Answer to Q82
A - 4B + 2C = 16, 2A + 7B - 5C = 83. What is A + B - C?
A - 4B + 2C = 16 (eqn i)
2A + 7B - 5C = 83 (eqn ii)
A + B - C (eqn iii)
Multiply (eqn i) by 2
2A - 8B + 4C = 32 (eqn iv)
Subtract (eqn ii) from (eqn iv)
-15B + 9C = -51
C = (-51 + 15B) ÷ 9 (eqn v)
Putting (eqn v) into (eqn i)
A - 4B - (102 ÷ 9) + (30B ÷ 9) = 16
A = 16 + 4B + (102 ÷ 9) - (30B ÷ 9) (eqn vi)
Putting (eqn vi) and (eqn v) into (eqn iii)
16 + 4B + (102 ÷ 9) - (30B ÷ 9) + B + (51÷ 9) - (15B ÷ 9)
Making 9 the common factor
(144 + 36B - 30B + 102 + 9B + 51 - 15B) ÷ 9
297 ÷ 9
= 33
Answer: 33
A - 4B + 2C = 16, 2A + 7B - 5C = 83. What is A + B - C?
A - 4B + 2C = 16 (eqn i)
2A + 7B - 5C = 83 (eqn ii)
A + B - C (eqn iii)
Multiply (eqn i) by 2
2A - 8B + 4C = 32 (eqn iv)
Subtract (eqn ii) from (eqn iv)
-15B + 9C = -51
C = (-51 + 15B) ÷ 9 (eqn v)
Putting (eqn v) into (eqn i)
A - 4B - (102 ÷ 9) + (30B ÷ 9) = 16
A = 16 + 4B + (102 ÷ 9) - (30B ÷ 9) (eqn vi)
Putting (eqn vi) and (eqn v) into (eqn iii)
16 + 4B + (102 ÷ 9) - (30B ÷ 9) + B + (51÷ 9) - (15B ÷ 9)
Making 9 the common factor
(144 + 36B - 30B + 102 + 9B + 51 - 15B) ÷ 9
297 ÷ 9
= 33
Answer: 33
Answer to Q83
1, 3, 8, 19, x. What is x?
Finding the difference between this series:
3 - 1 = 2
8 - 3 = 5
19 - 8 = 11
x - 19 = y (eqn i)
We have a new series here:
2, 5, 11, y and there still didn't seem to be a clear relationship between them, so we find their difference again.
5 - 2 = 3
11 - 5 = 6
y - 11 = z (eqn ii)
New series 3, 6, z so here we have our relationship. First element is 3, second element is twice of first element (2x3 = 6), so
z = 6 x 2 = 12
Putting z into eqn ii
y - 11 = 12
y = 12 + 11 = 23
Putting y into eqn i
x - 19 = 23
x = 23 + 19 = 42
Answer: 42
1, 3, 8, 19, x. What is x?
Finding the difference between this series:
3 - 1 = 2
8 - 3 = 5
19 - 8 = 11
x - 19 = y (eqn i)
We have a new series here:
2, 5, 11, y and there still didn't seem to be a clear relationship between them, so we find their difference again.
5 - 2 = 3
11 - 5 = 6
y - 11 = z (eqn ii)
New series 3, 6, z so here we have our relationship. First element is 3, second element is twice of first element (2x3 = 6), so
z = 6 x 2 = 12
Putting z into eqn ii
y - 11 = 12
y = 12 + 11 = 23
Putting y into eqn i
x - 19 = 23
x = 23 + 19 = 42
Answer: 42
Answer to Q84
528 = 15, 703 = 10, 397 = 19, 601 = x. What is x?
ABC = A+B+C
528 = 5 + 2 + 8 = 15
703 = 7 + 0 + 3 = 10
397 = 3 + 9 + 7 = 19
601 = 6 + 0 + 1 = 7
Answer: 7
528 = 15, 703 = 10, 397 = 19, 601 = x. What is x?
ABC = A+B+C
528 = 5 + 2 + 8 = 15
703 = 7 + 0 + 3 = 10
397 = 3 + 9 + 7 = 19
601 = 6 + 0 + 1 = 7
Answer: 7
Answer to Q85
Is a - b - c = a - (b - c)?
