official quant thread for cat08

[naga25french]

Originally Posted by nikunj14_83

Nope ans is 57.......

yeah u r right..made silly error

let me tell ma approach

68 = 17 * 4

7777(upto 200 times) divided by 17 , the remainder is 6

7777(upto 200 times) divided by 4 , the remainder is 1

so final remainder is 57 (smallest number satisfying above two condition)

so remainder is 57

[nikunj14_83]

Originally Posted by naga25french

yeah u r right..made silly error

let me tell ma approach

68 = 17 * 4

7777(upto 200 times) divided by 17 , the remainder is 6

7777(upto 200 times) divided by 4 , the remainder is 1

so final remainder is 57 (smallest number satisfying above two condition)

so remainder is 57

I think u didn't read my ques correctly how chk for divisibilty in such ques with 7,11,13,17,19 ..in this ques how are we getting 6 as remainder with 17??

[naga25french]

Originally Posted by nikunj14_83

I think u didn't read my ques correctly how chk for divisibilty in such ques with 7,11,13,17,19 ..in this ques how are we getting 6 as remainder with 17??

well jus apply fermat theorem when those numbers are the divisors.. that will reduce the complexity of the problem..

[nikunj14_83]

Originally Posted by naga25french

well jus apply fermat theorem when those numbers are the divisors.. that will reduce the complexity of the problem..

Ya i know Fermats theorm....but i am not getting how to apply in this ques ..so far i have applied in ques of the format like(A)^b/C where A,C are prime to eachother

Can u pls ellaborate how to apply in ques like this one(7777777......200times)/17??

[naga25french]

Originally Posted by nikunj14_83

Ya i know Fermats theorm....but i am not getting how to apply in this ques ..so far i have applied in ques of the format like(A)^b/C where A,C are prime to eachother

Can u pls ellaborate how to apply in ques like this one(7777777......200times)/17??

17 is a prime number

if p is a prime number greater than 5 , then any number formed by writing consecutively (p-1) times the same number is exactly divisible by p


eg . 111111 % 7 = 0

22( up to 12 terms ) % 13 = 0


in our problem 17 is the prime number

777( up to 16 times ) is exactly divisible by 17


this means 777( up to 16 * 12 times ) is exactly divisible by 17

so we r left with 77777777 % 17

dividing directly , we get 6 as the remainder..

hope its clear..

[the_hate]

Originally Posted by implex

New Problem!!

From one corner of a square field, a boy runs in random direction with random uniform velocity. The greatest distance the boy can run in one minute is the length of the diagonal of the field. What is the probability that the boy will be in the field after the end of one minute?

I'm little confused with wording of q's...hope i've interpreted it correctly..

let side of sq=x
so, diagonal = 2^(1/2)*x

now..area that can be covered by boy = circle with radius of 2^(1/2)*x
=pi*2*(x^2)
area of sq = x^2

so, prob = 1/(2*pi)

is it correct?

[milindagrawal]

[quote=nikunj14_83;1127958]Hi Guys,
Since the day I started my CAT prep there have been few typical type of ques that have troubled me either in 3) A survey was conducted among 100 men in a company & it was found out that
100 men use brand A
75 men use brand B
80 men use brand C
90 men use brand D
60 men use brand E
Find the minimum possible no of men using all 5 brands if all the 100 men use atleast one of the brands ans=5
I find these format of set theory ques really difficult as no intersection data is given

3)
v can see that 25 don't use brand B, 20 dont use brand C, 10 don't use brand D, and 40 don't use brand E.. now if we consider all these to be unique then we see that we get their total as 95.. wich means that there are atleast 5 persons using all 5 brands..(there is no question of brand A as all 100 are using it)..

[deep@k]

Originally Posted by naga25french

17 is a prime number

if p is a prime number greater than 5 , then any number formed by writing consecutively (p-1) times the same number is exactly divisible by p


eg . 111111 % 7 = 0

22( up to 12 terms ) % 13 = 0


in our problem 17 is the prime number

777( up to 16 times ) is exactly divisible by 17


this means 777( up to 16 * 12 times ) is exactly divisible by 17

so we r left with 77777777 % 17

dividing directly , we get 6 as the remainder..

hope its clear..

this is a very good explanation given by naga.....

excellent job naga.......

[nikunj14_83]

Originally Posted by naga25french

17 is a prime number

if p is a prime number greater than 5 , then any number formed by writing consecutively (p-1) times the same number is exactly divisible by p


eg . 111111 % 7 = 0

22( up to 12 terms ) % 13 = 0


in our problem 17 is the prime number

777( up to 16 times ) is exactly divisible by 17


this means 777( up to 16 * 12 times ) is exactly divisible by 17

so we r left with 77777777 % 17

dividing directly , we get 6 as the remainder..

hope its clear..

Hmmm its clear upto a certain extent
just one more ques 77777777/17 is there way to solve it using sme theorm or u have directly divided it??

[deep@k]

Originally Posted by the_hate

I'm little confused with wording of q's...hope i've interpreted it correctly..

let side of sq=x
so, diagonal = 2^(1/2)*x

now..area that can be covered by boy = circle with radius of 2^(1/2)*x
=pi*2*(x^2)
area of sq = x^2

so, prob = 1/(2*pi)

is it correct?

what logic you used to take radius is same as diagonal?????
I think diagonal is same as diameter of circle....

please clarify my doubt????