The units digit of n2 is 9,so the unit digit of n can be 3 or 7 (because 32 = 9 ; 72 = 49)

The units digit of (n + 1)2 is 6,so the unit digit of n + 1 can be 4 or 6

We see 3 + 1 = 4,so the units digit of n is 3 and the units digit of n - 1 is 2.Hence the units digit of (n - 1)2 is 4

S = (2 + 1)(22 + 1)(24 + 1)...(220 + 1)

   = (2 - 1)(2 + 1)(22 + 1)(24 + 1)...(220 + 1)

   = (22 - 1)(22 + 1)(24 + 1)...(220 + 1)

   = (24 - 1)(24 + 1)...(220 + 1)

   = (220 - 1)(220 + 1)

   = 240 - 1

Let the 3-digit number be abc.So we have :

abcabc = abc.1001 = abc.143.7 is divisible by 7

1998 = 2 x 33 x 37,then 1998 has : (1 + 1)(3 + 1)(1 + 1) = 16 (factors)

So x = 16

P/S : 16 is the number of positive factors of 1998,so 1998 has 32 integer factors

If a is odd,then a3 and a2 are also odd,so a3 + a2 + 1 is odd

If a is even,then a3 and a2 are also even,so a3 + a2 + 1 is odd

So a3 + a2 + 1 is always odd with any integer a

We have : abcabc = abc x 1001 = abc x 7 x 11 x 13

Because abc is a prime number,the number of divisors of abcabc is :

(1 + 1)4 = 16

We have : abcabc = abc x 1001 = abc x 7 x 11 x 13

Because abc is a prime number,the number of divisors of abcabc is :

(1 + 1)4 = 16

We have : (x + 2)(x + 2) = 24(x + 2)(x + 2) = 24

⇒x2 + 4x + 4 =24

=> x2 + 4x = 20

=> x(x + 4) = 20

=> x ,x + 4 thuộc Ư(20) = {1;2;4;5;10;20}

 When x = 1 thì x + 4 = 20 => x = 16 

Number of female students is :

  40 x 2525= 16 ( student )

Number of male students is :

   40 - 16 = 24 ( student )

      Answer : 24 student

Number of terms is :

  ( 1000 - 1 ) : 2 + 1 = 500,5 

The sum is :

  ( 1000 + 1 ) x 500,5 : 2 = 250500,25

Number of female students is : 50 . 2 : 5 = 20 (student)

Number of male students is : 50 - 20 = 30 (student)

              End : 30 (student)

Replacing x = 1/2 we have: 4x - 3a = 0  

Have 4.1/2 - 3a = 0

 Have 2 - 3a = 0

 Have 3a = 2

 Has a = 2/3

Dress a = 2/3 good

We have : ƯCLN(140;240) = 20

Dress the largest square can be 20 cm x 20 cm

We have : ab = 8(a + b) 

=> 10a + b = 8a + 8b

=> 10a - 8a = 8b - b

=> 2a = 7b

=> a = 7 ; b = 2

So ab is 72

That worker makes 3 tools out of time is:

                          12 hours - 7 hours 30 minute = 4 hours 30 minute = 4,5 hours

The worker makes a product time out is :  

                           4,5 : 3 = 1,5 (hours)

                                 Answer : 1,5 hours

No Copy 

Have : Half an hour = 0,5 hour

The speed of the car is :

   ( 25 - 5 ) : 0,5 = 40 ( km / hour )

Answer : 40 km / hour

a) Five fractions equals 3/5: 6/10; 9/15; 12/20; 15/25; 30/50.

b) Five fractions equals 5/8: 10/16; 15/24; 20/32; 25/40; 50/80.

c) Five fractions equals 36/108: 1/3; 2/6; 3/9; 12/36; 18/54.