Answer to Q136
Find a, b and x
From Pythagorean theorem,
(9+16)² = a² + b² (i)
b² = 16² + x² (ii)
a² = 9² + x² (iii)
from (i)
625 = a² + b² (iv)
put (ii) into (iv)
625 = a² + 16² + x²
625 = a² +256 + x² (v)
put (iii) into (v)
625 = 9² + x² + 256 + x²
625 = 81 + x² + 256 + x²
625 = 2x² + 337
2x² + 337 - 625 = 0
2x² - 288 = 0
2x² = 288
x² = 288 ÷ 2
x² = 144
x = √144
x = 12
put x into (v)
625 = a² +256 + x²
625 = a² + 256 + 144
625 = a² + 400
a² = 625 - 400
a² = 225
a = √225
a = 15
From (ii)
b² = 16² + x²
b² = 256 + 144
b² = 400
b = √400
b = 20
So, x = 12, a = 15, b = 20
Find a, b and x
From Pythagorean theorem,
(9+16)² = a² + b² (i)
b² = 16² + x² (ii)
a² = 9² + x² (iii)
from (i)
625 = a² + b² (iv)
put (ii) into (iv)
625 = a² + 16² + x²
625 = a² +256 + x² (v)
put (iii) into (v)
625 = 9² + x² + 256 + x²
625 = 81 + x² + 256 + x²
625 = 2x² + 337
2x² + 337 - 625 = 0
2x² - 288 = 0
2x² = 288
x² = 288 ÷ 2
x² = 144
x = √144
x = 12
put x into (v)
625 = a² +256 + x²
625 = a² + 256 + 144
625 = a² + 400
a² = 625 - 400
a² = 225
a = √225
a = 15
From (ii)
b² = 16² + x²
b² = 256 + 144
b² = 400
b = √400
b = 20
So, x = 12, a = 15, b = 20
Answer to Q136:
A woman steals $100 from a shop. Then she buys items worth $70 from the shop using the same $100 and gets $30 change. How much did the shop lose?
A woman steals $100 from a shop - at this point the shop is losing $100
Then she buys items worth $70 - at this point the shop is losing $100 + $70 = $170
using the same $100 - at the point where she hands over the $100 to the cashier, the shop is only losing the goods in her possession, $70
and gets $30 change. - now the shop is losing $70 (goods) + $30 (change) = $100
Answer: $100
A woman steals $100 from a shop. Then she buys items worth $70 from the shop using the same $100 and gets $30 change. How much did the shop lose?
A woman steals $100 from a shop - at this point the shop is losing $100
Then she buys items worth $70 - at this point the shop is losing $100 + $70 = $170
using the same $100 - at the point where she hands over the $100 to the cashier, the shop is only losing the goods in her possession, $70
and gets $30 change. - now the shop is losing $70 (goods) + $30 (change) = $100
Answer: $100
Answer to Q137
What is the value of "?"
I am not going to lie, this question threw me off at first but it's actually one of the simplest question I have come across:
The answer is 9, how? No need for any calculation, just check the graph paper.
The value 8 is in entirely 8 boxes, the value 6 is in entirely 6 boxes, and ? is in 9 boxes
Answer: 9
What is the value of "?"
I am not going to lie, this question threw me off at first but it's actually one of the simplest question I have come across:
The answer is 9, how? No need for any calculation, just check the graph paper.
The value 8 is in entirely 8 boxes, the value 6 is in entirely 6 boxes, and ? is in 9 boxes
Answer: 9
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Answer to Q138
Let small cup = S
Let big cup = B
Let handle-less paper coffee cup = H
S + B = 5
S + H = 7
B + H = 8
S + B + H = ?
It, can be written as:
S + B + 0 = 5
S + 0 + H = 7
0+ B + H = 8
Adding all together gives:
2S + 2B + 2H = 20
Divide all through by 2
s + B + H = 10
Answer: 10
Let small cup = S
Let big cup = B
Let handle-less paper coffee cup = H
S + B = 5
S + H = 7
B + H = 8
S + B + H = ?
It, can be written as:
S + B + 0 = 5
S + 0 + H = 7
0+ B + H = 8
Adding all together gives:
2S + 2B + 2H = 20
Divide all through by 2
s + B + H = 10
Answer: 10
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Answer to Q139
Two fathers and two sons went fishing in a boat and they all caught a fish. A total of three fishes were caught, how is that possible?
