Answer to Q63
4-9-10-15, 7-12-3-8, 14-7-9-?
With A-B-C-D, the pattern is A + D = B + C
4-9-10-15: 4 + 15 = 9 + 10 = 19
7-12-3-8: 7 + 8 = 12 + 3 =15
So, 14-7-9-x = 14 + x = 7 + 9 = 16
14 + x = 16
x = 16 - 14
x = 2
Answer: 2
4-9-10-15, 7-12-3-8, 14-7-9-?
With A-B-C-D, the pattern is A + D = B + C
4-9-10-15: 4 + 15 = 9 + 10 = 19
7-12-3-8: 7 + 8 = 12 + 3 =15
So, 14-7-9-x = 14 + x = 7 + 9 = 16
14 + x = 16
x = 16 - 14
x = 2
Answer: 2
Answer to Q64
If and equals et, is equals est. What is an?
A clever code or puzzle can be hiding in plain sight and that's the case for this one. It's actually no code or encryption of any kind, it's just English to French translation!
English = French
and = et
is = est
a(n) = un
Answer: un
If and equals et, is equals est. What is an?
A clever code or puzzle can be hiding in plain sight and that's the case for this one. It's actually no code or encryption of any kind, it's just English to French translation!
English = French
and = et
is = est
a(n) = un
Answer: un
Answer to Q66
[5, 7, 4], [10, 5, 5], [20, 7, x]. What is x?
[A, B, C]: C = (A + B) ÷ 3
[5, 7, 4]: (5 + 7) ÷ 3 = 12 ÷ 3 = 4
[10, 5, 5]: (10 + 5) ÷ 3 = 15 ÷ 3 = 5
[20, 7, x]: x = (20 + 7) ÷ 3 = 27 ÷ 3 = 9
Answer: 9
[5, 7, 4], [10, 5, 5], [20, 7, x]. What is x?
[A, B, C]: C = (A + B) ÷ 3
[5, 7, 4]: (5 + 7) ÷ 3 = 12 ÷ 3 = 4
[10, 5, 5]: (10 + 5) ÷ 3 = 15 ÷ 3 = 5
[20, 7, x]: x = (20 + 7) ÷ 3 = 27 ÷ 3 = 9
Answer: 9
Answer to Q67
If 73 = 32, 82 = 27 and 10.6 = 77. What is 57?
The pattern
AB = C: (A+1) x (B+1) = C
A.B = C: (A+1) x (B+1) = C
73 = 32: 8 x 4 = 32
82 = 27: 9 x 3 = 27
10.6 = 77: 11 x 7 = 77
57 = 6 x 8 = 48
Answer: 48
If 73 = 32, 82 = 27 and 10.6 = 77. What is 57?
The pattern
AB = C: (A+1) x (B+1) = C
A.B = C: (A+1) x (B+1) = C
73 = 32: 8 x 4 = 32
82 = 27: 9 x 3 = 27
10.6 = 77: 11 x 7 = 77
57 = 6 x 8 = 48
Answer: 48
Answer to Q68
141₅ = x ₁₀. What is x?
Converting from base 5 to base 10
141₅ becomings 1² 4¹ 1°
= (1 x 5²) + (4 x 5¹) + (1 x 5°)
= 25 + 20 + 1
= 46
Answer: 46
141₅ = x ₁₀. What is x?
Converting from base 5 to base 10
141₅ becomings 1² 4¹ 1°
= (1 x 5²) + (4 x 5¹) + (1 x 5°)
= 25 + 20 + 1
= 46
Answer: 46
Answer to Q69
If 1 = 0, 10 = 1 and 100 = 2. What is 63?
At first glance, you would have thought we are counting the numbers of zeros but a smart people will know it can't be as simple as that.
Any one good at math will notice a pattern immediately though logarithm
Log 1 base 10 is 0
Log 10 base 10 is 1
Log 100 base 10 is 2
So, log 63 base 10 is 1.799
Answer: 1.799
If 1 = 0, 10 = 1 and 100 = 2. What is 63?
At first glance, you would have thought we are counting the numbers of zeros but a smart people will know it can't be as simple as that.
Any one good at math will notice a pattern immediately though logarithm
Log 1 base 10 is 0
Log 10 base 10 is 1
Log 100 base 10 is 2
So, log 63 base 10 is 1.799
Answer: 1.799
Answer to Q70
[3,42,1] [5,82,3] [6,84,2] [4,x,1]. What is x?
