Answer to Q179
There are 85 people in a warehouse, out of which some have been turned into zombies while some are still alive. If the ratio of zombies to living human beings is 2:3, calculate the total number of zombies.
zombies : human = 2:3
∴
zombie = 2 ratio
human = 3 ratio
and,
zombies + human = 85
ratio = 2+3 = 5
so,
1 ratio = 85 ÷ 5
1 ration = 17
zombie = 2 x 17 = 34
human = 3 x 17 = 51
Answer: 34
There are 85 people in a warehouse, out of which some have been turned into zombies while some are still alive. If the ratio of zombies to living human beings is 2:3, calculate the total number of zombies.
zombies : human = 2:3
∴
zombie = 2 ratio
human = 3 ratio
and,
zombies + human = 85
ratio = 2+3 = 5
so,
1 ratio = 85 ÷ 5
1 ration = 17
zombie = 2 x 17 = 34
human = 3 x 17 = 51
Answer: 34
Answer to Q180
The first box is 8 + 2 + 5 - 3 = 12
The second box is 3 + 7 + 4 - 9 = 5
So, the third box is 5 + 8 + 7 - 6 = 14
Answer: 14
The first box is 8 + 2 + 5 - 3 = 12
The second box is 3 + 7 + 4 - 9 = 5
So, the third box is 5 + 8 + 7 - 6 = 14
Answer: 14
Answer to Q181
If you’re running in a race and you pass the person in second place, what place are you in?
When you pass the person in second place, you replaces them in that position, so you come from third place to second place.
Answer: Second place
If you’re running in a race and you pass the person in second place, what place are you in?
When you pass the person in second place, you replaces them in that position, so you come from third place to second place.
Answer: Second place
Answer to Q183:
Select the richest guy:
A: A guy with USD5,000,000
B: A guy that has just 1 cent but it will be doubled everyday for ONLY 30 days.
At the end of 30 days, guy A will still have USD5,000,000 but guy B will have
Day 1 - $0.02
Day 2 - $0.04
Day 3 - $0.08
Day 4 - $0.16
Day 5 - $0.32
Day 6 - $0.64
Day 7 - $1.28
Day 8 - $2.56
Day 9 - $5.12
Day 10 - $10.24
Day 11 - $20.48
Day 12 - $40.96
Day 13 - $81.92
Day 14 - $163.84
Day 15 - $327.68
Day 16 - $655.36
Day 17 - $1,310.72
Day 18 - $2,621.44
Day 19 - $5,242.88
Day 20 - $10,485.76
Day 21 - $20,971.52
Day 22 - $41,943.04
Day 23 - $83,886.08
Day 24 - $167,772.16
Day 25 - $335,544.32
Day 26 - $671,088.64
Day 27 - $1,342,177.28
Day 28 - $2,684,354.56
Day 29 - $5,368,709.12
Day 30 - $10,737,418.24
Guy B will have a whopping USD10,737,418.24
Answer: A guy that has just 1 cent but it will be doubled everyday for ONLY 30 days.
Select the richest guy:
A: A guy with USD5,000,000
B: A guy that has just 1 cent but it will be doubled everyday for ONLY 30 days.
At the end of 30 days, guy A will still have USD5,000,000 but guy B will have
Day 1 - $0.02
Day 2 - $0.04
Day 3 - $0.08
Day 4 - $0.16
Day 5 - $0.32
Day 6 - $0.64
Day 7 - $1.28
Day 8 - $2.56
Day 9 - $5.12
Day 10 - $10.24
Day 11 - $20.48
Day 12 - $40.96
Day 13 - $81.92
Day 14 - $163.84
Day 15 - $327.68
Day 16 - $655.36
Day 17 - $1,310.72
Day 18 - $2,621.44
Day 19 - $5,242.88
Day 20 - $10,485.76
Day 21 - $20,971.52
Day 22 - $41,943.04
Day 23 - $83,886.08
Day 24 - $167,772.16
Day 25 - $335,544.32
Day 26 - $671,088.64
Day 27 - $1,342,177.28
Day 28 - $2,684,354.56
Day 29 - $5,368,709.12
Day 30 - $10,737,418.24
Guy B will have a whopping USD10,737,418.24
Answer: A guy that has just 1 cent but it will be doubled everyday for ONLY 30 days.
Answer to Q184:
What is the value of the square, the circle and the triangle?
At first glance, this looks like a very complex puzzle to solve but it is actually one of the simplest.
The puzzle can be rewritten as 3 x (Square Circle Triangle) = 777
Square Circle Triangle = 777 ÷ 3
Square Circle Triangle = 259
Answer:
Square = 2
Circle = 5
Triangle = 9
What is the value of the square, the circle and the triangle?
At first glance, this looks like a very complex puzzle to solve but it is actually one of the simplest.
The puzzle can be rewritten as 3 x (Square Circle Triangle) = 777
Square Circle Triangle = 777 ÷ 3
Square Circle Triangle = 259
Answer:
Square = 2
Circle = 5
Triangle = 9
Answer to Q185:
If I had four eggs and a thief gave me three and my rooster laid five more. How many eggs do I have?
