official quant thread for cat08

[swagato1987]

1. What is the difference between the total number of rectangles and the total number of squares that can be made from a 8x8 chess board????


I do not remember the options but I could not solve this problem. Anyone please help.

[masoom]

Originally Posted by continental

Enjoy friends.....
1. In a class the teacher wrote a set of consecutive integers starting from one. Jhony came and earased one number. The average of the remaining was 355/13. what was the no. that jhony erased.

options: 24, 11, 30, 7

2. The product P of three positive integers is 9 times their sum, and one of the integers is the sum of the other two. The sum of all possible values of P is

options: 702, 1404, 336, 540

3. S is a six digit number beginning with 1. If the digit 1 is moved from the leftmost place to the rightmost place the number obtained is three times of S. Then the sum of the digits of S is

options: 21, 24, 26, 27

4. The equation 5(x - 2) = 27(x + 2)/ 7 is written throughout in base 9. Find the value of x in base 10.

options: 10, 11, 12, 13

5. In the value of the number 30! all the zeroes at the end are erased. Then, the unit digit of the number that is left is

options: 2, 4, 6, 8

We have miles to go before we sleep

some answers :

1. 11

2. 702

4. 12

5. 6..

[mrholmes]

questions....

What is the remainder when 2^2!^3!^4!...100! is divided by

1. 7

2. 9


Hi,
Can any one post detailed solutions for these two questions?

Thx.

[hi.shivani]

Originally Posted by swagato1987

1. What is the difference between the total number of rectangles and the total number of squares that can be made from a 8x8 chess board????


I do not remember the options but I could not solve this problem. Anyone please help.

See total number of vertical and horizontal lines are 9 and 9.
For forming a rectangle we need 2 verical and two horizontal lines.

this can be selected in 9c2 ways for horizontal line and 9c2 for vertical lines..
i hope this will help u..

[masoom]

Originally Posted by swagato1987

1. What is the difference between the total number of rectangles and the total number of squares that can be made from a 8x8 chess board????


I do not remember the options but I could not solve this problem. Anyone please help.

For a given nxn matrix,
the formula to find no of squares is
( n * (n+1) * (2n + 1) ) / 6.
so a chess board contains 204 squares

For a given nxm matrix,
And to find no of rectangles is
((n * (n + 1) )/2) * ((m * (m +1))/2)
the no of rectangles in chess board is 1296

so the difference is 1296-204= 1100...

if you are not getting the above formulae kindly revert

[dare2]

Originally Posted by swagato1987

1. What is the difference between the total number of rectangles and the total number of squares that can be made from a 8x8 chess board????


I do not remember the options but I could not solve this problem. Anyone please help.

.

there are direct formulae for finding the number of squares and rectangles in a n x n board.

squares = 1^2 + 2^2 + 3^2 + ...... + n^2

rectangles=1^3 + 2^3 + 3^3 +... + n^3


hope that helps..

[swagato1987]

Originally Posted by hi.shivani

See total number of vertical and horizontal lines are 9 and 9.
For forming a rectangle we need 2 verical and two horizontal lines.

this can be selected in 9c2 ways for horizontal line and 9c2 for vertical lines..
i hope this will help u..

So total number of possible rectangles= (9c2)^2

and total number of possible squares = 1^2+2^2+3^2+.......+8^2
= 1+4+9+16+25+36+49+64 = 204

Hence, the answer is = (9C2)^2-204=(36)^2-204=1296-204=1092

Ok.Thnx a lot.

[masoom]

Originally Posted by dare2

.

there are direct formulae for finding the number of squares and rectangles in a n x n board.

squares = 1^2 + 2^2 + 3^2 + ...... + n^2

rectangles=1^3 + 2^3 + 3^3 +... + n^3


hope that helps..

yups dude.. you are right.. if we want to generalize this into a n*m matrix.. then the no of rectangles can be determined but is there any general formula for finding number of sqaures in such cases..

[dare2]

Originally Posted by hi.shivani

See total number of vertical and horizontal lines are 9 and 9.
For forming a rectangle we need 2 verical and two horizontal lines.

this can be selected in 9c2 ways for horizontal line and 9c2 for vertical lines..
i hope this will help u..

nice one..

but what square?

[hi.shivani]

New Questions:
1) Last non-zero digit of 96!
2) Remainder of 121212...300 times divided by 99.