Two fathers and two sons = The grandpa, the father, and the grandchild = 3 people
The grandpa and the father (2 fathers)
The Father and the Son (2 sons)
Two fathers and two sons went fishing in a boat and they all caught a fish. A total of three fishes were caught, how is that possible?
Two fathers and two sons = The grandpa, the father, and the grandchild = 3 people
The grandpa and the father (2 fathers)
The Father and the Son (2 sons)
Answer to Q140
Many have heard me but no one has seen me. I will never speak unless spoken to.
What am I?
Answer: The Echo
Many have heard me but no one has seen me. I will never speak unless spoken to.
What am I?
Answer: The Echo
Answer to Q141
Four siblings were in a room...
John was reading a book.
Philip was playing chess.
Mary was arranging the shelf.
What was Bill doing?
Philip is playing chess, it takes two people to play chess so Bill is playing with him.
Answer: Bill is playing chess
Four siblings were in a room...
John was reading a book.
Philip was playing chess.
Mary was arranging the shelf.
What was Bill doing?
Philip is playing chess, it takes two people to play chess so Bill is playing with him.
Answer: Bill is playing chess
Answer to Q142
A man buys a book for $150, he then sells for $160. He bought the same book back for $170, then resells it again for $180.
How much did he gain or lose?
Let's assume this man has $500 in his pocket to start with (note, any amount you assume will work, we are just assuming 500).
So he bought a book for $150: at this point, he has $350 left in his pocket.
he then sells for $160: at this point he has (350+160) = $510
He bought the same book back for $170: now he has (510 - 170) = $340
hen resells it again for $180: now he has (340 + 180) = $520
He started out with $500 and at the end he has $520, that means he has made a gain of $20
Answer: He gained $20
A man buys a book for $150, he then sells for $160. He bought the same book back for $170, then resells it again for $180.
How much did he gain or lose?
Let's assume this man has $500 in his pocket to start with (note, any amount you assume will work, we are just assuming 500).
So he bought a book for $150: at this point, he has $350 left in his pocket.
he then sells for $160: at this point he has (350+160) = $510
He bought the same book back for $170: now he has (510 - 170) = $340
hen resells it again for $180: now he has (340 + 180) = $520
He started out with $500 and at the end he has $520, that means he has made a gain of $20
Answer: He gained $20
Answer to Q143
2ˣ + 2ˣ⁻¹ = 6144. Find x
This is eqn i: 2ˣ + 2ˣ⁻¹ = 6144
eqn i can be rewritten as:
2ˣ + (2ˣ ÷ 2) = 6144 eqn ii
2ˣ (1 + ½) = 6144
2ˣ (³⁄₂) = 6144 eqn iii
divide eqn iii through by ³⁄₂
2ˣ = 6144 ÷ ³⁄₂
2ˣ = 6144 x ⅔
2ˣ = 4096
logarithm rule comes in here
log⁴⁰⁹⁶ ÷ log² = x
x = 12
Answer: 12
2ˣ + 2ˣ⁻¹ = 6144. Find x
This is eqn i: 2ˣ + 2ˣ⁻¹ = 6144
eqn i can be rewritten as:
2ˣ + (2ˣ ÷ 2) = 6144 eqn ii
2ˣ (1 + ½) = 6144
2ˣ (³⁄₂) = 6144 eqn iii
divide eqn iii through by ³⁄₂
2ˣ = 6144 ÷ ³⁄₂
2ˣ = 6144 x ⅔
2ˣ = 4096
logarithm rule comes in here
log⁴⁰⁹⁶ ÷ log² = x
x = 12
Answer: 12
Answer to Q144
The 30% of a number is 43,589. What is 20% of that number?
If 30% of a number is 43,589, what is the 100% of that number? That will be that number divided by 30 then multiplied by 100.
(43,589 ÷ 30) x 100 = 145,296.67.
What's 20% of 145,296.67. That will be 145,296.67 divided 100 multiplied by 20.
(145,296.67 ÷ 100) x 20 = 29,059.33
Answer: 29,059.33
The 30% of a number is 43,589. What is 20% of that number?
If 30% of a number is 43,589, what is the 100% of that number? That will be that number divided by 30 then multiplied by 100.
(43,589 ÷ 30) x 100 = 145,296.67.
What's 20% of 145,296.67. That will be 145,296.67 divided 100 multiplied by 20.
