[marijuana_user]

Well i agree with CAt 2007 and Nsrikanth that the answer to the first is 63.

but for the second one i am getting the answer as 162.(and not 129)

regards!

[CAT 2007]

Originally Posted by Pojo

@Cat2007 Hi..dont we have to divide 63 by 19 again?
so will the remainder not be 63%19=6?
or do we have to consider 19*9 as the divisor, in case of which 63 will be the right answer.
Pls reply

Sorry buddy.. It was by mistake that I wrote that the remainder of 7*(10^37-1) wrt 19 is 63... Actually it is 6....

But when you combine the two divisors 9 and 19, you need to find the minimum number which gives the same remainders when divided by 9 and 19...

So a number which gives a rmainder of 0 wrt 9 and a remainder of 6 wrt 19 is 63

[mohit1984]

Ok guys to remove confusion about my questions let me put question again:
1.Question was Remainder of 7777.....37 times divided by 19?
So I approached in following manner:
7(10^36+10^36....+10^0) so that can b written as 7/9(10^37-1)..
Now after this step i posed the question to u guys....What will be the Rem when we divide
7/9(10^37-1) by 19.......AND the answer is 7....Can someone revert back if my method is wrong?

2.Second question there was slight mistake from my side it shud have been Remainder of
7/9(10^50-1) by 74....Answer for this is 3.......This question earlier was of the form 7777777...50 times divided by 74 whats remainder.......I know a method where we divide 111/37 then make pairs of 48 1s and then remains 77/74 and anser is 3 Marijuana only answerd it once but i tried doing this by Euler Method to generalise the Cases but it didnt Work!!

So U guys can look at my method and rework ur solutions and let me know how to solve the above 2 ques by Euler theorem?

[marijuana_user]

hey mohit!~

I am trying to find the question by euler method but not able to as of now.

your second method is correct.Indeed the concept is that 37 divides 10101 and 74 divides 101010,so that way the pairs can be formed.

ill try coming up with the solutions.

reegards!

[marijuana_user]

Originally Posted by mohit1984

Ok guys to remove confusion about my questions let me put question again:
1.Question was Remainder of 7777.....37 times divided by 19?
So I approached in following manner:
7(10^36+10^36....+10^0) so that can b written as 7/9(10^37-1)..
Now after this step i posed the question to u guys....What will be the Rem when we divide
7/9(10^37-1) by 19.......AND the answer is 7....Can someone revert back if my method is wrong?

So U guys can look at my method and rework ur solutions and let me know how to solve the above 2 ques by Euler theorem?

hey !!

Well while solving the first question i just somehow had a feeling that you dont introduce an unnecessary divisor in the questions.(like 9 in this question)

now let me post the solution which used euler and inverse euler both

777777777777......37 times

7(10^36+++++..................+++++++ 10^0).............(1)

now euler number for 19=18

so 10^18 and 10^36 gives 1 as the remiander wen divided by 19.
thus for 19::
10^36 =10^18
10^35 = 10^17
10^34= 10^16
so onnnnnnn........till 10^19 = 10


now (1) can be written as 7(2(10^18+.........10) +10^0 ) (why???)

now 10^18 = 1
10^17 = 10^-1
10^16 = 10^-2

till 10^1 = 10^-17

what will be the inverse number of 10^-1 / 19 ????

a number which wen multiplied with 10 and the product divided by 19 will guve remainder as 1.

thus inverse euler number here = 2

so further (1) reduces to 7(2(1+2+2^2 + ................+ 2^17 ) + 10^0)

thus 7(2(2^18-1)+1) / 19

14(2^1 - 7 / 19

14-7/19

7/19

PHEW...... 7 is the answer.

looks like a tough method but its easy, trust me. Now i m still wondering y the answer in the earlier case was different.

[marijuana_user]

Also if you want to avoid using inverse euler then here is another one.

hope you got till

7[2(10^18+10^17 +.............+ 10) + 10^0]

7[20(1+...............+10^17)+1]

7[(19+1)[(10^18-1)/9] + 7

thus 7/9 (1)(10^18-1) + 7

suppose 7/9 = a

a(10^18-1)/19 + 7/19

1st part gives 0 remainder and answer is 7 from the second part.

P.S- i would suggest you to avoid inverse method and follow this one.

Regards!

[mohit1984]

Originally Posted by marijuana_user

hey !!

