[administration]

25200=2^4*3^2*5^2*7
so we have 2,4,8,16,3,9,5,25,7 as some factors

now a divisor can be 4n+3 only for two cases
i)when it is of the form 4n+3 and has 1 prime factor

ii)when (4n+1)(4m+3)–>4k+3 with two prime numbers

iii) when (4n+1)(4k+1)(4m+3)=4p+3 with 3 prime factors

case i)–>3,7
2 divisors

case ii)4n+1=5,9,25
so no.of divisors representible this way=3*2-1=5 divisors
3*5
3*25
7*5
7*9
7*25

case iii)4n+1—>5,9,25
we have
7*5*9 2 more cases
7*9*25
so total=2+5+2=9 divisors

 

answered by Souvik Sinha Roy

[administration]

79⁵⁹ can be written as (80-1)⁵⁹

expand it using binomal theorem ⁵⁹C₀80⁰(-1)⁵⁹ +⁵⁹C₁ 80¹(-1)⁵⁸ +…….+⁵⁹C₅₉ 80⁵⁹ (-1)⁰
So in the expansion  we see that all higher terms contain 100 except for the first 2 terms
which are 59*80 and -1
= 4720-1 = 4719 

So last two digits is 19

 

answer by Harsha Vardhan ‎

[administration]

Try to solve it or let others solve . I will post sol tomorrow. :).meanwhile try other questions

[administration]

 

abcde*4=edcba

a= 1 or 2 if >2 will give a carry over and it will result in 6 digit number
now ba should be divisible by 4 so a=2 (cant be 1)

now ba can be 12,32… so b =1 or 3
also e has to end with 2 at its units place …so it can be 3 or 8 (3*4=12 and 4*8=32)

if ba=12 we get e=8 therefore b=1

now d8*4 should be 12 so d can so when 4*8=32 carry over 3 now d must be 7 as 4*7=28+3 = 31

21X78*4=87X12

so X=3,5,6,9
so trial and error methods se X=9

so answer is 21978*4=87912

Sum of digits = 27

Answer given by Vaibhav Autade

[administration]

Let the amount with amar be X.

so Others(Bhavan , chetan and dinesh) have amount = 4X

Total amount = X + 4X = 5X = 150 –> X= 30

Hence Amar has Rs. 30 

[administration]

start removing smallest digits  1,2,3,5 ..

you will get the largest possible number as 9876

 

hence largest omitted digit is 5.

 

[administration]

Let the cheque amount be x rupees and y paise.

so total amount of cheque is 100x +y paise.

and transposed amount = 100y + x paisa.

so 100y+x – 50 = 3(100x+y)

97y = 50 + 299x

Also since y is paisa so, 0<y<100

–> 0<=50+299x<=99×97 –> 47<= 299x <=96673

[administration]

Preparation for 3 months with cool mind and proper planning is required and one can surely fetch score above 700

[Author]

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