Answer to Q159
A farmer has 17 sheep and all but 9 die. How many are left?
The question says all but 9 dies, this means all except 9 of the sheep are died. 9 sheep didn't die.
Answer: 9
A farmer has 17 sheep and all but 9 die. How many are left?
The question says all but 9 dies, this means all except 9 of the sheep are died. 9 sheep didn't die.
Answer: 9
Answer to Q160
What is a group of ravens called?
An Unkindness of Ravens. There is even a book by Ruth Rendell with that title.
Answer: Unkindness
What is a group of ravens called?
An Unkindness of Ravens. There is even a book by Ruth Rendell with that title.
Answer: Unkindness
Answer to Q161
You are given two ropes with different lengths. However if you set both ropes of fire from the tip, they will both burn at exactly one hour.
You are asked to measure 45 minutes using just these two ropes and you and NOT allowed to cut the ropes at all.
How will you do this?
1. Burn one of the ropes from both ends. The rope will burn completely at half time (i.e. 30 minutes).
2. Also burn the other rope from one end at the same time. At the time rope #1 completely burns, rope #2 will be half length. That is, it now has 30 minutes left to burn.
3. Immediately set the other side of rope #2 on fire too. It will burn at half the time left (i.e. 15 minutes).
4. Let rope #2 burn completely too.
You have successfully measured 30minutes + 15 minutes = 45 minutes.
You are given two ropes with different lengths. However if you set both ropes of fire from the tip, they will both burn at exactly one hour.
You are asked to measure 45 minutes using just these two ropes and you and NOT allowed to cut the ropes at all.
How will you do this?
1. Burn one of the ropes from both ends. The rope will burn completely at half time (i.e. 30 minutes).
2. Also burn the other rope from one end at the same time. At the time rope #1 completely burns, rope #2 will be half length. That is, it now has 30 minutes left to burn.
3. Immediately set the other side of rope #2 on fire too. It will burn at half the time left (i.e. 15 minutes).
4. Let rope #2 burn completely too.
You have successfully measured 30minutes + 15 minutes = 45 minutes.
Answer to Q162:
An object with more density, displaces more water. Remember Archimedes story.
The pin is the object with the lest density here so will displace the lest amount of water.
For Cup B to have the same level of water as the rest, that means Cup B has more water to begin with.
Answer: B
An object with more density, displaces more water. Remember Archimedes story.
The pin is the object with the lest density here so will displace the lest amount of water.
For Cup B to have the same level of water as the rest, that means Cup B has more water to begin with.
Answer: B
Answer to Q164:
The pipe to Cup 3 will receive fluid first however, the pipes to 6 and 7 are blocked so no fluid will flow to cup 6 and 6.
So, Cup 3 will get filled first.
Answer: 3
The pipe to Cup 3 will receive fluid first however, the pipes to 6 and 7 are blocked so no fluid will flow to cup 6 and 6.
So, Cup 3 will get filled first.
Answer: 3
Answer to Q165
There was this competition where the contestants had to hold something for as long as they can. At the end of the event, the winner was a person who was physically disabled (he had no hands and no feet)!
How was that possible?
Answer: He held his breath
There was this competition where the contestants had to hold something for as long as they can. At the end of the event, the winner was a person who was physically disabled (he had no hands and no feet)!
How was that possible?
Answer: He held his breath
Answer to Q166
I am an odd number. Take away one letter and I become even. What number am I?
I am an odd number. Take away one letter:
This alone shows the number is spelt in words and not in digits so can't be like 127 or 349 or etc
and I become even:
so I have to add a letter to "even" to make it a number. Seven!
Answer: Seven
I am an odd number. Take away one letter and I become even. What number am I?
I am an odd number. Take away one letter:
This alone shows the number is spelt in words and not in digits so can't be like 127 or 349 or etc
and I become even:
so I have to add a letter to "even" to make it a number. Seven!
Answer: Seven
Answer to Q167
What is 3³⁰ + 3³⁰ + 3³⁰ equal to?