[A,B,C]: B = (A+C)(A-C)
[3,42,1] (3+1)(3-1) = 42
[5,82,3] (5+3)(5-3) = 82
[6,84,2] (6+2)(6-2) = 84
[4,x,1] x = (4+1)(4-1) = 53
Answer: 53
[3,42,1] [5,82,3] [6,84,2] [4,x,1]. What is x?
[A,B,C]: B = (A+C)(A-C)
[3,42,1] (3+1)(3-1) = 42
[5,82,3] (5+3)(5-3) = 82
[6,84,2] (6+2)(6-2) = 84
[4,x,1] x = (4+1)(4-1) = 53
Answer: 53
Answer to Q70
There are x oranges and were divided between 2 boys but 1 orange remained so it was divided between 3 boys and again 1 orange remained. Also between 4, 5 and 6 boys, still 1 orange remained. It was however equally divided among 7 boys.
What is X?
To answer this, let's first arrange the options in desending order: 7, 33, 49, 301
The question simply put says the correct number when divided by 2 to 6 must always have 1 as it reminder and must be exactly divisible by 7
7:
Divided by 2: 3 rem 1
Divided by 3: 2 rem 1
Divided by 4: 1 rem 3
So not our answer
33:
Divided by 2: 16 rem 1
Divided by 3: 11 rem 0
So not our answer
49:
Divided by 2: 24 rem 1
Divided by 3: 16 rem 1
Divided by 4: 12 rem 1
Divided by 5: 9 rem 4
So not our answer
301:
Divided by 2: 150 rem 1
Divided by 3: 100 rem 1
Divided by 4: 75 rem 1
Divided by 5: 60 rem 1
Divided by 6: 50 rem 1
Divided by 7: 43 rem 0
Our answer!
Answer 301
There are x oranges and were divided between 2 boys but 1 orange remained so it was divided between 3 boys and again 1 orange remained. Also between 4, 5 and 6 boys, still 1 orange remained. It was however equally divided among 7 boys.
What is X?
To answer this, let's first arrange the options in desending order: 7, 33, 49, 301
The question simply put says the correct number when divided by 2 to 6 must always have 1 as it reminder and must be exactly divisible by 7
7:
Divided by 2: 3 rem 1
Divided by 3: 2 rem 1
Divided by 4: 1 rem 3
So not our answer
33:
Divided by 2: 16 rem 1
Divided by 3: 11 rem 0
So not our answer
49:
Divided by 2: 24 rem 1
Divided by 3: 16 rem 1
Divided by 4: 12 rem 1
Divided by 5: 9 rem 4
So not our answer
301:
Divided by 2: 150 rem 1
Divided by 3: 100 rem 1
Divided by 4: 75 rem 1
Divided by 5: 60 rem 1
Divided by 6: 50 rem 1
Divided by 7: 43 rem 0
Our answer!
Answer 301
Answer to Q71
What is the smallest number that can be exactly divided by all the numbers from 1 to 10.
First we have to find out the prime factors of each of the numbers between 1 and 10.
1 = 1 x 1
2 = 2 x 1
3 = 3 x 1
4 = 2 x 2
5 = 5 x 1
6 = 2 x 3
7= 7 x 1
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
Then we check the prime numbers for their highest occurance.
2: Highest occurance 3 times (8 = 2 x 2 x 2)
3: Highest occurance 2 times (9 = 3 x 3)
5: Highest occurance 1 time (5 = 5 x 1)
7: Highest occurance 1 time (7 = 7 x 1)
So, we have 2³ x 3² x 5¹ x 7¹ = 2520
Answer: 2520
What is the smallest number that can be exactly divided by all the numbers from 1 to 10.
First we have to find out the prime factors of each of the numbers between 1 and 10.
1 = 1 x 1
2 = 2 x 1
3 = 3 x 1
4 = 2 x 2
5 = 5 x 1
6 = 2 x 3
7= 7 x 1
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
Then we check the prime numbers for their highest occurance.
2: Highest occurance 3 times (8 = 2 x 2 x 2)
3: Highest occurance 2 times (9 = 3 x 3)
5: Highest occurance 1 time (5 = 5 x 1)
7: Highest occurance 1 time (7 = 7 x 1)
So, we have 2³ x 3² x 5¹ x 7¹ = 2520
Answer: 2520
Answer to Q72
If n > i then cⁿ > cⁱ for all value of c?
cⁿ > cⁱ will be true for c > 0
E.g. 3³ > 3²
cⁿ > cⁱ will not always be true for c ≤ 0
E.g. 0³ = 0²; -3³ < 3²
Answer: False
If n > i then cⁿ > cⁱ for all value of c?
cⁿ > cⁱ will be true for c > 0
E.g. 3³ > 3²
cⁿ > cⁱ will not always be true for c ≤ 0
E.g. 0³ = 0²; -3³ < 3²
Answer: False
Answer to Q73
If a brick weighs 3kg plus half of a similar brick. How much does a brick and a half weigh?
