Mind Blowing Questions: Season 2

[esh.nil]

Originally Posted by STALWART

32^32 = 2^160 ......... 160 = 4n ... where n is any natural number..... so the last digit of this wud be 6 . as the cyclicity is ... 2 ,4 , 8 and 6 . .... and whenever the last digit is 6 tens digit is either 1 , 5 , 9 , 3 , 7 ......... a difference of four is maintained ..... and we cud easily note that whenever the power of 2 ends with the digit 0 and the power can be expressed in terms of 4n ... the tens digit always 7 ......... take 2^20 , 2^40 , 2^40000 as examples . so just understand the sequence .. no need to derive any formula or don get entangled too much ...... u will notice that every power of evry number follows a particular sequence . just demystify that and go ahead !!

@Stalwart.... does that ever happen?? does a power of 2 end with 0?? did i misinterpret anything??
And this sequence that u are explaining is the Euler theorem right???

[getneonow]

Originally Posted by esh.nil

@Stalwart.... does that ever happen?? does a power of 2 end with 0?? did i misinterpret anything??
And this sequence that u are explaining is the Euler theorem right???

esh..stalwart meant a case when power of 2 i.e the number which is raised to the power of 2 ends with a 0 like in 2^20 , 2^40 or 2^100 where power ends in 0.

U misinterpreted it as the power of 2 when evaluated gives 0 .
It is not so.

@Stalwart
Nice deductions. Want to put it in different way.

32^32 = 2 ^160 = (1024) ^ 16

Now 24 (last two digits) raised to the power of any even number ends in 76. We can check its cyclivity.

So last two digits of 32^32 = 76 .

Neo

[CaRbOnZ]

Hey pguyz ,

Please help me out with this question frm profit n loss chapter.......

A trader marks up an article by x% and gives a discount of y/2 % and gets a profit of y%. Another trader marks up another article by y% and gives a discount of x/2% and gets a loss of x/4%. If I mark up an article by 2x% which I bought for Rs. 500 and give a discount of y% on the article , then what would be my profit ????

a) Rs.250

b) Rs.500

c) Rs.100

d) Cannot be determined

[hameed]

Originally Posted by CaRbOnZ

Hey pguyz ,

Please help me out with this question frm profit n loss chapter.......

A trader marks up an article by x% and gives a discount of y/2 % and gets a profit of y%. Another trader marks up another article by y% and gives a discount of x/2% and gets a loss of x/4%. If I mark up an article by 2x% which I bought for Rs. 500 and give a discount of y% on the article , then what would be my profit ????

a) Rs.250

b) Rs.500

c) Rs.100

d) Cannot be determined

assuming mark up is on the CP and the CP = 100, now using "A trader marks up an article by x% and gives a discount of y/2 % and gets a profit of y%. "

we can say x = 100 and y = 50 ( 100% increase on 100 is 200, now (50/2)% decrease on 200 is 150 which is 50% more than 100)

Using this 2x = 200% and y = 50 and the answer = 1500*(50/100) = 750 which gives a profit of 250.

Note:
Here the second statement "Another trader marks up another article by y% and gives a discount of x/2% and gets a loss of x/4%." is redundant, and the highlighted word should give us the clue.

Because if we take CP = 100 here, we get by applying 50% (y%)mark up = 150, then 100/2% discount 75, which gives us a loss of 25 which is 100/4 which is x/4%. Hence this is statement would also have given us the same answer.

Let me know if i am right...

Rock on!
hameed

[STALWART]

Originally Posted by esh.nil

@Stalwart.... does that ever happen?? does a power of 2 end with 0?? did i misinterpret anything??
And this sequence that u are explaining is the Euler theorem right???

Hello Esh.nil ...


As getneonow has already expounded enuf on the related things , I need not elaborate it further . Yeah I was talking about the powers ending with 0 not the number which we get after having recockoned the value.

Yah .. Suppose if we want to find out the last 3 or say 4 digits in 2^999 expansion , the way I just scribed might be the laborious one . In this case u can find the remainder after having divided the number by 1000 or 10000 to get last 3 or 4 digits respectively .

Write --- 1000 = (2^3) * (5^3) , and

10,000 = (2^4) * (5^4)

So now u can go ahead and find the last three digits of 2^999 . And after that last 4 digits !! Beyond that , even i have to thing before taking this venture on .

Happy Solving !!

... Sayonara

[ashima chopra]

i dint understand dis.........
cn u plz tel in a mr explanig way

[ankitthakur]

Originally Posted by the_CONSTANTINE

hmm..

Is the Answer 7.
Seems to be a pretty decent question..Lets see...The question is not the last digit(which can be effortlessly found out to be 6)....But the ten's digit!

32^32, can be written as (2^5)^32..which is 2^160=

2^12=4096=-4mod 100
2^12^6=2^72=-4^6=4096=-4mod100
2^72^2=16mod100=2^144
2^144*2^12=2^156=16mod100*(-4)mod100
2^156= -64mod100
2^156*2^4=2^160= -64*16mod 100=-1024mod100
Which is nothing but -24mod100
which is 76...
Hence Ten's Digit is 7...

Method is long....Hoping that some1 gives a better n fast solution!!

Cheers

Hi brother
here there is very simple logic that is (2^10)^even gives last two digit 76 and (2^10)^odd digit gives 24
so 32^32=2^160=(2^10)^16=76
So ten's digit is 76

[mattoo]

3/5 part of a kerosene tin is filed.if 6 bottles are taken out of it and 3 bottles are filled again, then half the tin is full.What is the capacity of the tin? (in bottles)
a) 20
b) 30
c) 45



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it takes40 days for a pond to get filled with rain water. if the level of water doubles every day,then how long would it take to fill 1/4 of pond?

ans is 38 days

[jain12345]

Originally Posted by mattoo

3/5 part of a kerosene tin is filed.if 6 bottles are taken out of it and 3 bottles are filled again, then half the tin is full.What is the capacity of the tin? (in bottles)
a) 20
b) 30
c) 45

hi the answer is 30
see 6 bottles are taken out and then 3 bottles are again filled means only 3 bottles are taken out..
now the tin is 1/2 full... that is equal to 2.5/5 or 5/10
n it was initially 3/5 or 6/10.. so three bottles equal to .5/5 or 1/10 then 5/5 or 10/10 will be equal to 30

hence the answer is 30

[mattoo]

plz solve these problems:

Q1. two numbers are such that their diff. , their sum and their product are in ratio 1:7:24, the product of the numbers are
a)6 b)12 c)24 d)48

Q2. if 64 is divided into three parts proportional to 2,4 and x and the smallest part is 10 2/3, then x equals:

a) 5 1/3 b) 6 c)20



Q3. if a packet containing a dozen glasses is dropped , which of following cannot be ratio of broken glasses to unbroken glasses?

a) 3:1 b) 6:1 c)4:2


Q4. A, B, C together earn Rs. 1450 and spend 60 %, 65% and 70% of their salaries respectively. If their savings are 14:21:15. The salary of B is:

a) Rs 750 b)500 c) 350 d)Rs. 600