official quant thread for cat08

[the_egonomist]

Came across this proof (seems simple )

Its Euclid's Theory (condensed by Burton MacKenzie on his blog post Prime Motivation)

1. Assume that prime numbers are finite and that "P" is the largest prime. For the sake of example, let's say the largest prime number is P = 7. That would mean that 2, 3, 5, and 7 are the only prime numbers, and 7 is the largest of them; that there are no prime numbers bigger than 7.
2. Create a new number, "Q", by multiplying all the known primes together, and adding "1". e.g. Q = (2 * 3 * 5 * 7) +1 = 211
3. Divide Q by any of the known prime numbers. It will never divide evenly and always have a remainder of "1". e.g. 211/2 = 105R1, 211/3 = 70R1, 211/5 = 42R1, and 211/7 = 30R1
4. If a number is indivisible by any primes, that means that it, itself, is a prime number.
5. P = 7 cannot be the largest prime because Q = 211 is larger than P and is prime. This is true for any value of P.
6. Therefore, there cannot be a largest prime. Reductio Ad absurdum, our initial assumption that there can be a "largest" prime is incorrect. The prime numbers go on forever.

[prince_chittu]

There are infinite number of Red , Green , Yellow and Black colored balls . In how many ways one can choose 20 balls ?

22C2

[shivam_01]

Questions
I have solved these questions but the answer is not matching as given in the book
please confirm puys

1)What is the last digit of

1!^1! + 2!^2! + 3!^3! +................100!^100!

answer given 9 i am getting answer as 7

2)Find the number of zeros in 1!*2!*3!....*100!

answer given 178 i am getting answer as 170

[prince_chittu]

@shivam
can u please explain how u r getting 170?

i m getting 7 as last digit !!

[themystique]

Originally Posted by shivam_01

Questions
I have solved these questions but the answer is not matching as given in the book
please confirm puys

1)What is the last digit of

1!^1! + 2!^2! + 3!^3! +................100!^100!

answer given 9 i am getting answer as 7

me too getting 7 last digit

</div>

[raghav507]

Originally Posted by prince_chittu

@shivam
can u please explain how u r getting 170?

i m getting 7 as last digit !!

hi puys,
can you plz post the complete approach...
it will help a lot...

[jain12345]

Originally Posted by shivam_01

Questions
I have solved these questions but the answer is not matching as given in the book
please confirm puys

1)What is the last digit of

1!^1! + 2!^2! + 3!^3! +................100!^100!

answer given 9 i am getting answer as 7

2)Find the number of zeros in 1!*2!*3!....*100!

answer given 178 i am getting answer as 170

hi
1)What is the last digit of

1!^1! + 2!^2! + 3!^3! +................100!^100!

answer for this question is 7

app. 1 to power 1 = 1
2 to power 2 = 4
6 to power 6 = 6
24 to power 24 = 6
after that every expression will end with a 0..
so 1 + 4 + 6 + 6 = 17


cheers.............

[shivam_01]

Originally Posted by shivam_01
Questions
I have solved these questions but the answer is not matching as given in the book
please confirm puys

1)What is the last digit of

1!^1! + 2!^2! + 3!^3! +................100!^100!

answer given 9 i am getting answer as 7

2)Find the number of zeros in 1!*2!*3!....*100!

answer given 178 i am getting answer as 170

@prince_chittu @Raghav @The mystique

for first one i took the approach that
after 5! onwards all the last digit would be zero only and for the 1! to 4! we need to take so

1 to power 1 last digit 1
2 to power 2 last digit 4
6 to power 6 last digit 6
24 to power 24 last digit 6
so 1 + 4 + 6 + 6 = 17
hence answer as 7

now second one the factorials
we need to check with powers of 5 only hence in that case the 1
1! to 4! has no powers of 5 so
from 5! to 9! each digit will contain the power of 5 just once so 5 appear 5 times
now from 10! to 14! 5 appear 10 times
15! to 19! appear 15 times
20! to 24! appear 20 times
keeping on same trend and summing it up i got the answer as
(5+10+15+20)+(30+35+40+45+50)+(60+65+70+75+80)+(90 +95+100+110+24)

answer as 419
please check puys there may be shorter method

[prince_chittu]

@shivam
the answer cannot be 419 .please check the answer again.
somehow i m getting 1084

[shivam_01]

@shivam
the answer cannot be 419 .please check the answer again.
somehow i m getting 1084

post ur approach the answer given is 170 in book which i definately not true and i am getting the answer as 419
provide ur aproach lets c >>>>