If I had four eggs: 4 eggs
and a thief gave me three: 3 eggs (the word thief here was just introduced to cause confusion, it has nothing to do with the word problem).
and my rooster laid five more: That is impossible as roosters don't lay eggs so, 0 eggs
How many eggs do I have?: 4 + 3 + 0 = 7
Answer: 7
If I had four eggs and a thief gave me three and my rooster laid five more. How many eggs do I have?
If I had four eggs: 4 eggs
and a thief gave me three: 3 eggs (the word thief here was just introduced to cause confusion, it has nothing to do with the word problem).
and my rooster laid five more: That is impossible as roosters don't lay eggs so, 0 eggs
How many eggs do I have?: 4 + 3 + 0 = 7
Answer: 7
Answer to Q186:
If one person chases 1,000 and two persons chase 10,000. How many does 5 persons chase?
So,
1 = 1,000 (10³ = 10ⁿ⁺²)
2 = 10,000 (10⁴ = 10ⁿ⁺²)
Then 5 = (10ⁿ⁺²) = 10⁵⁺² = 10⁷ = 10,000,000
Answer: 10,000,000
If one person chases 1,000 and two persons chase 10,000. How many does 5 persons chase?
So,
1 = 1,000 (10³ = 10ⁿ⁺²)
2 = 10,000 (10⁴ = 10ⁿ⁺²)
Then 5 = (10ⁿ⁺²) = 10⁵⁺² = 10⁷ = 10,000,000
Answer: 10,000,000
Answer to Q187:
From the diagram above, what is the area of the shaded parts?
We can take the squares roll by roll, starting from roll 1 (the topmost):
Roll 1:
The total area of roll 1 is 4 unit sq. (1 sq. unit x 4),
But the half of the area is not shaded so ¹⁄₂ x 4 sq, unit = 2 sq. unit
And also the first square as the bottom half not shaded = ¹⁄₂ x 1 sq. unit = ¹⁄₂ sq. unit
So, shaded part of roll 1 is = 2 sq. unit - ¹⁄₂ sq. unit = 1¹⁄₂ sq. unit
Roll 2:
We have a whole square and half of a square shaded = 1¹⁄₂ sq. unit
Roll 3:
We have only half of a square shaded = ¹⁄₂ sq. unit
Total area shaded = 1¹⁄₂ +1¹⁄₂ + ¹⁄₂ = 3¹⁄₂ sq. unit
Answer: 3¹⁄₂ sq. unit
From the diagram above, what is the area of the shaded parts?
We can take the squares roll by roll, starting from roll 1 (the topmost):
Roll 1:
The total area of roll 1 is 4 unit sq. (1 sq. unit x 4),
But the half of the area is not shaded so ¹⁄₂ x 4 sq, unit = 2 sq. unit
And also the first square as the bottom half not shaded = ¹⁄₂ x 1 sq. unit = ¹⁄₂ sq. unit
So, shaded part of roll 1 is = 2 sq. unit - ¹⁄₂ sq. unit = 1¹⁄₂ sq. unit
Roll 2:
We have a whole square and half of a square shaded = 1¹⁄₂ sq. unit
Roll 3:
We have only half of a square shaded = ¹⁄₂ sq. unit
Total area shaded = 1¹⁄₂ +1¹⁄₂ + ¹⁄₂ = 3¹⁄₂ sq. unit
Answer: 3¹⁄₂ sq. unit
Answer to Q188:
A girl got killed, the killer took her iPhone, diamond, money, and necklace. What was first thing the killer took?
Answer: The killer took her life first
A girl got killed, the killer took her iPhone, diamond, money, and necklace. What was first thing the killer took?
Answer: The killer took her life first
Answer to Q189:
From the above diagram, what is the area of the shaded portion?
The area of the shaded portion will be area of the square - area of the circle
= L² - (πr²) (where L = 2r)
= (20x20) - (π x x 10 x 10)
= 400 - 314.16
= 85.84
Answer: 85.84 sq. unit
From the above diagram, what is the area of the shaded portion?
The area of the shaded portion will be area of the square - area of the circle
= L² - (πr²) (where L = 2r)
= (20x20) - (π x x 10 x 10)
= 400 - 314.16
= 85.84
Answer: 85.84 sq. unit
Answer to Q190:
If three cats catch three rats in three minutes, how many cats will catch 100 rats in 100 minutes?
If three cats catch three rats in three minutes: then one cat will catch one rat in three minutes (not one minutes, three minutes).
So, to catch 100 rats:
= (1 cat/rat x 100 rats) every three minutes
= 1cat/rat x 100 rats x 3 minutes
= 300 cats minutes
So, 1 cats can finish the job in 300 minutes, but we were asked to calculate for 100 minutes.
But we have 100 minutes, so:
= 300 cat minutes ÷ 100 minutes
= 3 cats
Answer: 3 cats
If three cats catch three rats in three minutes, how many cats will catch 100 rats in 100 minutes?
If three cats catch three rats in three minutes: then one cat will catch one rat in three minutes (not one minutes, three minutes).
So, to catch 100 rats:
= (1 cat/rat x 100 rats) every three minutes
= 1cat/rat x 100 rats x 3 minutes
= 300 cats minutes
So, 1 cats can finish the job in 300 minutes, but we were asked to calculate for 100 minutes.
But we have 100 minutes, so:
= 300 cat minutes ÷ 100 minutes
= 3 cats
Answer: 3 cats
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
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"
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
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
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
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.