Number System

[rahulshaitan]

Originally Posted by prateek7563

Solve the question:
1.K is a 3 digit number such that the ratio of number to the sum of its digits is least? What is the difference between the hundreds and tens digits of K?
2. Find the remainder when 7^99 is divided by 2400?

ans2).343

please confirm the answer

regards

[rahulshaitan]

Originally Posted by prateek7563

Solve the question:
1.K is a 3 digit number such that the ratio of number to the sum of its digits is least? What is the difference between the hundreds and tens digits of K?
2. Find the remainder when 7^99 is divided by 2400?

the number is 199 and the diff is 9-1=8

[poojadatta]

1.K is a 3 digit number such that the ratio of number to the sum of its digits is least? What is the difference between the hundreds and tens digits of K?
answer for first one I think is 1
199/19 (not sure)


2. Find the remainder when 7^99 is divided by 2400?
Ans is 343
(7^4)^24 * 7^3
(2401)^24 * 343
(2401^24 * 343) mod 2400 = 343

[Neerajrawat]

i think the ans to that 3 digit problem is 199/19. therefore the difference is 8.
as 199/19 <109/10.

[toxic]

Solve the question:
1.K is a 3 digit number such that the ratio of number to the sum of its digits is least? What is the difference between the hundreds and tens digits of K?
2. Find the remainder when 7^99 is divided by 2400?

1.number will be 199
it's sure that hundred digit will be min. i.e 1 nd last(unit) digit will be 9.we hav to only take care of tens digit.after a little bit calculation we can find that no. is 199.
2.ans has already given in above posts

[shivam_01]

Solve the question:
1.K is a 3 digit number such that the ratio of number to the sum of its digits is least? What is the difference between the hundreds and tens digits of K?
2. Find the remainder when 7^99 is divided by 2400?

Answer to first is 199 199/19
difference between the hundreds and tens digits of K is 8

Answer to second
7^99 mod 2400
((7^4)*24)*(7^3) mod 2400

as ((7^4)*24) will give remainder as 1 so the answer is 7^3 ===> 343

[prateek7563]

Originally Posted by shivam_01

Answer to first is 199 199/19
difference between the hundreds and tens digits of K is 8

Answer to second
7^99 mod 2400
((7^4)*24)*(7^3) mod 2400

as ((7^4)*24) will give remainder as 1 so the answer is 7^3 ===> 343

But how can you guess that its 199 directly? please tell me the thinking process?

[prateek7563]

Originally Posted by poojadatta

1.K is a 3 digit number such that the ratio of number to the sum of its digits is least? What is the difference between the hundreds and tens digits of K?
answer for first one I think is 1
199/19 (not sure)


2. Find the remainder when 7^99 is divided by 2400?
Ans is 343
(7^4)^24 * 7^3
(2401)^24 * 343
(2401^24 * 343) mod 2400 = 343

But how can you guess that its 199 directly? please tell me the thinking process?

[naiquevin]

Originally Posted by prateek7563

But how can you guess that its 199 directly? please tell me the thinking process?

This is how arrived at the no...

For min ratio we need a max denominator (D) and a min numerator (N)....
The max obtainable D is 9+9+9= 27 but in this case the N is also max..
so we have to arrive at a balance..
999/27 = 37
The next max D= 26 so one of the digits has to be reduced to 8
We reduce the digit that will reduce N by max value
so 899/26 = 3.4....
again reduce 799/25..and so on .
At 199 we get199/19 = 10.4 which is min so far
Now 1 cannot be reduced further , so reduce one 9 to 8
189 is the next no....but 189 / 18 = 10.5 > 199/19
so 199

[Wynand]

Guys, please help me out with this with the full solution

If (9)n, (11)n, (K)n, (20)n are four nos in the base n, and in A.P. What is the value of K ???