This question generates from a mistake I made while in a rush to do the calculation 18 - 3 - 2. Immediately I saw the question, I (been in a hurray and not thinking clearly) did a stupid 3 - 2 = 1; 18 - 1 = 17
Immediately I saw my answer, my instinct told me something is wrong with it. then I saw my mistake!
What I should have done was -3-2 = -5; 18 - 5 = 13!
a - b - c can not be equals to a - (b - c)
Expanding a - (b - c) will give you a -b -(-c) = a - b + c
That was why I got 17 earlier (18 - 3 + 2)
Answer: False
Is a - b - c = a - (b - c)?
This question generates from a mistake I made while in a rush to do the calculation 18 - 3 - 2. Immediately I saw the question, I (been in a hurray and not thinking clearly) did a stupid 3 - 2 = 1; 18 - 1 = 17
Immediately I saw my answer, my instinct told me something is wrong with it. then I saw my mistake!
What I should have done was -3-2 = -5; 18 - 5 = 13!
a - b - c can not be equals to a - (b - c)
Expanding a - (b - c) will give you a -b -(-c) = a - b + c
That was why I got 17 earlier (18 - 3 + 2)
Answer: False
Answer to Q86
What are the three consecutive integers whose sum are equal to 93?
Let the first integer be x. The consecutive integers will then be x+1 and x+2.
So, x + (x+1) + (x+2) = 93
x + x+1 + x+2 = 93
3x + 3 = 93
3x = 93 - 3
3x = 90
x = 90 ÷ 3
x = 30
So, first integer is 30.
Answer: 30, 31, 32
What are the three consecutive integers whose sum are equal to 93?
Let the first integer be x. The consecutive integers will then be x+1 and x+2.
So, x + (x+1) + (x+2) = 93
x + x+1 + x+2 = 93
3x + 3 = 93
3x = 93 - 3
3x = 90
x = 90 ÷ 3
x = 30
So, first integer is 30.
Answer: 30, 31, 32
Answer to Q87
A+B=36; A-B=24; A÷B=?
A + B = 36 - - (i)
A - B = 24 - - (ii)
A ÷ B = ?
From (i)
B = 36 - A - - (iii)
Putting (iii) into (ii)
A - (36 - A) = 24
A - 36 + A = 24
2A = 24 + 36
2A = 60
A = 30
Putting A into (iii)
B = 36 - 30
B = 6
So, A ÷ B = 30 ÷ 6 = 5
Answer: 5
A+B=36; A-B=24; A÷B=?
A + B = 36 - - (i)
A - B = 24 - - (ii)
A ÷ B = ?
From (i)
B = 36 - A - - (iii)
Putting (iii) into (ii)
A - (36 - A) = 24
A - 36 + A = 24
2A = 24 + 36
2A = 60
A = 30
Putting A into (iii)
B = 36 - 30
B = 6
So, A ÷ B = 30 ÷ 6 = 5
Answer: 5
Answer to Q88
A flock of birds flying met a single bird.
The single bird greeted the flock "hello hundred" but the flock replied "we are not hundred, half of us plus you will make us hundred". How many birds were flying?
Let the number of birds in the flock be x
But half of x plus 1 will make a hundred
so,
(x ÷ 2) + 1 = 100
x ÷ 2 = 99
x = 99 * 2
x = 198
So, number of birds in the flock is 198.
But here is the tricky part, the question asked "How many birds were flying?" NOT "What is the number of birds in the flock?". The single bird that greeted the flock was also flying (if he wasn't flying how would he have met the flying flock?).
So, number of birds flying = number of flock + single bird
= 198 + 1
= 199
Answer: 199
A flock of birds flying met a single bird.
The single bird greeted the flock "hello hundred" but the flock replied "we are not hundred, half of us plus you will make us hundred". How many birds were flying?
Let the number of birds in the flock be x
But half of x plus 1 will make a hundred
so,
(x ÷ 2) + 1 = 100
x ÷ 2 = 99
x = 99 * 2
x = 198
So, number of birds in the flock is 198.
But here is the tricky part, the question asked "How many birds were flying?" NOT "What is the number of birds in the flock?". The single bird that greeted the flock was also flying (if he wasn't flying how would he have met the flying flock?).
