Question

HEEELLLPP!
Q1: The product of five consecutive odd integers is 945. waht is the greatest possible value of any of these integers?
Q2: a sequence of numbers begins with the numbers -10, 20, 30.... and each term afterward is the product of the precding three terms. How many of the first 101 terms of this sequence is positive?
Q3: in how many ways can 2mango, 3 black berry and 3 tamarind trees can be planted in a straight line. if one does not distinguish between trees of the same kind.
EXPLAIN IN THE EASIEST POSSIBLE WAY!

Answer 1

On Q1 just multiply 5 consecutive odd integers with answer 945 (1x3x5x7x9), what is the greatest value

Answer 2

how will we find out that which 5 consecutive odd integers we should use?

Answer 3

1. Let your first odd number be - 2n+1 (even +1 = odd)
=> 5 consecutive odd nos. = (2n+1)(2n+3)(2n+5)(2n+7)(2n+9)

Answer 4

@Aditi_Singh well i have to do this sum in a min, i don't think i can do all this calculation in 1 min :(. i tried and i got confused :(

Answer 5

To be honest, I got confused too :P
I'm extremely sorry for the same :(

Answer 6

You know what? When you don't understand anything, start by taking examples.
Like here, let's take the basic consecutive odd numbers - 1,3,5,7,9
here, 1x3x5x7x9 = 945 , thus, your answer would be 9 :P

p.s : that's all i could think of :P

Answer 7

Let the middle no is x. then the no will be x-4, x-2, x, x+2, x+4. now product of these is x(x^2-4)(x^2-16) = 945, which is a cubic equation so analytically you can solve this and it leads to x = 5.

Answer 8

my line of thought for 1st,
945 hmm...its divisible by 5,
so 189
189 is divisible by 3 (note : divisibility test for 2 to 5 are very easy)
so, 189/3 = 63
and 63 easily is 9*7
so, 1,3,5,7,9 ...

Answer 9

Dude. 945 is also divisible by 3,15 and so many no..So I do not think this approach leads to a better way..:-) Because what no to take at first that always keeps importance..

Answer 10

ya ya , since last digit was 5, i attempted to divide it by 5...i never said its fullproof method :P

Answer 11

No issue hartnn..:-) Its also fine..:-)

Answer 12

@RahulKumar11 i actually did what @hartnn did but i wanted a formula type of stuff which is easy !
So thanks both of you :)

Answer 13

could you guys help me with the other two!

Answer 14

Heyyyyyyyyy

Answer 15

See term 1 = -ve, term 2 = +ve, term 3 = +ve, term4 -ve, term 5 = -ve..and so on..so if u exclude the first term u will get a pattern in which 50 terms will be positive and rest fifty term will be -ve..so total +ve term will be 51..:-)

Answer 16

hey @saifoo.khan
@RahulKumar11 ah i see, but how did you get this idea ! i mean i won't be able to find out that whether i should drop the first term or not :/

Answer 17

in how many ways can 2mango, 3 black berry and 3 tamarind trees can be planted in a straight line. if one does not distinguish between trees of the same kind.
9!/(3!3!2!)

n! = total ways that's 9.
3! bc there are 3 similar blackberries, 2! bc there are 2 similar mangoes and another 3! bc there are 3 similar tamarind.

PS "similar" is the key here.

Answer 18

@saifoo.khan the options for the answers are
a) 320, b)380 ,c)450 d) 560 ,e) 640


and what's up with this exclamation mark? what does it represent :@

Answer 19

Awesome tutorial here.
https://www.khanacademy.org/math/probability/probability-and-combinatorics-topic/permutations_and_combinations/v/permutations

Answer 20

Which calc do you have Farheen?

Answer 21

so what about the options? does the answer lies in one of those?

Answer 22

in how many ways can 2mango, 3 black berry and 3 tamarind trees can be planted in a straight line. if one does not distinguish between trees of the same kind.
8!/(3!3!2!)

n! = total ways that's 8.
3! bc there are 3 similar blackberries, 2! bc there are 2 similar mangoes and another 3! bc there are 3 similar tamarind.

PS "similar" is the key here.

It's d.

Answer 23

@saifoo.khan i am watching the video but if i don't get it you will be explaining me in detail ! Deal?

Answer 24

InshAllah.

Answer 25

@saifoo.khan i got what is in the video and i somewhat got what you wrote but they gave a formula which is n!/(n-k!).
here n and k are similar. i mean we have total 8 ways and total 8 spots to fill and so this will give a 0 in the denominator.

ab mein kya ghalat kar rahi hun explain karo?

Answer 26

@Farheen28...Sorry for keep delaying you. But rarely I use this site. If you have any query then you can post your message in my inbox of Facebook account, id is:-
schonrahul@gmail.com