If a brick weighs 3kg plus half of a similar brick, we can write this as an equation:
Let brick weight be x, so
x = 3kg + ½x
We can now find x
x = (6+x) ÷ 2
2x = 6+x
x = 6kg
So a brick weighs 6kg
How much does a brick and a half weigh?
Now since a brick weighs 6kg, half a brick will weigh 3kg
So, a brick and half will weigh 6 + 3 = 9
Answer: 9kg
If a brick weighs 3kg plus half of a similar brick. How much does a brick and a half weigh?
If a brick weighs 3kg plus half of a similar brick, we can write this as an equation:
Let brick weight be x, so
x = 3kg + ½x
We can now find x
x = (6+x) ÷ 2
2x = 6+x
x = 6kg
So a brick weighs 6kg
How much does a brick and a half weigh?
Now since a brick weighs 6kg, half a brick will weigh 3kg
So, a brick and half will weigh 6 + 3 = 9
Answer: 9kg
Answer to Q74
My sister was half my age when I was 12, when I was 30 she got married and had her daughter a year later. I am now 70, how old is my niece?
My sister was half my age when I was 12:
That means my sister is 6 years younger than me.
when I was 30 she got married:
If she is 6 years younger than me, that means she got married at 24
and had her daughter a year later:
She had her daughter at 25
I am now 70, how old is my niece?
If I am 70 now, that means my sister is now 64. She gave birth at 25. Her daughter, my niece will now be 64 - 25 = 39
Answer: 39
My sister was half my age when I was 12, when I was 30 she got married and had her daughter a year later. I am now 70, how old is my niece?
My sister was half my age when I was 12:
That means my sister is 6 years younger than me.
when I was 30 she got married:
If she is 6 years younger than me, that means she got married at 24
and had her daughter a year later:
She had her daughter at 25
I am now 70, how old is my niece?
If I am 70 now, that means my sister is now 64. She gave birth at 25. Her daughter, my niece will now be 64 - 25 = 39
Answer: 39
Answer to Q75
[8, 2, 20], [10, 5, 52], [6, 3, 20], [4, 2, x]
[A, B, C]: C = (A x B) + (A ÷ B)
[8, 2, 20]: (8 x 2) + (8 ÷ 2) = 16 + 4 = 20
[10, 5, 52]: (10 x 5) + (10 ÷ 5) = 50 + 2 = 52
[6, 3, 20]: (6 x 3) + (6 ÷ 3) = 18 + 2 = 20
[4, 2, x]: x = (4 x 2) + (4 ÷ 2) = 8 + 2 = 10
Answer: 10
[8, 2, 20], [10, 5, 52], [6, 3, 20], [4, 2, x]
[A, B, C]: C = (A x B) + (A ÷ B)
[8, 2, 20]: (8 x 2) + (8 ÷ 2) = 16 + 4 = 20
[10, 5, 52]: (10 x 5) + (10 ÷ 5) = 50 + 2 = 52
[6, 3, 20]: (6 x 3) + (6 ÷ 3) = 18 + 2 = 20
[4, 2, x]: x = (4 x 2) + (4 ÷ 2) = 8 + 2 = 10
Answer: 10
Number of digit 3 bewteen 300 and 400.html
611 B
Answer to Q76:
If I wrote all the numbers from 300 to 400 on a piece of paper, how many times did I write the digit 3?
We all can write 300 to 400 and bring the numbers all together looks like this
300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400
We can now count the number of times 3 occurs. I don't have to manually do that so I wrote a little javascript code for that.
Answer: 120
If I wrote all the numbers from 300 to 400 on a piece of paper, how many times did I write the digit 3?
We all can write 300 to 400 and bring the numbers all together looks like this
300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400
We can now count the number of times 3 occurs. I don't have to manually do that so I wrote a little javascript code for that.
Answer: 120
Answer to Q77
In sharing a bottle of coke with my two sons, Tom and Harry. Tom brought a 3cm diameter, 6cm tall cup which I filled to the brim. Harry brought a 6cm diameter, 3cm tall cup which I also filled to the brim.
Who had the most coke?