So, number of birds flying = number of flock + single bird
= 198 + 1
= 199
Answer: 199
Answer to Q89
Add me to myself and multiply by 4. Divide me by 8 and you will have me once more. What number am I?
Let myself be x
Add me to myself: x + x = 2x
And multiply by 4: 4(2x) = 8x
Then divide by 8: 8x ÷ 8 = x
Answer: Any number in the world!
Add me to myself and multiply by 4. Divide me by 8 and you will have me once more. What number am I?
Let myself be x
Add me to myself: x + x = 2x
And multiply by 4: 4(2x) = 8x
Then divide by 8: 8x ÷ 8 = x
Answer: Any number in the world!
Answer to Q90
Sally is 54 years old and her mother is 80, how many years ago was Sally's mother three times her age?
Let Sally's age be x
Let her mother's age be y
Now, x = 54 and y = 80
So, y - x = 26 (the mother will always be 26 years older than Sally at all time)
But there was a time when the mother's age was three times Sally's age.
So at that time: y = 3x - - eq i
But remember: y - x = 26 - - eq ii
From eq ii
y = 26 + x - - eq iii
Putting eq iii into eq i
26 + x = 3x
26 = 3x - x
26 = 2x
x = 26 ÷ 2
x = 13
So, when Sally was 13 her mother was 3 x 13 = 39. And to check, is 39 - 13, 26? Yes, so we are good.
But here is the tricky part, the question asked for how many years ago that scenario was not Sally's age at that time.
Sally is now 54 and the scenario was when she was 13, so that was 54 - 13 years ago
Answer: 41
Sally is 54 years old and her mother is 80, how many years ago was Sally's mother three times her age?
Let Sally's age be x
Let her mother's age be y
Now, x = 54 and y = 80
So, y - x = 26 (the mother will always be 26 years older than Sally at all time)
But there was a time when the mother's age was three times Sally's age.
So at that time: y = 3x - - eq i
But remember: y - x = 26 - - eq ii
From eq ii
y = 26 + x - - eq iii
Putting eq iii into eq i
26 + x = 3x
26 = 3x - x
26 = 2x
x = 26 ÷ 2
x = 13
So, when Sally was 13 her mother was 3 x 13 = 39. And to check, is 39 - 13, 26? Yes, so we are good.
But here is the tricky part, the question asked for how many years ago that scenario was not Sally's age at that time.
Sally is now 54 and the scenario was when she was 13, so that was 54 - 13 years ago
Answer: 41
Answer to Q91
What is half of two plus two?
This question is more of a logical question, the answer depends on how you interpret the question. So, logically speaking, what's the difference between:
A: What is half of two plus two?
B: What is the half of the summation of two and two?
Logically, A is telling you to half two and add it to two ((2÷2) + 2 = 3) while B is telling you to half the summation of two and two ( (2 + 2) ÷ 2 = 2)
Answer: 3 (but again, it all depends on your logic)
What is half of two plus two?
This question is more of a logical question, the answer depends on how you interpret the question. So, logically speaking, what's the difference between:
A: What is half of two plus two?
B: What is the half of the summation of two and two?
Logically, A is telling you to half two and add it to two ((2÷2) + 2 = 3) while B is telling you to half the summation of two and two ( (2 + 2) ÷ 2 = 2)
Answer: 3 (but again, it all depends on your logic)
Answer to Q92
In two years I know, I'll be twice as old as five years ago, said Tom. How old is Tom?
Let Tom's current age be y
But in 2 years time (y + 2), Tom will be twice is age five years ago (y - 5)
(y + 2) = 2 x (y - 5)
y + 2 = 2y - 10
2 + 10 = 2y - y
12 = y
So, Tom is currently 12
Answer: 12
In two years I know, I'll be twice as old as five years ago, said Tom. How old is Tom?
Let Tom's current age be y
But in 2 years time (y + 2), Tom will be twice is age five years ago (y - 5)
(y + 2) = 2 x (y - 5)
y + 2 = 2y - 10
2 + 10 = 2y - y
12 = y
So, Tom is currently 12
Answer: 12
Answer to Q92
Mom and dad have four daughters, and each daughter has one brother. How many people are in the family?
