## QUESTION FROM MATH FLT 20

how we can solve dat problem given in math flt 20....the problm waz lyk dat....
a red lite flashes 3 in one minute n green flashes 5 in 2 mins..what z da no f times both lights vil flash in 1 hour...???
n da othr 1 is 77777777.....(101 digits)/440

## First QuestionA red light

First Question
A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?
ANS:
First light flashes at 0sec, 20sec, 40sec,| 60sec, 80sec, 100sec,| 120sec, 140sec, 160sec| . . .
Second light flashes at 0Sec, 24sec, 48sec, 72sec, 96 sec, 120 sec|
So in two minutes both the light flashes together in 2 instances at 0sec and at 120sec.
So in 1 hour they flash 30times together.
I couldnt get the second.
Please tell the exact question number

## the question z what is da

the question z what is da remainder when 7777777..(101 digits)is divided by 440
and i ve got 1 more problm which is : There were 165 questions in CAT 2000. If 1 mark is awarded for every correct answer and 1/3rd mark is deducted for every wrong answer, how many different net scores are possible?

## Please refer to

Please refer to http://www.cat4mba.com/node/1324 for the detail explanation about solving such kind of problems
7777777..(101 digits)is divided by 440
440= 4 x 11 x 10
7777777..(101 digits) can be written
7777...(97digits)0000 + 7777
The first part is divisible by 4, 11 and 10
So its divisible by 440
Thus the reminder of the whole number = reminder of 7777
i.e 297
The answer is 297.

## Not sure about second one

Not sure about second one but it shd be something like
1 + 2 + 3 + 4 +. . . . + 166
= 167 x 83 = 13861
is it correct ??

## i too am getting 13861

i too am getting 13861 however i havent checked for repetitions and i get the feeling that there is more than one way to arrive at one particular score.
let x = right answer
y = wrong answer
z = not attempted
so x + y + z =165 where x,y,z >=0
this can be solved in 167!/(165! * 2 !) = 13861 ways.
see the link below for the explanation:
http://www.cat4mba.com/node/1397

## Guys can you explain how you

Guys can you explain how you are getting the number 165

## guyyyyss.........um nt

guyyyyss.........um nt gettin dat though ive refeered 2 dat link also...plzzz give a detailed approach..

## The way I solved it

There were 165 questions in CAT 2000. If 1 mark is awarded for every correct answer and 1/3rd mark is deducted for every wrong answer, how many different net scores are possible?
There are 166 ways you can attempt the paper.
1. Attempt No question
2. Attempt only 1 question
3. Attempt only 2 questions
. . . . .. .
Attempt all the 165 questions
For case1: Total possible mark = 0, possible number of marks =1
For case2: 1 question attempted and it can be either Right or Wrong
, possible number of marks =2
For case3: 2 questions attempted and it can be either Right or Wrong
R R
R W
W W
Possible number of marks =3
For case4: 3 questions attempted and it can be either Right or Wrong
R R R
R R W
R W W
W W W
Possible number of marks =4
Like so
For case165: 165 questions attempted and it can be either Right or Wrong
Possible number of marks = 166
1 + 2 + 3 + . . . . . . + 166

## hii

u are goin 2 CRACK CAT dis tym...um sure bout thatt......

## Let see how it goesAny how

Let see how it goes
Any how best of luckfor you also.

## i believe the question is

i believe the question is how many DIFFERENT net scores are possible,
and 3 wrongs can nullify a right. Also your solution (also mine ) does not take into account the -1/3 negative mark. infact it seems that no matter what be the negative mark the anser will always remain the same! Absurd isn't it ?

## ans for CAT 165 prob........................

Examinee can ans 0 q right and 165 wrong --------definitely 1 way of score
or
Examinee can ans 1 q right and any 164 wrong --------definitely 1 way of score or
Examinee can ans 2 q right and any 163 wrong --------definitely 1 way of score
or
Examinee can ans 3 q right and any 162 wrong --------definitely 1 way of score
.
.
.
.
Examinee can ans 165 q right and 0 wrong --------definitely 1 way of score.
hence
Ans- 165+1=166

## Definitely a better

Definitely a better solution
But I donâ€™t the Weightage of negative marking wld make any difference

## ok! let me try again ! the

ok! let me try again !
the max score possible is 165 (all correct)
the min score possible is -55 (all wrong)
1. we can obtain scores like = -1/3, -2/3 , -1 and so on till -55 by combining
wrongs and no attempts. So total ways = 55 * 3 = 165
2. we can obtain all whole nos like = 0,1,2 ... ,165 by combining corrects and no attempts . So total ways = 166
3. we can obtain 1/3 by combining 1 correct and two wrongs.
Therefore we can obtain +ve nos. of the form k + 1/3 , k = whole number where the max value of k = 162 (Remember we need 1 correct and two wrongs to get the 1/3).
Thus, total ways = 163
4. we can obtain 2/3 by combining 1 correct and 1 wrongs.
Therefore we can obtain +ve nos. of the form k + 2/3 , k = whole number where the max value of k = 163 (Remember we need 1 correct and two wrongs to get the 2/3).
Thus, total ways = 164
Thus the total ways = 163 + 164 + 165 + 166 = 658
NOTE : 13861 IS DEFINITELY NOT A SOLUTION because that is the solution of:
In how many ways can we attempt a paper with 165 questions.
and around 55 different attempts can get a net score of zero and so on an so forth.
THE NEGATIVE MARKS IS NOT THERE FOR NOTHING.
Also Neeraj , there is no hard and fast rule that one must attempt each and every question.

## Thanks rajorshi for

Thanks rajorshi for explaining it in details
It seems flawless
Btw what do u do - working or in college
There is nthing in your profile.

## well! i passed from IIT

well! i passed from IIT Madras 2006 , presently i am sitting in the US (banking stuff ). just thought to give CAT a shot so....

## qoes no 24 moo1

in my opinion the ans is 337 because every odd digit gives 337 n every even gives 297.so 101th digit will give 337 as remainder

## solution given is wrong

odd number of 7's cannot be divisible by 11. It should be even number of 7's. The approach is definetly correct. its only a calculation error. it should have been
777....777(98 times)000 + 777
hence the remainder is 777/440 which is 337

## A valid pointYes kartik you

A valid point
Yes kartik you are right and i feel sorry for being so wrong in logic