Volume of Tom's cup:
Height of cup = 6cm
Diameter of cup = 3cm
Radius (r) = 1.5cm
Volume = πr²h
= π x 1.5² x 6
= 42.41cm³
Volume of Harry's cup:
Height of cup = 3cm
Diameter of cup = 6cm
Radius (r) = 3cm
Volume = πr²h
= π x 3² x 3
= 84.82cm³
Not only did Harry had more coke, he had exactly twice of Tom's coke.
Answer: Harry
Moral: This question is very similar to Q55, diameter matters alot.
In sharing a bottle of coke with my two sons, Tom and Harry. Tom brought a 3cm diameter, 6cm tall cup which I filled to the brim. Harry brought a 6cm diameter, 3cm tall cup which I also filled to the brim.
Who had the most coke?
Volume of Tom's cup:
Height of cup = 6cm
Diameter of cup = 3cm
Radius (r) = 1.5cm
Volume = πr²h
= π x 1.5² x 6
= 42.41cm³
Volume of Harry's cup:
Height of cup = 3cm
Diameter of cup = 6cm
Radius (r) = 3cm
Volume = πr²h
= π x 3² x 3
= 84.82cm³
Not only did Harry had more coke, he had exactly twice of Tom's coke.
Answer: Harry
Moral: This question is very similar to Q55, diameter matters alot.
Answer to Q78
12am is what?
AM is short for Ante Meridiem which means before noon, so 12am is the 12 before noon (i.e. 12 midnight)
Answer: 12 midnight
12am is what?
AM is short for Ante Meridiem which means before noon, so 12am is the 12 before noon (i.e. 12 midnight)
Answer: 12 midnight
Answer to Q79
[6, 7, 11, 20] [5, 3, 2] [x, 4] [10]. What is x?
Let's rewrite the series like this:
[A, B, C, D] [E, F, G] [H, I] [J]
Then:
E, A, B
F, B, C
G, C, D
H, E, F
I, F, G
J, H, I
all forms sub - series.
Let's test the theory,
5, 6, 7 that's a series with difference of 1
3, 7, 11 that's a series with difference of 4
2, 11, 20 that's a series with difference of 9
x, 5, 3 (5 and 3 has a difference of 2 so x should be 5 + 2 = 7)
4, 3, 2 that's a series with difference of -1
10, x, 4 (10 - 4 is 6 so the difference here can only be 6 ÷ 2 = 3) so series becomes 10, 7, 4. x was also 7 in our x, 5, 3 which means we are correct.
Answer: 7
[6, 7, 11, 20] [5, 3, 2] [x, 4] [10]. What is x?
Let's rewrite the series like this:
[A, B, C, D] [E, F, G] [H, I] [J]
Then:
E, A, B
F, B, C
G, C, D
H, E, F
I, F, G
J, H, I
all forms sub - series.
Let's test the theory,
5, 6, 7 that's a series with difference of 1
3, 7, 11 that's a series with difference of 4
2, 11, 20 that's a series with difference of 9
x, 5, 3 (5 and 3 has a difference of 2 so x should be 5 + 2 = 7)
4, 3, 2 that's a series with difference of -1
10, x, 4 (10 - 4 is 6 so the difference here can only be 6 ÷ 2 = 3) so series becomes 10, 7, 4. x was also 7 in our x, 5, 3 which means we are correct.
Answer: 7
Answer to Q80
[9, 25, 49, x] [7, 10, 15, 8, 7]. What is x?
Let's rewrite the series as [A, B, C, D] [E, F, G, H, I]
(F - E)² = A : (10 - 7)² = 9
(G - F)² = B : (15 - 10)² = 25
(H - G)² = C : (8 - 15)² = 49
(I - H)² = D : (7 - 8)² = 1
Answer: 1
[9, 25, 49, x] [7, 10, 15, 8, 7]. What is x?
Let's rewrite the series as [A, B, C, D] [E, F, G, H, I]
(F - E)² = A : (10 - 7)² = 9
(G - F)² = B : (15 - 10)² = 25
(H - G)² = C : (8 - 15)² = 49
(I - H)² = D : (7 - 8)² = 1
Answer: 1
Answer to Q81
A + B - C = 6; A - B + C = 8. What is A?
A + B - C = 6 (eqn i)
A - B + C = 8 (eqn ii)
Add eqn i to eqn ii, it becomes
2A = 14
A = 14 ÷ 2
A = 7
Answer: 7
A + B - C = 6; A - B + C = 8. What is A?
A + B - C = 6 (eqn i)
A - B + C = 8 (eqn ii)
Add eqn i to eqn ii, it becomes
2A = 14
A = 14 ÷ 2
A = 7
Answer: 7