Mom and dad have four daughters, so number of daughters = 4
Each daughters has one brother, this is the tricky part. If each daughters has one brother, this means there is just one brother in the family.
Say there is a Brother Z and Sisters A, B, C and D. Z is a brother to all A, B, C and D not just A or B.
So, number of sons = 1
How many people are in the family = daughters + son + dad + mom = 4 + 1 + 1 + 1 = 7
Answer: 7
Mom and dad have four daughters, and each daughter has one brother. How many people are in the family?
Mom and dad have four daughters, so number of daughters = 4
Each daughters has one brother, this is the tricky part. If each daughters has one brother, this means there is just one brother in the family.
Say there is a Brother Z and Sisters A, B, C and D. Z is a brother to all A, B, C and D not just A or B.
So, number of sons = 1
How many people are in the family = daughters + son + dad + mom = 4 + 1 + 1 + 1 = 7
Answer: 7
Answer to Q94
In a bicycle race, the man who came two places in front of the last man finished one ahead of the man who came fifth. How many contestants were there?
...the man who came two places in front of the last man: Let the last three people in the race be x, y and z. This means our man is x and the last man is z and there is y in between them.
... finished one ahead of the man who came fifth: so x is one position ahead of the 5th guy, that means x is in the 4th position.
So if x is 4th position, y will be 5th position and z will be 6th position. So there are 6 people in the race
Answer: 6
In a bicycle race, the man who came two places in front of the last man finished one ahead of the man who came fifth. How many contestants were there?
...the man who came two places in front of the last man: Let the last three people in the race be x, y and z. This means our man is x and the last man is z and there is y in between them.
... finished one ahead of the man who came fifth: so x is one position ahead of the 5th guy, that means x is in the 4th position.
So if x is 4th position, y will be 5th position and z will be 6th position. So there are 6 people in the race
Answer: 6
Answer to Q95
A man says: "Brothers and sisters, have I none, but that man's father is my father's son." Who is he pointing at?
The man does not have any brother and sister but he points at a person and said that man's father is my father's son.
...is my father's son means he is talking about himself (remember he doesn't have brothers and sisters) so we can replace that in the statement and it becomes:
...but that man's father is me.
It's now clear he is pointing at his son.
Answer: son
A man says: "Brothers and sisters, have I none, but that man's father is my father's son." Who is he pointing at?
The man does not have any brother and sister but he points at a person and said that man's father is my father's son.
...is my father's son means he is talking about himself (remember he doesn't have brothers and sisters) so we can replace that in the statement and it becomes:
...but that man's father is me.
It's now clear he is pointing at his son.
Answer: son
Answer to Q96
In 1986, a person is 13 years old. In 1995, this very same person is 4 years old.
How can this be?
In the BC era, years are counted backwards towards 0. That is 1986BC is followed by 1985BC and then 1984BC.
Answer:
So if a person is 4 years old in 1995BC, by 1986BC (9 years later) he will be 13 years old.
In 1986, a person is 13 years old. In 1995, this very same person is 4 years old.
How can this be?
In the BC era, years are counted backwards towards 0. That is 1986BC is followed by 1985BC and then 1984BC.
Answer:
So if a person is 4 years old in 1995BC, by 1986BC (9 years later) he will be 13 years old.
Answer to Q97
If 9 is subtracted from the product of p and 4, the result is 11. What is the value of p?
Product of p and 4 = 4p
If 9 is subtracted from the product of p and 4: 4p - 9
4p - 9 = 11
4p = 11 + 9
4p = 20
p = 20 ÷ 4
p = 5
Answer: 5
If 9 is subtracted from the product of p and 4, the result is 11. What is the value of p?
Product of p and 4 = 4p
If 9 is subtracted from the product of p and 4: 4p - 9
4p - 9 = 11
4p = 11 + 9
4p = 20
p = 20 ÷ 4
p = 5
Answer: 5
Answer to Q98
Sally likes 225 but not 224; she likes 900 but not 800; she likes 144 but not 145. Which does she like - 1600 or 1700?
