Answer to Q54

A rectangle and a square both has the same area. Which one of them has the highest perimeter?

To answer this question let's imagine a square of length and breath 4m. The area will be L x B = 4 x 4 = 16m²

The perimeter is said square is L+L+B+B = 4 + 4 + 4 + 4 = 16m

Now imagine a rectangle with the same area 16m² which has a side as 2m. The other side will be L x 2 = 16m²

L = 16 ÷ 2 = 8m

Perimeter of the rectangle is L+L+B+B = 8 + 8 + 2 + 2 = 20m

So, the perimeter of a rectangle will be large than that of a square with equal area.

Answer: Rectangle

Answer to Q55

During a banquest, I finished a 18cm diameter pizza and my wife finished two 12cm diameter pizza. Who ate the most?

Let's start by calculating the surface area of the pizza I ate. πr²

Diameter = 18cm. Radius = 18 ÷ 2 = 9cm

A = π x 9²
A = 254.47cm²

And my wife ate two 12cm diameter pizzas

Diameter = 12cm. Radius = 12 ÷ 2 = 6cm

A = π x 6²
A = 113.10cm²

But she ate 2 so,

A = 113.10 x 2 = 226.20cm²

I ate 254.47cm² of pizza and she ate 226.20cm²

Answer: Me

[Moral of the question: there are more pizza in a single 18cm diameter than in two 12cm diameter]

Answer to Q56

There are 4 numbers w, x, y & z. w + x = 14, w + y = 15, x + z = 16 and y - z = 10. What is x and y?

w + x = 14
w + y = 15
x + z = 16
y - z = 10

y = 10 + z
w = 15 - y

Then,
w = 15 - (10 + z)
w = 15 - 10 - z
w = 5 - z

But,
w + x = 14
5 - z + x = 14
x = 14 - 5 + z
x = 9 + z

And,
x + z = 16
9 + z + z = 16
9 + 2z = 16
2z = 16 - 9
2z = 7
z = 7 ÷ 2 = 3.5
z = 3.5

x = 9 + z = 9 + 3.5
x = 12.5

w = 5 - z = 5 - 3.5
w = 1.5

y = 10 + z = 10 + 3.5
y = 13.5

So, w = 1.5, x = 12.5, y = 13.5 and z = 3.5

Answer: x = 12.5 and y = 13.5

Answer to Q57

Mr Brown was killed on a Sunday afternoon. The wife said she was reading a book. The butler said he was taking a walk. The chef said he was making breakfast. The maid said she was folding clothes. The gardener said he was planting herbs. Who did it?

All but one had genuine excuses. The chef lied, he said he was cooking breakfast when it was actually afternoon so he is most likely the killer.

Answer: Chef

Answer to Q58

How many months in the year have 28 days?

All the months of the year has atleast 28 days!

Answer: 12

Answer to Q59

There are 120 people at a party and everyone shook hands. How many handshake will there be?

If you got Q34 right or atleast studied the answer, you should get this question right!

It is known that the number of handshake within a group of people is the sum of integer between 1 and (number of people in the group - 1). Say there are persons A, B, C, D and E (5 people) in a group and all shook hands, the number of handshakes will be sum of integers between 1 and (5-1) i.e. 1 + 2 + 3 + 4 = 10.

Let's confirm this:
- Person A shakes B, C, D, and E (4 handshakes)
- Person B shakes C, D, and E (no need to shake A again because A already shook him) (3 handshakes)
- Person C shakes D and E (2 handshakes)
- Person D shakes E (1 handshake)
- Person E don't have to shake anybody, they have all shook him

So, 4 + 3 + 2 + 1 = 10

And also we know that the sum of 1 to n = (n(n+1)) ÷ 2. Say you want to add 1 to 10 that will be
= (10 x (10 + 1)) ÷ 2
= (10 x 11) ÷ 2
= 110 ÷ 2
= 55 (also try it with your calculator)

With this information, we now know the number of handshakes in a group of 120 people will be 1 + 2 + 3 + ... + 119

But we don't have to add sequentially like that, we just do (119 x 120) ÷ 2
= 14280 ÷ 2
= 7140

Answer: 7140

Answer to Q60

Who did Matthew Perry play in 'Friends'?

Ok, we can't be always serious here 😀. Friends is one of the greatest TV shows of all time and who ever watched that show would surely enjoy Chandler Bing's (played by Matthew Perry) humor!

Answer: Chandler Bing

Answer to Q61

You were handed a rectangle of 2m x 3m and asked to cut out a circle from it.

The diameter of the largest circle you can cut out of a rectangle will be the shortest side of the rectangle. With a rectangle of 2m x 3m, the diameter of the circle will be 2m

Area of a circle = πr²
And radius = diameter ÷ 2
r = 2m ÷ 2 = 1m

A = π x 1² = π

Answer: π

Answer to Q62

If D + E = G and C + G = H. What is A + C?

Let A = 1, B = 2, C = 3, etc

D + E = G i.e. 4 + 5 = 9 but G is not 9 but 7
C + G = H i.e. 3 + 7 =10 but H is not 10 but 8
So the pattern is A + B - 2

4 + 5 - 2 = 7
3 + 7 - 2 = 8
So, A + C = 1 + 3 - 2 = 2 (B)

Answer: B

Answer to Q63

Complete this series 3.8.13, 9.14.19 and 6.11.?

The series is an Arithmetic Progression with difference of 5

See, 8 - 3 = 5; 13 - 8 =5; 14 - 9 = 5, 19 - 14 = 5; 11 - 6 = 5

x - 11 = 5
x = 5 + 11 = 16

Answer: 16

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

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

Answer to Q65

What has a neck but no heads, arms but no hands?

Answer: Shirt

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

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

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

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

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

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