(145,296.67 ÷ 100) x 20 = 29,059.33
Answer: 29,059.33
Answer to Q145
What is 9% equal to?
x% is always equal to x/100, so 9% equals 9/100 = 0.09
Answer: 0.09
What is 9% equal to?
x% is always equal to x/100, so 9% equals 9/100 = 0.09
Answer: 0.09
Answer to Q146
A problem in mathematics is given to 3 students whose chances of solving individually are ½ , ⅓ and ¼. The probability that the problem will be solved at least by one, is what?
The best way to solve this is to first find the probability of them not been able to solve the question individually, then from that find the probability of them not been able to solve the question collectively. From there, you can then find the probability of one of them solving it (which will be 1 - probability of them not solving it).
Probability of them not been able to solve the question individually will be (1 - ½ ), (1 - ⅓) and (1 - ¼)
Which are: ½, ⅔ and ¾
Probability of them not been able to solve the question collectively will then be: ½ x ⅔ x ¾ = ⁶⁄₂₄
⁶⁄₂₄ can be reduced to ¼
The probability of then solving the question collectively will then be 1 - ¼ = ¾
Answer: ¾
A problem in mathematics is given to 3 students whose chances of solving individually are ½ , ⅓ and ¼. The probability that the problem will be solved at least by one, is what?
The best way to solve this is to first find the probability of them not been able to solve the question individually, then from that find the probability of them not been able to solve the question collectively. From there, you can then find the probability of one of them solving it (which will be 1 - probability of them not solving it).
Probability of them not been able to solve the question individually will be (1 - ½ ), (1 - ⅓) and (1 - ¼)
Which are: ½, ⅔ and ¾
Probability of them not been able to solve the question collectively will then be: ½ x ⅔ x ¾ = ⁶⁄₂₄
⁶⁄₂₄ can be reduced to ¼
The probability of then solving the question collectively will then be 1 - ¼ = ¾
Answer: ¾
Answer to Q147
(−36) + (+12) is equal to
This can be rewritten as -36 + 12, which is same as 12 - 36, which is -24
Negative 24 is not part of the options given so the answer is "None of the above"
Answer: None of the above
(−36) + (+12) is equal to
This can be rewritten as -36 + 12, which is same as 12 - 36, which is -24
Negative 24 is not part of the options given so the answer is "None of the above"
Answer: None of the above
Answer to Q148
The side of a square is 2 cm. Semicircles are constructed on two sides of the square. What is the area of the whole figure?
The area of the whole figure will be = the area of the square + (2 x the area of semicircle)
This is same as = the area of the square + the area of a circle.
Area of the square = L x B = 2 x 2 = 4 cm²
Area of a circle = πr²
The side of the square is 2cm which means the diameter of the circle is also 2cm, that makes the radius 1cm
Area of the circle = π x 1² = πcm²
So, the area of the figure = 4 cm² + π cm² = (4 + π) cm²
Answer: (4 + π) cm²
The side of a square is 2 cm. Semicircles are constructed on two sides of the square. What is the area of the whole figure?
The area of the whole figure will be = the area of the square + (2 x the area of semicircle)
This is same as = the area of the square + the area of a circle.
Area of the square = L x B = 2 x 2 = 4 cm²
Area of a circle = πr²
The side of the square is 2cm which means the diameter of the circle is also 2cm, that makes the radius 1cm
Area of the circle = π x 1² = πcm²
So, the area of the figure = 4 cm² + π cm² = (4 + π) cm²
Answer: (4 + π) cm²
Answer to Q149
What is the value of an integer, if the sum of the integer and its inverse is ⁴⁄₂?
Let the integer be x. So inverse of x is ¹⁄ₓ
:sum of the integer and its inverse is ⁴⁄₂
x + ¹⁄ₓ = ⁴⁄₂
x + ¹⁄ₓ can be rewritten as (x² + 1) ÷ x
(x² + 1) ÷ x = 2
x² + 1 = 2x
x² - 2x + 1 = 0
Using the quadratic formula
x = 2 ÷ 2
x = 1
Answer: 1
What is the value of an integer, if the sum of the integer and its inverse is ⁴⁄₂?
Let the integer be x. So inverse of x is ¹⁄ₓ
:sum of the integer and its inverse is ⁴⁄₂
x + ¹⁄ₓ = ⁴⁄₂
x + ¹⁄ₓ can be rewritten as (x² + 1) ÷ x
(x² + 1) ÷ x = 2
x² + 1 = 2x
x² - 2x + 1 = 0
Using the quadratic formula
x = 2 ÷ 2
x = 1
Answer: 1
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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