Answer to Q150
ABCD is a square with side a. In centres A,B,C and D four circles are drawn such that each circle touches externally two of the three remaining circles. Let δ be the area interior of the square and exterior of the circles. What is the value of δ?
δ = Shaded area
δ = Area of a square - (4 x ¼ area of a circle)
= a² - (area of a circle)
= a² - πr²
but r = ᵃ⁄₂
= a² - π(ᵃ⁄₂)²
= a² - ((πa²) ÷ 4)
= (4a² - πa²) ÷ 4
= a² [(4 - π) ÷ 4]
Answer: a² [(4 - π) ÷ 4]
ABCD is a square with side a. In centres A,B,C and D four circles are drawn such that each circle touches externally two of the three remaining circles. Let δ be the area interior of the square and exterior of the circles. What is the value of δ?
δ = Shaded area
δ = Area of a square - (4 x ¼ area of a circle)
= a² - (area of a circle)
= a² - πr²
but r = ᵃ⁄₂
= a² - π(ᵃ⁄₂)²
= a² - ((πa²) ÷ 4)
= (4a² - πa²) ÷ 4
= a² [(4 - π) ÷ 4]
Answer: a² [(4 - π) ÷ 4]
Answer to Q151
The radius of a circle is twice its diameter.
What is the radius of a circle? Radius of a circle is half of it diameter i.e. radius (r) of a circle is it diameter (d) divided by 2.
So radius of a circle is NOT twice its diameter but rather half of its diameter.
Answer: False
The radius of a circle is twice its diameter.
What is the radius of a circle? Radius of a circle is half of it diameter i.e. radius (r) of a circle is it diameter (d) divided by 2.
So radius of a circle is NOT twice its diameter but rather half of its diameter.
Answer: False
Answer to Q152
In a class of 500 students, 350 take mathematics and 284 take science. How many take both mathematics and science? (All take math and/or science.)
Let the total number of student be A
So, A = 500
Let the total number of students that takes mathematics be M
So, M = 350
Let the total number of students that takes science be S
So, S = 284
Let the total number of students that takes both mathematics and science be X
And we are told all of them takes mathematics and/or science, which means each student must take mathematics or science or both.
So, the total number of student must be equal to the total that takes mathematics + number that takes science - number that takes both.
A = M + S - X
500 = 350 + 284 - X
500 = 634 - X
X = 634 - 500
x = 134
Answer: 134
In a class of 500 students, 350 take mathematics and 284 take science. How many take both mathematics and science? (All take math and/or science.)
Let the total number of student be A
So, A = 500
Let the total number of students that takes mathematics be M
So, M = 350
Let the total number of students that takes science be S
So, S = 284
Let the total number of students that takes both mathematics and science be X
And we are told all of them takes mathematics and/or science, which means each student must take mathematics or science or both.
So, the total number of student must be equal to the total that takes mathematics + number that takes science - number that takes both.
A = M + S - X
500 = 350 + 284 - X
500 = 634 - X
X = 634 - 500
x = 134
Answer: 134
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Answer to Q153
785 = 2510 - X. What is X?
785 = 2510 - X
2510 - X = 785
-X = 785 - 2510
-X = -1,725
X = 1,725
Answer: 1725
785 = 2510 - X. What is X?
785 = 2510 - X
2510 - X = 785
-X = 785 - 2510
-X = -1,725
X = 1,725
Answer: 1725
Answer to Q154
Assuming a≠b, can aᵇ = bᵃ if both a and b are positive integers?
The question asked can aᵇ = bᵃ, not will at all time aᵇ = bᵃ. So if we can find at least one instance in which aᵇ = bᵃ, then the statement is true.
And, 2⁴ = 4² (this is however the only instance where aᵇ = bᵃ)
2⁴ = 16
4² = 16
Answer: true
Assuming a≠b, can aᵇ = bᵃ if both a and b are positive integers?
The question asked can aᵇ = bᵃ, not will at all time aᵇ = bᵃ. So if we can find at least one instance in which aᵇ = bᵃ, then the statement is true.
And, 2⁴ = 4² (this is however the only instance where aᵇ = bᵃ)
2⁴ = 16
4² = 16
Answer: true
Answer to Q156
A group of 20 students boarded your school bus. At Point A, 5 students got down and 3 more boarded. At Point B, 10 got down and 7 more boarded. At Point C, 5 got down and 7 more boarded.
Who is the driver?
Who is the driver? A group of 20 students boarded your school bus
Answer: You are the driver
A group of 20 students boarded your school bus. At Point A, 5 students got down and 3 more boarded. At Point B, 10 got down and 7 more boarded. At Point C, 5 got down and 7 more boarded.
Who is the driver?
Who is the driver? A group of 20 students boarded your school bus
Answer: You are the driver
Answer to Q157
What is the next number in the series? 7645, 5764, 4576
The series moves the last number to the front, 7645 becomes 5764 (5 moves to the front), 5764 becomes 4576 (4 moves to the front), so the next will be 6457 (6 moves to the front)
Answer: 6457
What is the next number in the series? 7645, 5764, 4576
The series moves the last number to the front, 7645 becomes 5764 (5 moves to the front), 5764 becomes 4576 (4 moves to the front), so the next will be 6457 (6 moves to the front)
Answer: 6457
Answer to Q158
Tom was asked to paint the apartment number on plates for 100 apartments which means he will have to paint numbers 1 through 100. How many times will he paint the number 8?
He will have to print 8 in 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 98
Answer: 20 times
Tom was asked to paint the apartment number on plates for 100 apartments which means he will have to paint numbers 1 through 100. How many times will he paint the number 8?
He will have to print 8 in 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 98
Answer: 20 times
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
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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
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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
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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
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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
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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
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