3³⁰ + 3³⁰ + 3³⁰
Finding the common factor
= 3³⁰ (1 + 1 + 1)
= 3³⁰ (3)
= 3³⁰ x 3¹
but aˣ x aʸ = a⁽ˣ⁺ʸ⁾
= 30⁽³⁰⁺¹⁾
= 30³¹
Answer: 30³¹
What is 3³⁰ + 3³⁰ + 3³⁰ equal to?
3³⁰ + 3³⁰ + 3³⁰
Finding the common factor
= 3³⁰ (1 + 1 + 1)
= 3³⁰ (3)
= 3³⁰ x 3¹
but aˣ x aʸ = a⁽ˣ⁺ʸ⁾
= 30⁽³⁰⁺¹⁾
= 30³¹
Answer: 30³¹
Answer to Q168
Calculate the force of the block:
F = Ma
M = 5kg
a = acceleration due to gravity (9.8m/s²)
F = 5 x 9.8
F = 49N
Since 49N is greater than 40N, the block will pull the 40N force down, hence the block will move in the direction of B
Answer: B
Calculate the force of the block:
F = Ma
M = 5kg
a = acceleration due to gravity (9.8m/s²)
F = 5 x 9.8
F = 49N
Since 49N is greater than 40N, the block will pull the 40N force down, hence the block will move in the direction of B
Answer: B
Answer to Q169
Alex pays A for rent and then it was increased by 50%. The new rent was also increased by another 50%. What is the percentage increase of the old rent A to Alex current rent?
Let us assume the initial rent is $100.
then it was increased by 50%: 50% of $100 = $50
So new rent is 100 + 50 = $150
The new rent was also increased by another 50%: 50% of $150 = $75
Current rent = 150 + 75 = $225
What is the percentage increase of the old rent A to Alex current rent: = (difference between current rent and old rent) ÷ old rent
= ((225-100) ÷ 100) x 100%
= (125 ÷ 100) x 100%
= 125%
Answer: 125%
Alex pays A for rent and then it was increased by 50%. The new rent was also increased by another 50%. What is the percentage increase of the old rent A to Alex current rent?
Let us assume the initial rent is $100.
then it was increased by 50%: 50% of $100 = $50
So new rent is 100 + 50 = $150
The new rent was also increased by another 50%: 50% of $150 = $75
Current rent = 150 + 75 = $225
What is the percentage increase of the old rent A to Alex current rent: = (difference between current rent and old rent) ÷ old rent
= ((225-100) ÷ 100) x 100%
= (125 ÷ 100) x 100%
= 125%
Answer: 125%
Answer to Q170:
Any object whose height reduces with use is a correct answer here:
Answer: Candle, Drilling Bits, Pencil, etc
Any object whose height reduces with use is a correct answer here:
Answer: Candle, Drilling Bits, Pencil, etc
Answer to Q171
You have a 100-page book and tore out pages 3, 4, 25, 26, 75, 76, and 97 to 100. How many sheets are left in the book?
A sheet of paper makes 2 pages so 100 pages will be 50 sheets.
tore out pages 3, 4, 25, 26, 75, 76, and 97 to 100
So pages 3, 4, 25, 26, 75, 76, 97, 98, 99 and 100 were torn, making 10 pages (i.e. 5 sheets)
How many sheets are left in the book?
50 sheets - 5 sheets = 45 sheets
Answer: 45 sheets
You have a 100-page book and tore out pages 3, 4, 25, 26, 75, 76, and 97 to 100. How many sheets are left in the book?
A sheet of paper makes 2 pages so 100 pages will be 50 sheets.
tore out pages 3, 4, 25, 26, 75, 76, and 97 to 100
So pages 3, 4, 25, 26, 75, 76, 97, 98, 99 and 100 were torn, making 10 pages (i.e. 5 sheets)
How many sheets are left in the book?
50 sheets - 5 sheets = 45 sheets
Answer: 45 sheets
Answer to Q173
From the picture above, if A + B = 8 (horizontally) and A + C = 13. Using other information that can be deducted from the picture, what is the value for A, B, C and D?
