are not labelled. Each switch corresponds to one of three light bulbs in a room. Each bulb is either on or off. You can turn the switches on and off as many times as you want, but you can only enter the room once to observe the bulbs. How can you figure out which switch controls which light bulb?
Answer:
Turn on Switch 1 and leave it on for about 5–10 minutes.
Then turn Switch 1 off.
Turn on Switch 2.
Leave Switch 3 off the whole time.
Now enter the room once.
What you’ll observe:
The bulb that is on → controlled by Switch 2.
The bulb that is off but warm → controlled by Switch 1 (it was on long enough to heat up).
The bulb that is off and cold → controlled by Switch 3.
Answer to Q204:
A robbery occurred on a snowy day, and four suspects were interviewed. Each suspect claimed they had not left their house that day. However, one of them is lying, and that individual is the thief. Based on the picture of their houses that day, can you identify the thief?
Answer: Rick is the thief because his car is parked on freshly fallen snow, proving it was moved after the snow began. That means he left the house, so he must be lying.
A robbery occurred on a snowy day, and four suspects were interviewed. Each suspect claimed they had not left their house that day. However, one of them is lying, and that individual is the thief. Based on the picture of their houses that day, can you identify the thief?
Answer: Rick is the thief because his car is parked on freshly fallen snow, proving it was moved after the snow began. That means he left the house, so he must be lying.
Answer to Q205:
A number is greater than another number by 5. If the smaller number is added to twice the larger number, the result is 28. What are the numbers?
Answer:
Let the smaller number be x.
The larger number is x + 5 (since it is greater by 5).
According to the question:
The smaller number + twice the larger number = 28
So we form the equation:
x + 2(x + 5) = 28
Now solve it:
x + 2x + 10 = 28
3x + 10 = 28
3x = 18
x = 6
So the smaller number is 6.
The larger number is: 6 + 5 = 11
The numbers are 6 and 11.
A number is greater than another number by 5. If the smaller number is added to twice the larger number, the result is 28. What are the numbers?
Answer:
Let the smaller number be x.
The larger number is x + 5 (since it is greater by 5).
According to the question:
The smaller number + twice the larger number = 28
So we form the equation:
x + 2(x + 5) = 28
Now solve it:
x + 2x + 10 = 28
3x + 10 = 28
3x = 18
x = 6
So the smaller number is 6.
The larger number is: 6 + 5 = 11
The numbers are 6 and 11.
Answer to Q206:
A man needs to cross a river with a wolf, a goat, and a cabbage. The boat can only carry the man and one other item at a time. If left alone together, the wolf will eat the goat, and the goat will eat the cabbage. How can the man safely transport all three across the river?
Answer:
Step 1: Take the goat across first.
(If you take the wolf, the goat eats the cabbage. If you take the cabbage, the wolf eats the goat.)
Step 2: Go back alone.
Step 3: Take the wolf across.
Now you can’t leave wolf + goat together, so…
Step 4: Bring the goat back with you.
Step 5: Take the cabbage across.
Step 6: Go back alone.
Step 7: Finally, take the goat across.
Everyone arrives safely
A man needs to cross a river with a wolf, a goat, and a cabbage. The boat can only carry the man and one other item at a time. If left alone together, the wolf will eat the goat, and the goat will eat the cabbage. How can the man safely transport all three across the river?
Answer:
Step 1: Take the goat across first.
(If you take the wolf, the goat eats the cabbage. If you take the cabbage, the wolf eats the goat.)
Step 2: Go back alone.
Step 3: Take the wolf across.
Now you can’t leave wolf + goat together, so…
Step 4: Bring the goat back with you.
Step 5: Take the cabbage across.
Step 6: Go back alone.
Step 7: Finally, take the goat across.
Everyone arrives safely
Answer to Q207:
A farmer has 17 sheep, and all but 9 run away. How many sheep ran away?
Answer:
“A farmer has 17 sheep, and all but 9 run away.”
“All but 9” means everyone except 9 ran away.
So:
17 − 9 = 8
8 sheep ran away.
A farmer has 17 sheep, and all but 9 run away. How many sheep ran away?
Answer:
“A farmer has 17 sheep, and all but 9 run away.”
“All but 9” means everyone except 9 ran away.
So:
17 − 9 = 8
8 sheep ran away.
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Answer to Q208:
I am a three-digit number. My tens digit is five more than my ones digit, and my hundreds digit is eight less than my tens digit. What number am I?
Answer:
Let the digits be:
Ones digit = x
Tens digit = x + 5
Hundreds digit = (tens − 8)
Since tens = x + 5,
Hundreds = (x + 5) − 8 = x − 3
So the number is:
(x − 3)(x + 5)(x)
Now remember: digits must be between 0 and 9.
Let’s find a value of x that keeps all digits valid:
if x = 0:
... (won't show x = 0 to x = 3 to keep the answer short)
If x = 4:
Ones = 4
Tens = 4 + 5 = 9
Hundreds = 4 − 3 = 1
That gives us:
194
So the number is 194.
I am a three-digit number. My tens digit is five more than my ones digit, and my hundreds digit is eight less than my tens digit. What number am I?
Answer:
Let the digits be:
Ones digit = x
Tens digit = x + 5
Hundreds digit = (tens − 8)
Since tens = x + 5,
Hundreds = (x + 5) − 8 = x − 3
So the number is:
(x − 3)(x + 5)(x)
Now remember: digits must be between 0 and 9.
Let’s find a value of x that keeps all digits valid:
if x = 0:
... (won't show x = 0 to x = 3 to keep the answer short)
If x = 4:
Ones = 4
Tens = 4 + 5 = 9
Hundreds = 4 − 3 = 1
That gives us:
194
So the number is 194.
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Answer to Q209:
I speak without a mouth and hear without ears. I have no body, but I come alive with wind. What am I?
Answer:
Answer is echo
Explanation:
“I speak without a mouth” → An echo repeats sounds, but it doesn’t have a mouth.
“Hear without ears” → It responds to sounds, even though it has no ears.
“I have no body, but I come alive with wind” → Sound travels through air (wind), giving the echo life.
I speak without a mouth and hear without ears. I have no body, but I come alive with wind. What am I?
Answer:
Answer is echo
Explanation:
“I speak without a mouth” → An echo repeats sounds, but it doesn’t have a mouth.
“Hear without ears” → It responds to sounds, even though it has no ears.
“I have no body, but I come alive with wind” → Sound travels through air (wind), giving the echo life.
Answer to Q210:
There is a woman on a boat in a lake wearing a coat. In this riddle, I've told you her name. What is it?
Answer:
The riddle is all about wordplay:
“boat in a lake” → the letters t‑in‑a → Tina
The rest of the sentence is just fluff to distract you.
Answer: Tina
There is a woman on a boat in a lake wearing a coat. In this riddle, I've told you her name. What is it?
Answer:
The riddle is all about wordplay:
“boat in a lake” → the letters t‑in‑a → Tina
The rest of the sentence is just fluff to distract you.
Answer: Tina