The Official CAT 2007 Quant Thread

[Destiny's_Child]

Originally Posted by hanuman

Ans is b) 1332
No of rectangles including squares in chess board is 64*48/2=1536
No of squares in the chess board is 1^2+2^2+..8^2=204

hence no of rectangles in chess board is = 1536-204=1332

Is there some direct formula to calculate the number of squares and rectangles in a n*n square or m*n rectangle...
My quant is real bad.........

[vikram_k51]

Originally Posted by Destiny's_Child

Is there some direct formula to calculate the number of squares and rectangles in a n*n square or m*n rectangle...
My quant is real bad.........

Hi DC,
The generic formula for the no. of squares in an n*n square is: 1^2+2^2+3^2...n^2
And the number of squres in an m*n rectangle is (1+2+3...m)(1+2+...+n)
BTW ur display image is really cute nd goes well wid ur id

[vikram_k51]

Originally Posted by tatimatla

An interesting prob:
Two villages lie on the opposite sides of a river, whose banks are parallel lines. A bridge is to be built over the river, perpendicular to the banks. Where should the bridge be built so that the path from one village to the other is as short as possible? (the villages need not lie on a perpendicular to the river)

I am looking for a generic answer...if someone can attach an image, that'd be great

Tati given below is a generic soln:

Suppose the villages v1 & v2 r connected by a line v1v2 and o be the mid-point of v1v2.Then the perpendicular to the sides thru o will probably result in the shortest distance.
Sorry was too lazy for an image.

[tatimatla]

Originally Posted by the.bombardier

is this the correct answer? (c attachment)
A and B are the villages,ACDB is the shortest routes,n CD is the bridge..
i think u need to knw how far the villages r respectively from the banks..in this case i have assumed that A is farther away from the river than B.

sorry ...
that's wrong...but good to see a few attempts

[tatimatla]

Originally Posted by vikram_k51

Tati given below is a generic soln:

Suppose the villages v1 & v2 r connected by a line v1v2 and o be the mid-point of v1v2.Then the perpendicular to the sides thru o will probably result in the shortest distance.
Sorry was too lazy for an image.

thoda aur socho vikram bhai...
a little hint: shortest distance is always a straight line...but in this problem's case, we have a bridge in between...straight like kaha se dhoondenge?

[Destiny's_Child]

Originally Posted by vikram_k51

Hi DC,
The generic formula for the no. of squares in an n*n square is: 1^2+2^2+3^2...n^2
And the number of squres in an m*n rectangle is (1+2+3...m)(1+2+...+n)
BTW ur display image is really cute nd goes well wid ur id

Thanks Vikram!!!
And whats the formula for the number of rectangles in a n*n square and m*n rectangle???
And thanks for the complement i.e for my display image ....

[sastry751]

Hi,
VILLAGES PROBLEM
the perpendicular line is mid way between the villages dividing them in the ratio of their respective perpendicular distances from their banks.
d1/d2 = x/y (from figure attached)

river.zip

[dpu666]

if the numbers from 1 to 1000 divisible by 3 are written in ascending order then wat wud be the 100th digit from the left.

I guess there is a quick method to do such kinda probs. Can nyone help me with this.

[tatimatla]

Originally Posted by sastry751

Hi,
VILLAGES PROBLEM
the perpendicular line is mid way between the villages dividing them in the ratio of their respective perpendicular distances from their banks.
d1/d2 = x/y (from figure attached)

Attachment 5310

any proof for that?

[Krack_CAT]

the distance AC = BD shd be criteria.