Post mathematic related questions here

[rst]

Re: mathematic related questions

ok

we can also solve it in simple way

N is even( so socks are in pair)
suppose we have 2 pairs of socks in different color(2 socks of white color and 2 socks of black color) in a drawer
If we draw 3 socks from drawer then definitely, we will get a pair

similarly if we have 3 pairs of socks in different color(2 socks of white color, 2 socks of black color and 2 socks of red color) a drawer
If we draw 4 socks from drawer then definitely,we will get a pair

so in general if we have N pairs of socks in different color
then we have to draw N+1 socks to get a pair

----------------------------------------
NEW OBJECTIVE QUESTION


Also plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)

 

[Niilesh]

Re: mathematic related questions

ans is 3
sol. their will be 3 intersection points on each of the 4 lines(so they would be collinear), now every point will have 4 points on old lines(I think you will be able understand what I mean) so only one new line be formed form each point

so ans = 6/2 = 3

 

[rst]

Re: mathematic related questions

absolutely right
-----------------------------------
NEW OBJECTIVE QUESTION


Also plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)

 

[Niilesh]

Re: mathematic related questions

is it 49/100?

I just applied the unitary method so ans = ((100/100)/100)*7*7

 

[rst]

Re: mathematic related questions

no
ans is 100 minutes

 

[thetechfreak]

Re: mathematic related questions

100 minutes. Each one catches one in 100 minutes and hence 7 will take 7 minutes.

 

[rst]

Re: mathematic related questions

100 minutes. Each one catches one in 100 minutes and hence 7 will take 7 minutes.

yeah
Its looks like 7 minutes

But actual answer is "100 minutes"
--------------------------------------------------------
here is the solution
Let C1 be the number of cats who catch R1 rats in T1 minutes and

Let C2 be the number of cats who catch R2 rats in T2 minutes

C1T1/R1 = C2T2/R2

(100 x 100) /100 = (7 x T2) / 7
T2= 100

so time = 100 minutes
--------------------------------------------
Another method:-

let time be x

Now number of cat and time are in indirect proportion
Also number of rat and time are in direct proportion

So 100 * 100 * 7= 7 * x *100
x=100

I read the question wrong the first time
, n+1 is the right answer

max no of turns till one of each colour is taken out is N, in the next turn a pair will be found so ans is N+1

we can also solve it in simple way.

N is even( so socks are in pair)
suppose we have 2 pairs of socks in different color(2 socks of white color and 2 socks of black color) in a drawer
If we draw 3 socks from drawer then definitely, we will get a pair

similarly if we have 3 pairs of socks in different color(2 socks of white color, 2 socks of black color and 2 socks of red color) a drawer
If we draw 4 socks from drawer then definitely, we will get a pair

so in general if we have N pairs of socks in different color
then we have to draw N+1 socks to get a pair

no its not clear and I will not be satisfied with hit and trial

OK
then here is the proof

case 4: a and b are both even
we want to prove that a^2 + 6b^2 and b^2 + 6a^2 are not perfect square
here we will use contradiction method

If possible suppose that a^2 + 6b^2 and b^2 + 6a^2 is perfect square
then (a/2)^2 + 6(b/2)^2 and (b/2)^2 + 6(a/2)^2 will also be perfect square

But in (a/2)^2 + 6(b/2)^2 and (b/2)^2 + 6(a/2)^2
(a/2)^2 and (b/2)^2 can be even or odd

So by case 1,2 and 3 (which I discussed in detail in my previous post)
(a/2)^2 + 6(b/2)^2 and (b/2)^2 + 6(a/2)^2 are not perfect square
which is a contradiction
Hence our assumption is wrong

a^2 + 6b^2 and b^2 + 6a^2 are not perfect square

 

[Niilesh]

Re: mathematic related questions

we can also solve it in simple way.

N is even( so socks are in pair)
Whether no. of colours is odd or even it dosen't matter, What did you meant by "socks are in pair"
suppose we have 2 pairs of socks in different color(2 socks of white color and 2 socks of black color) in a drawer
If we draw 3 socks from drawer then definitely, we will get a pair

similarly if we have 3 pairs of socks in different color(2 socks of white color, 2 socks of black color and 2 socks of red color) a drawer
If we draw 4 socks from drawer then definitely, we will get a pair
That's what i said/meant but giving a general solution directly

OK
then here is the proof

case 4: a and b are both even
we want to prove that a^2 + 6b^2 and b^2 + 6a^2 are not perfect square
here we will use contradiction method

If possible suppose that a^2 + 6b^2 and b^2 + 6a^2 is perfect square
then (a/2)^2 + 6(b/2)^2 and (b/2)^2 + 6(a/2)^2 will also be perfect square

But in (a/2)^2 + 6(b/2)^2 and (b/2)^2 + 6(a/2)^2
(a/2)^2 and (b/2)^2 can be even or odd