A + B = 8 (eqn i)
C - D = 6 (eqn ii)
A + C = 13 (eqn iii)
B + D = 8 (eqn iv)
From eqn i:
B = 8 - A (eqn v)
From eqn iii:
A = 13 - C (eqn vi)
Put eqn vi into eqn v:
B = 8 - 13 + C
B = -5 + C
B = C - 5 (eqn vii)
From eqn ii:
C = 6 + D (eqn viii)
Put eqn viii into eqn vii:
B = 6 + D - 5
B = 6 - 5 + D
B = 1 + D (eqn ix)
From eqn iv:
D = 8 - B (eqn x)
Put eqn x into ix:
B = 1 + 8 - B
B + B = 1 + 8
2B = 9
B = 9 ÷ 2
B = 4.5
From eqn x:
D = 8 - 4.5
D = 3.5
From eqn viii:
C = 6 + 3.5
C = 9.5
From eqn vi:
A = 13 - 9.5
A = 3.5
Answer: A = 3.5, B = 4.5, C = 9.5, D = 3.5
From the picture above, if A + B = 8 (horizontally) and A + C = 13. Using other information that can be deducted from the picture, what is the value for A, B, C and D?
A + B = 8 (eqn i)
C - D = 6 (eqn ii)
A + C = 13 (eqn iii)
B + D = 8 (eqn iv)
From eqn i:
B = 8 - A (eqn v)
From eqn iii:
A = 13 - C (eqn vi)
Put eqn vi into eqn v:
B = 8 - 13 + C
B = -5 + C
B = C - 5 (eqn vii)
From eqn ii:
C = 6 + D (eqn viii)
Put eqn viii into eqn vii:
B = 6 + D - 5
B = 6 - 5 + D
B = 1 + D (eqn ix)
From eqn iv:
D = 8 - B (eqn x)
Put eqn x into ix:
B = 1 + 8 - B
B + B = 1 + 8
2B = 9
B = 9 ÷ 2
B = 4.5
From eqn x:
D = 8 - 4.5
D = 3.5
From eqn viii:
C = 6 + 3.5
C = 9.5
From eqn vi:
A = 13 - 9.5
A = 3.5
Answer: A = 3.5, B = 4.5, C = 9.5, D = 3.5
Answer to Q174
A 100m train training at 100m/s needs to clear a track of 100m. How many seconds will it take?
A 100m train wants to clear a track of 100m. When the train travels 100m, it will be sitting perfectly on the track but remember, it needed to clear it. So the train, needs to travel another 100m to completely clear the track.
Total distance travelled = 2 x 100m = 200m
How many seconds will it take the train?
v = d ÷ t
t = d ÷ v
t = 200m ÷ 100m/s
t = 2s
Answer: 2s
A 100m train training at 100m/s needs to clear a track of 100m. How many seconds will it take?
A 100m train wants to clear a track of 100m. When the train travels 100m, it will be sitting perfectly on the track but remember, it needed to clear it. So the train, needs to travel another 100m to completely clear the track.
Total distance travelled = 2 x 100m = 200m
How many seconds will it take the train?
v = d ÷ t
t = d ÷ v
t = 200m ÷ 100m/s
t = 2s
Answer: 2s
Answer to Q175
There are 100 pairs of dogs in a zoo; a pair of babies are born for each dog. Unfortunately, 23 of the dogs have not survived. How many dogs are left in total?
100 pairs of dogs = 100 x 2 = 200 dogs
a pair of babies are born for each dog
That is, each dog has 2 babies. Each of them has apair of babies NOT a pair has pair of babies
= 200 x 2
= 400 babies
Unfortunately, 23 of the dogs have not survived.
= 400 - 23
= 377 babies left
Total dogs = 200 dogs + 377 babies
Answer: 577 dogs
There are 100 pairs of dogs in a zoo; a pair of babies are born for each dog. Unfortunately, 23 of the dogs have not survived. How many dogs are left in total?
