Official Quant thread for CAT 2013

@Buck.up said:
What is the probability of getting a word with all 'T's together for the word ATTEMPT ?
1/7 ??
5!/(7!/3!)
@Buck.up said:
Find the no of ways in which 10 different balls can be placed in 4 different boxes such that at max 2 boxes are empty.
must be 4^10 -4 , as all boxes are different
In how many ways can 12 different books be divided equally among
(i)4 persons
(ii)4 sets
@techgeek2050 said:
Find all pairs of positive integers (a,b) satisfying b^3=3a^2+3a+7
no solution
their graphs never intersect??
@abhishek.2011 said:
no solutiontheir graphs never intersect??
i also got that. i didn't have the OA so i just wanted to check.
@albiesriram said:
Q2. A=10
@Tusharrr said:
ABC is an isosceles triangle where AB=AC and BC=60. D is a point on BC such that the perpendicular distance from D to AB and AC is 16 and 32, respectively. What is the length of AB?
do u have options ?? its 1 line work with options
@abhishek.2011 I hv gt answer from pratskool
While I get make option
A-54
B-52
C-50
D-23

Question

Find minimum value of N not equal 23 in this
(N-23)/(7N+6) is not in its simplest form
N belonge to natural number
@Tusharrr
EDIT: silly mistake re visualizing...
@Tusharrr N= 190? for second one? doubtful...
50 for first one?
@Tusharrr said:
QuestionFind minimum value of N not equal 23 in this(N-23)/(7N+6) is not in its simplest formN belonge to natural number
(N - 23) and (7N + 6) have a common factor. Let's say it is k.

7*(N - 23) = 7a*k
7N + 6 = b*k

where a,b are co-prime numbers.

6 + 23*7 = (b - 7a)*k
167 = (b-7a)*k

Factors of 167 = 1, 167 .

k = 167 , (b-7a) = 1

7N + 6 = b*167 => N = (167*b - 6)/7

b = 1,8,15 etc gives Integer N
b = 1 is rejected as then a = 0

=> N = (167*8 - 6)/7 = 190

So, minimum such N = 190 ?

what is the last non-zero digit in 2000!?


100 students of a class appeared in monthly test of at least one of the three subjects; Physics, Chemistry or Mathematics. Number of students who appeared in Mathematics test is more than who appeared in Chemistry test which is more than who appeared in Physics test which is more than who appeared in exactly two subjects which is more than who appeared in all three. At least one student appeared in test of all three subjects.
What is the minimum number of students who appeared in test of Chemistry?

@jayrajdabral said:
what is the last non-zero digit in 2000!?
8 ?

@bullseyes yea bro i also got 8 but according to this link its 4

http://cat.wordpandit.com/finding-last-non-zero-digit-of-any-factorial/
@abhishek.2011 said:
do u have options ?? its 1 line work with options
sides will be 50
triangle bde is similar to cdf
now side of triangle with perpendicular as 16 comes as 16,20,12
of other 32,40,24
now (a-12)^2 + 16^2 = (a-24)^2 + 32^2
solving it a= 50
sorry for late reply m in office :)
@jayrajdabral said:
@bullseyes yea bro i also got 8 but according to this link its 4http://cat.wordpandit.com/finding-last-non-zero-digit-of-any-factorial/
Sadly, he seems to be wrong after all that calculation (and all that boasting) 😛 It is 8.

Double-checked using Wolframalpha (since long and painful process mein kuch mistake hone ka kaafi chance tha...)

http://www.wolframalpha.com/input/?i=last+non-zero+digit+in+2000!

regards
scrabbler