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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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!

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