100 pairs of dogs = 100 x 2 = 200 dogs
a pair of babies are born for each dog
That is, each dog has 2 babies. Each of them has apair of babies NOT a pair has pair of babies
= 200 x 2
= 400 babies
Unfortunately, 23 of the dogs have not survived.
= 400 - 23
= 377 babies left
Total dogs = 200 dogs + 377 babies
Answer: 577 dogs
Answer to Q176:
Find the area of the entire square!
We can take the other side of the orange rectangle to be a.
That means the area of the orange rectangle is 2 x a = 2a.
But we were told all the areas are equal, so the entire square should be 5 x 2a = 10a.
We can also take the length of the yellow rectangle to be c. That means the total length of the entire square is 2 + c.
That means the length and width of the four rectangles (excluding the blue one) will be 2+c and a.
This means the area of those four rectangles will be (2+c) x a which will be equals to 4 x (2a), remember?
so,
(2+c) x a = 4 x (2a)
2a + ac = 8a
divide all through by a
2 + c = 8
c = 8 - 2
c = 6
We now know the total length of the left hand side is 2 + c = 2 + 6 = 8
And remember we were told the entire shape is a square, so the width of the entire square will also be 8.
Area of entire square = 8 x 8
= 64
Answer: 64 sq. unit
Find the area of the entire square!
We can take the other side of the orange rectangle to be a.
That means the area of the orange rectangle is 2 x a = 2a.
But we were told all the areas are equal, so the entire square should be 5 x 2a = 10a.
We can also take the length of the yellow rectangle to be c. That means the total length of the entire square is 2 + c.
That means the length and width of the four rectangles (excluding the blue one) will be 2+c and a.
This means the area of those four rectangles will be (2+c) x a which will be equals to 4 x (2a), remember?
so,
(2+c) x a = 4 x (2a)
2a + ac = 8a
divide all through by a
2 + c = 8
c = 8 - 2
c = 6
We now know the total length of the left hand side is 2 + c = 2 + 6 = 8
And remember we were told the entire shape is a square, so the width of the entire square will also be 8.
Area of entire square = 8 x 8
= 64
Answer: 64 sq. unit
Answer to Q177:
What is the value of 3⁴ ÷ 3⁻² ?
xᵃ ÷ xᶜ = x⁽ᵃ⁻ᶜ⁾
3⁴ ÷ 3⁻² = 3⁽⁴ ⁻ ⁻²⁾
= 3⁽⁴⁺²⁾
= 3⁶
= 729
Answer: 729
What is the value of 3⁴ ÷ 3⁻² ?
xᵃ ÷ xᶜ = x⁽ᵃ⁻ᶜ⁾
3⁴ ÷ 3⁻² = 3⁽⁴ ⁻ ⁻²⁾
= 3⁽⁴⁺²⁾
= 3⁶
= 729
Answer: 729
Answer to Q178:
I am a three-digit number xyz.
y = 4z
x = y-3
What is xyz?
y = 4z (eqn i)
For eqn i to be valid, that means z be only be 0, 1 or 2.
that is because at 3, y becomes 12 (which is not a single digit)
At 0:
z = 0
y = 4 x 0
y = 0
so, z can also not be 0 because y should be 4x larger than z
At 1:
z = 1
y = 4 x 1
y = 4
and x = y - 3
x = 4 - 3
x = 1
xyz = 141
At 2:
z = 2
y = 4 x 2
y = 8
and x = y - 3
x = 8 - 3
x = 5
xyz = 583
Answer 141 or 583
I am a three-digit number xyz.
y = 4z
x = y-3
What is xyz?
y = 4z (eqn i)
For eqn i to be valid, that means z be only be 0, 1 or 2.
that is because at 3, y becomes 12 (which is not a single digit)
At 0:
z = 0
y = 4 x 0
y = 0
so, z can also not be 0 because y should be 4x larger than z
At 1:
z = 1
y = 4 x 1
y = 4
and x = y - 3
x = 4 - 3
x = 1
xyz = 141
At 2:
z = 2
y = 4 x 2
y = 8
and x = y - 3
x = 8 - 3
x = 5
xyz = 583
Answer 141 or 583