1. Maybe she likes largest numbers?
225 > 224
900 > 800
but 144 < 145
So, no
2. Maybe she likes numbers that adds up to 9?
225 = 2+2+5 = 9
900 = 9+0+0 = 9
144 = 1+4+4 = 9
But 1600 = 1+6+0+0 = 7 and 1700 = 1+7+0+0 = 8
So, no 😔 (so close)
Let's try again, maybe she likes perfect squares
√225 = 15
√900 = 30
√144 = 12
√1600 = 40 and √1700 = 41.2311
We got our answer, she likes perfect squares!
Answer: 1600
Sally likes 225 but not 224; she likes 900 but not 800; she likes 144 but not 145. Which does she like - 1600 or 1700?
1. Maybe she likes largest numbers?
225 > 224
900 > 800
but 144 < 145
So, no
2. Maybe she likes numbers that adds up to 9?
225 = 2+2+5 = 9
900 = 9+0+0 = 9
144 = 1+4+4 = 9
But 1600 = 1+6+0+0 = 7 and 1700 = 1+7+0+0 = 8
So, no 😔 (so close)
Let's try again, maybe she likes perfect squares
√225 = 15
√900 = 30
√144 = 12
√1600 = 40 and √1700 = 41.2311
We got our answer, she likes perfect squares!
Answer: 1600
Answer to Q99:
What number is one fifth of one fourth of one ninth of 900?
This is actually a no brainer:
one ninth of 900 = 900÷9 = 100
one fourth of that is = 100 ÷ 4 = 25
one fifth of that is = 25 ÷ 5 = 5
Answer: 5
What number is one fifth of one fourth of one ninth of 900?
This is actually a no brainer:
one ninth of 900 = 900÷9 = 100
one fourth of that is = 100 ÷ 4 = 25
one fifth of that is = 25 ÷ 5 = 5
Answer: 5
Answer to Q100
Two men, starting at the same point, walk in opposite directions for 4 meters, turn left and walk another 3 meters. What is the distance between them?
So they started at the same point and walked in opposite direction for 4 meters. This means they are not 8 meters apart.
They turned left and walked another 3 meters. For them to both turn left, that means one is turning to the north and the other to the south. (See the rough sketch above).
To find the distance between them, we can take the triangle ASD, find AS and multiply by 2.
AS² = DS² + DA²
AS² = 4² + 3²
AS² = 16 + 9
AS² = 25
AS = √25
AS = 5
So, distance between them is 5 x 2 = 10
Answer: 10
Two men, starting at the same point, walk in opposite directions for 4 meters, turn left and walk another 3 meters. What is the distance between them?
So they started at the same point and walked in opposite direction for 4 meters. This means they are not 8 meters apart.
They turned left and walked another 3 meters. For them to both turn left, that means one is turning to the north and the other to the south. (See the rough sketch above).
To find the distance between them, we can take the triangle ASD, find AS and multiply by 2.
AS² = DS² + DA²
AS² = 4² + 3²
AS² = 16 + 9
AS² = 25
AS = √25
AS = 5
So, distance between them is 5 x 2 = 10
Answer: 10
Answer to Q101
If it were two hours later, it would be half as long until midnight as it would be if it were an hour later. What time is it now?
Let x be our current time and a whole day is 24 hours.
If it were two hours later (x + 2), it would be half (½) as long until midnight (24) as it would be if it were an hour later (x + 1).
So,
24 - (x + 2) = ½(24 - (x + 1))
24 - x - 2 = ½ (24 - x - 1)
48 - 2x - 4 = 24 - x - 1
48 - 24 - 4 + 1 = -x + 2x
21 = x
So, 21:00hrs is same as 21 - 12 = 9pm
Answer: 9pm
If it were two hours later, it would be half as long until midnight as it would be if it were an hour later. What time is it now?
Let x be our current time and a whole day is 24 hours.
If it were two hours later (x + 2), it would be half (½) as long until midnight (24) as it would be if it were an hour later (x + 1).
So,
24 - (x + 2) = ½(24 - (x + 1))
24 - x - 2 = ½ (24 - x - 1)
48 - 2x - 4 = 24 - x - 1
48 - 24 - 4 + 1 = -x + 2x
21 = x
So, 21:00hrs is same as 21 - 12 = 9pm
Answer: 9pm