PFA the solution:

S – Kn2 at n = 4 , S – K42 = 120 … (1) at n = 6 , S – K62 = 60 … (2) From (1) and (2) S = 168 and K = 3. So 168 - 3n2 Should be greater than 0. 168 -...

1 x 2 x 3 x 4 x 5x ...... x 13 i.e 13! is a multiple of 16 . Hence 13! raised to any power would be a multiple of 16. Therefore the remainder will be...

Let the time in which tank will be filled is x minutes So, x/60 + ( x -10)/30 + ( x-20)/20 = 1 on solving x = 70/3 i.e 23 minutes 20 seconds Hence ,...

1. _ _ _ _ 0 _ _ _ _ : for first four digits there are 9C4 ways , for last four digits there are 5C4 ways. => 9C4 x 5C4 = 630 numbers _ _ _ _ 1 _ _...

PFA the solution

N = DQ + 52=> 5N = D (5Q) + 52 x 5 5N = 5DQ + 260 Also 5N = Dx + 4 So , D divides (260 - 4) i.e 256 hence , All factors of 256 > 52 . [ 256 , 1...

(Any odd number )^ (4k ) ends with 1 or 5 *( odd multiples of 5 )^(Any natural number ) ends with 5. (Any even number )^4k ends with 6 or 0 *(Even m...

25 pages consist of 25 odd numbers and 25 even numbers So there sum should always be odd Hence 1900 an even sum is never possible.

Since digits of 10digits number n sum to 45 , n should be divisible by 9n should be divisible by 99999 10 digits number will be of typen = 100000x + y...

77777...... 1001 times Any digit repeated 6 times is always divisible by 1001 so 77777.... Written 996 times is a multiple of 1001 Hence , 7...

B is multiplied by 25, LCM (A,B) remains unchanged so A has 5^3 in its prime factorization . When A is multiplied by 8 ,LCM (A,B) remains unchanged so...

Total number of flowers : T (Tn/100) + 20 = (T + 20)( n + 10)/100 Tn + 2000 = Tn + 10T + 20n + 200 1oT + 20n = 1800 10T = 1800 - 20n T = 180 - 2n n c...

The quicker way to calculate last three digits of a number is to calculate the remainder by 1000. 1000 = 125 x 8 79999/8 = (-1)9999 = -1 or 7. 79999/1...