So by case 1,2 and 3 (which I discussed in detail in my previous post)
(a/2)^2 + 6(b/2)^2 and (b/2)^2 + 6(a/2)^2 are not perfect square
which is a contradiction
Hence our assumption is wrong

a^2 + 6b^2 and b^2 + 6a^2 are not perfect square

Why?
let
a^2 + 6b^2 and b^2 + 6a^2 = k^2
=> (a/2)^2 + 6(b/2)^2=(k^2)/4
Now since a square no. divided by 4 is not necessarily a square, therefore the statement is wrong

_______________________________________________________________________________________

A Question -
Find the smallest number such that if its rightmost digit is placed at its left end, the new number so formed is precisely 50% larger than the original number

 

[rst]

Re: mathematic related questions

Why?
let
a^2 + 6b^2 and b^2 + 6a^2 = k^2
=> (a/2)^2 + 6(b/2)^2=(k^2)/4
Now since a square no. divided by 4 is not necessarily a square, therefore the statement is wrong

now k^2 is square
then (k^2)/4 will also be square
how???
(k^2)/4= (k/2)^2

note :- even square no. divisible by 4 will always be square no.
If not, give an example

 

[Niilesh]

Re: mathematic related questions

I said it is not 'ALWAYS' a square
since you didn't prove that k is even, hence the statement is wrong

 

[rst]

Re: mathematic related questions

N is even( so socks are in pair)
suppose we have 2 pairs of socks in different color(2 socks of white color and 2 socks of black color) in a drawer
If we draw 3 socks from drawer then definitely, we will get a pair

similarly if we have 3 pairs of socks in different color(2 socks of white color, 2 socks of black color and 2 socks of red color) a drawer
If we draw 4 socks from drawer then definitely, we will get a pair

so in general if we have N pairs of socks in different color
then we have to draw N+1 socks to get a pair

it means each color socks are in even pair(there will be 2 socks of black color,2 socks of white color(as I explained in my answer)]
for example :-2,4,6, or 8 etc pair of socks

I said it is not 'ALWAYS' a square
since you didn't prove that k is even, hence the statement is wrong

if k^2 is odd
then also (k^2)/4= (k/2)^2 is perfect square

note :- when we divide two perfect square then result is always perfect square

 

[Niilesh]

Re: mathematic related questions

it means each color socks are in even pair(there will be 2 socks of black color,2 socks of white color(as I explained in my answer)]
for example :-2,4,6, or 8 etc pair of socks
N is the no. of colours...
It was given that it is even just because they wanted to prevent people from eliminating (D) option


if k^2 is odd
then also (k^2)/4= (k/2)^2 is perfect square

note :- when we divide two perfect square then result is always perfect square
It wont be a perfect square as odd no./2=a fraction(not an integer).
Like for example take K=3(or 2n+1)

Chars

 

[rst]

Re: mathematic related questions

they give even no. of socks
so that we start counting from 2 (i.e 2 pair of shocks)

In case of odd
counting starts from 1(i.e 1 pair of shocks)
which looks meaningless (as they are of same color)
-------------------------------------------------------
yeah

perfect square is in fraction form (in case of odd perfect square)

Note :- we require integral solution

don't relate it with perfect square
perfect square can be in fraction form

 

[Niilesh]

Re: mathematic related questions

Read the question again

-------------------

I think perfect square means whose square root is a integer

if it can be fraction than almost every no. will be a perfect square . BTW in the solution it should be square of of a integer

 

[rst]

Re: mathematic related questions

Read the question again

In question they write socks of N different color

In case of odd number
N can be 1

there is no sense "socks of 1 different color"

 

[Niilesh]

Re: mathematic related questions

ya, in the case of N=1 language seems funny but answer will be the same.

 

[rst]

Re: mathematic related questions

I think perfect square means whose square root is a integer

if it can be fraction than almost every no. will be a perfect square . BTW in the solution it should be square of of a integer

you are right

But in case 4

As both both a and b are even
so a^2 +6b^2 and b^2 +6a^2 are even perfect square (as we assume them to be perfect square)-------(1)

(a/2)^2 +6(b/2)^2 = (a^2 +6b^2)/4
=(even perfect square)/4
=perfect square

similarly we can prove for (b/2)^2 +6(a/2)^2

hence (a/2)^2 +6(b/2)^2 and (b/2)^2 +6(a/2)^2 are perfect square

 

[Niilesh]

Re: mathematic related questions

ohh...
I shouldn't have missed it

 

[rst]

Re: mathematic related questions

A Question -
Find the smallest number such that if its rightmost digit is placed at its left end, the new number so formed is precisely 50% larger than the original number

I think Its only possible with "hit and trial" method
If not, plz explain

ans is 3
sol. their will be 3 intersection points on each of the 4 lines(so they would be collinear), now every point will have 4 points on old lines(I think you will be able understand what I mean) so only one new line be formed form each point

so ans = 6/2 = 3

can you explain your answer in more simple language ??
i.e average student can also understand it.

 

[dashing.sujay]

Re: mathematic related questions

I'm really enjoying this thread, makes me feel like going back to school days