Official Quant thread for CAT 2013

@Calvin4ever said:
In a certain mixed school, where a special feature was made of the inculcation of good manners, they had a curious rule on assembling every morning. There were twice as many girls as boys. Every girl made a bow to every other girl, to every boy, and to the teacher. Every boy made a bow to every other boy, to every girl, and to the teacher. In all there were nine hundred bows made in that model academy every morning. Now, can you say exactly how many boys there were in the school?
10?..
let no .of boys = x
no. of girls = 2x

x((x - 1) + 2x +1) + 2x(x + (2x-1) + 1) = 900
x = 10
@Calvin4ever said:
In a certain mixed school, where a special feature was made of the inculcation of good manners, they had a curious rule on assembling every morning. There were twice as many girls as boys. Every girl made a bow to every other girl, to every boy, and to the teacher. Every boy made a bow to every other boy, to every girl, and to the teacher. In all there were nine hundred bows made in that model academy every morning. Now, can you say exactly how many boys there were in the school?
number of boys = 10... ?
@venomizer 28 ? am i ri8 ?
@somnathbhatta nope..
tell me the method
@venomizer is it 25 then ?
@somnathbhatta nahi... its 31.

sorry then my method doesn't work .. no idea ..
what i did was - assigned values to the numbers accordingly in their order in the alphabet series given in the question
no other logic came to my mind

well its a type of cryptarithm...u have to arrive at ur sol by logically deducing on the results of multiplication of numbers..http://en.wikipedia.org/wiki/Cryptarithm

@somnathbhatta
@venomizer never tried this stuff . will surely give it a try. quite an exhaustive problem too.
@venomizer so far all the examples that i came across the internet, each and everyone of them dealt with addition and subtraction. making it easier to find the corresponding digits. with multiplication its a lot more complicated. can't set an algo for multiplication. however in any exam attempting this should prove to be immensely time consuming (no-offense, just my feeling). but for the sake of finding an answer quite a few codes in C are available over the internet. you can download one and find the answer.

@anitito123
@anitito123 said:
how to find the greatest among 17^105 and 31^84?
taking log to the base 2 in both the cases :
105 log 17 > 105 log 16 = 420
84 log 31
hence 17^105 is greater
@Calvin4ever it is a simple question if it is going like "the teacher" and not teachers in general.
So i have assumed that therz only 1 teacher. gong like wise, each student gave a bow to every other student nd to the teacher so if x is number of students every stud gave x bows.... and hence total bows dstrbuted are x*x
so number of studs= SqRt(900)=30 and boys:girls=2:1... hence number of boyz is 10...temme f i have gone wrong somewhere
@ravi.theja said:
saar also add dis to ur list ... sm thing number line wala method or any other easy method.
@Estallar12 said:
2 - 3 methods. You can use any.Oh. Mera Chinese Rem ka Post bhi due hain.
plz discuss those methods

@naveenkrs nice method bro.

What is the rightmost nonzero digit of (44!)^(44!) ?

@catahead said:
What is the rightmost nonzero digit of (44!)^(44!) ?
6?

@catahead said:
What is the rightmost nonzero digit of (44!)^(44!) ?
44!=2^41*3^19*5^9...........and so on.....



to remove all zeroes, we remove all 5s and an equal number of 2s. Thus we now have....


2^32*3^19*7^6.....and so on....

we have 2^32 in the expression, we will definitely have the last digit of this expression as an even digit.........Now 44! is a multiple of 4.........any even digit raised to the power of 4 yields 6


ans=6

the value of ((1.001001001)^(1/3)) -((1.001001)^(1/3)) is closest to:


options: 0, 10^(-6), 3*10^(-9) , 3.3*10^(-10)

Plz mention the approach.
Plz Help!!

A tradesman fixes the sale price of his articles 30% more than the C.P.. Half of the articles , he sells at this increased sale price and portion , he sells at 15% discount of this sale price. And the remaining , he sells at 30% discount of this sale price . what % profit did occur to the tradesman?
@ani6 said:
Plz Help!!A tradesman fixes the sale price of his articles 30% more than the C.P.. Half of the articles , he sells at this increased sale price and portion , he sells at 15% discount of this sale price. And the remaining , he sells at 30% discount of this sale price . what % profit did occur to the tradesman?
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