2022-2023 Maths Club AGM

101x101

• 10101

• 10201

• 11111

• 10001

Answer explanation

101x101=10201

10101x10101=102030201

1111x1111

• 1234321

• 1111111

• 11111111

• 1233321

Answer explanation

11x11=121

111x111=12321

1111x1111=1234321

11111x11111=123454321

1+2+3+4+...+98+99+100=?

• 4950

• 4975

• 5000

• 5050

Answer explanation

(1+100)+(2+99)+...+(50+51)

=101x(100/2)

=5050

1+2+3+...+(n-1)+n= n(n-1)/2

• 25

• 23

• 27

• 29

Answer explanation

last digit : 9 -> 3x3 / 7x7

20x20 < 729 < 30x30

i.e 23 / 27

23 x 23 = 529

27 x 27 = 729

• 12

• 13

• 14

• 15

Answer explanation

last digit: 8 -> 2x2x2

10x10x10 < 1728 < 20x20x20

i.e 12

哪一個數除3餘2, 除4餘3, 除5餘4

• 139

• 131

• 119

• 104

Answer explanation

5m last digit : 0/5

5m+4 last digit: 4/9

4m last digit: even number

4m+3 last digit: odd number

i.e 5m+4 last digit: 9

3m: sum of all digits = 3m

3m: sum of all digits = 3m+2

i.e 119

sum of squares in 4x4 square

• 16

• 30

• 21

• 25

Answer explanation

1 x 1 square: 16

2 x 2 square: 9

3 x 3 square: 4

4 x 4 square: 1

total: 30

product of LCM and HCF of 27 and 36

• 936

• 924

• 972

• 948

Answer explanation

LCM x HCF

= product of two numbers

• 0

• 1

• -1

• undefined

Answer explanation

n! = 1 x 2 x 3 x ... x (n-1) x n

= n x (n-1)!

1! = 1 x 0!

0! = 1

n^0= n/n = 1

what is 0?

• positive odd integer

• negative even decimals

• imaginary odd number

• complex even number

Answer explanation

0 is not positive or negative

0 is an even number

all real numbers are complex numbers