Well while solving the first question i just somehow had a feeling that you dont introduce an unnecessary divisor in the questions.(like 9 in this question)

now let me post the solution which used euler and inverse euler both

777777777777......37 times

7(10^36+++++..................+++++++ 10^0).............(1)

now euler number for 19=18

so 10^18 and 10^36 gives 1 as the remiander wen divided by 19.
thus for 19::
10^36 =10^18
10^35 = 10^17
10^34= 10^16
so onnnnnnn........till 10^19 = 10


now (1) can be written as 7(2(10^18+.........10) +10^0 ) (why???)

now 10^18 = 1
10^17 = 10^-1
10^16 = 10^-2

till 10^1 = 10^-17

what will be the inverse number of 10^-1 / 19 ????

a number which wen multiplied with 10 and the product divided by 19 will guve remainder as 1.

thus inverse euler number here = 2

so further (1) reduces to 7(2(1+2+2^2 + ................+ 2^17 ) + 10^0)

thus 7(2(2^18-1)+1) / 19

14(2^1 - 7 / 19

14-7/19

7/19

PHEW...... 7 is the answer.

looks like a tough method but its easy, trust me. Now i m still wondering y the answer in the earlier case was different.

Cool Marijuana u r great actually this soln is very similar to Seed Concept which Aarav uses a lot......Actually seed of 19 is 2 so we can write 10^36+.......as 2^36+......which will allow us to use Euler method but i still dunno why from eariler method whn u guys solvd answer was coming 63?????

[ankur483]

1. In a city, 40% males and 60% females are married....what is the % of married population in the city?

Suppose number of males in city = 300 , 40% married = 120
Suppose number of females in city = 200 , 60% married = 120


Total people = 500 married = 240 , % married = 240/5 = 48%

(Supposing some values works easier and faster for me )

2. Rate of electricity per unit in Junoon's city has decreased by 40% but he wants to reduce his electricity bill by 30%. What shud be the % change in his consumption?

Let initial consumption = 100
consumption after reduction by 40% = 60

now consumption after reduction should be = 70 (only reduced by 30%)

increase in consumption needed = 10
%increase in consumption needed = 10 * 100 / 60 = 16.67%



A batsman scored 120 runs in his 18th inning and improved his batting average by an integer...n he never remained not-out....for cricket non - followers...battin average = total runs in career/no. of times a batsman got out.

3. what is the sum of his possible new batting averages?

didnt got the question ??????

4. By how many different integral values he cud have improved his average?

Now suppose his earlier average would have been 'x' ....then for calculating the latest average we will deduct this x from 120 and divide the remainder by 18.

Now whatever comes should also be an integer ....So all the possible cases are :-
we start with 12 + 108/18
30 + 90/18
48 + 72/18
66 + 54/18
84 + 36/18
102 + 18/18
120 + 0/18



Dont know whether to count 0 as an integer or not .....
with 0 = 7
without 0 = 6 cases


5. what is the A.M. of his possible old batting averages?

No idea !!!!


6. What are the values of A,B,? if C = 123.

st1. A.M. of A,B,C = G.M. of A,B,C
st2. A.M. of A,B,C = 100.

Both together will give the answer


Looking forward to solutions for some of the problems in was not able to solve. And for those that i have solved please correct me if i am wrong anywhere.

Cheers!!

[maxximus]

?[/quote]

Originally Posted by mohit1984

Ok guys to remove confusion about my questions let me put question again:
1.Question was Remainder of 7777.....37 times divided by 19?
So I approached in following manner:
7(10^36+10^36....+10^0) so that can b written as 7/9(10^37-1)..
Now after this step i posed the question to u guys....What will be the Rem when we divide
7/9(10^37-1) by 19.......AND the answer is 7....Can someone revert back if my method is wrong?

hi mohit...the question is 7777...37 times % 19...try doing it by a practical way...write it as 19) 7777777... (

now as u bring 7s down, u'll get a pattern in remainders...7,1,17..etc. now the divisor is 19...with lil deliberation u'll understand that after few remainders, same remainders will keep repeating n wud show a cyclicity....lets try n find that cyclicity...by sheer observation, i can say remainders wud repeat after 18 or 19 7s...

lets do it..

7%19 = 7
77%19 = 1
777%19 =17%19=17
7777%19=177%19 = 6
77777%19=67%19=10
then 12,13,4,9,2,8,11,3,18,16,15,5,0,7

got 7 again at 19 7s...

hence, 1 seven or 19 seven or 37 sevens will give same remainder...i.e. 7

so the answer is 7



for 7777...50 times

50 % 18 (thats 19-1) = 14

14th remainder in above case is 18...hence, answer is 18



had the question been 77777...37000 times % 19 =?

37000 % 18 (thats 19-1) = 10, 10th remainder in above list is 2...so the answer wud be 2.




important:

in such questions....where the same no. is being repeated....look for a pattern...am damn sure...u'll find 1 in every case....i know the method is crude and sounds cumbersome...but i find it practical...the flow is visible...and it tuk me hardly 3 mins..




regards
maxximus

[maxximus]

hie...

for 7777....50 times % 74

7%74 = 7
77%74 = 3
777%74 = 37%74 =37
7777%74 = 377 % 74 = 7

here we go, cyclicity is jus 4-1 = 3

so for 50 7s,

50%3 = 2

second remainder is 3

so, the answer is 3


regards
maxximus

PS: tuk me 30 secs