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Varun Tyagi
@varun.tyagi
14,220

We can not assume random sides

No, its not correct!!!

Assume smallest square to be of dimension 'a' and next one in size (immediate right one) of dimension 'b'

Then equate the dimensions of opposite sides, you will get an equation in a and b, from there you can find somethingEDIT:-Dimension of squares will be:-

a

b

a + b

2a + b

3a + 2b

5a + 3b

8a + 4b

9a + 3b

9a + 2b

=> (9a + 2b) + (9a + 3b) = (8a + 4b) + (5a + 3b)

=> 5a = 2b

Height = 18a + 5b

Width = 17a + 7b

=> a = 2 and b = 5 (for any other value heigh and width will not be coprime)

=> Height = 61

Width = 69

=> Perimeter = 260

Chill bhai I got something like this

a

b

a+b

2a+b

3a+2b

5a+3b

8a+4b

4a+4b

4a+5b

Dimensions of length = 8a+9b = 13a+7b

Therefore: 5a = 2b

Length = 8a+9b

Breadth = 12a+9b

a = 2 and b = 5

Length = 61

Breadth = 69

Perimeter = 2*130 =

- 1 Like

Hemant Yadav
@chillfactor
46,735

is it 68 sir ??

sum of squares of sides of 9 squares = area of rectangle

say sides are 1,2,3....9

area = 9(10)(19)/6 = 15 * 19

so length and breadth are 19 and 15...Perimeter= 2(15+19) = 68

We can not assume random sides

Chill bhai Length = 51 and breadth = 43

Perimeter = 188 ??

No, its not correct!!!

Assume smallest square to be of dimension 'a' and next one in size (immediate right one) of dimension 'b'

Then equate the dimensions of opposite sides, you will get an equation in a and b, from there you can find something

a

b

a + b

2a + b

3a + 2b

5a + 3b

8a + 4b

9a + 3b

9a + 2b

=> (9a + 2b) + (9a + 3b) = (8a + 4b) + (5a + 3b)

=> 5a = 2b

Height = 18a + 5b

Width = 17a + 7b

=> a = 2 and b = 5 (for any other value heigh and width will not be coprime)

=> Height = 61

Width = 69

=> Perimeter = 260

- 3 Likes

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Varun Tyagi
@varun.tyagi
14,220

chillfactor SaysGiven diagram shows a rectangle formed by 9 non-overlapping squares. Find the perimeter of the rectangle if width and height of the rectangles are relatively co-prime positive integers.

Chill bhai Length = 51 and breadth = 43

Perimeter = 188 ??

Chill bhai I did the same as you are saying:

I got b=2a

Length = 30a

Breadth = 26a

It means it is not possible to have such a rectangle with co-prime length and breadth ???

Please refer to the first post in the next page :)

- 1 Like

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chillfactor SaysGiven diagram shows a rectangle formed by 9 non-overlapping squares. Find the perimeter of the rectangle if width and height of the rectangles are relatively co-prime positive integers.

sum of squares of sides of 9 squares = area of rectangle

say sides are 1,2,3....9

area = 9(10)(19)/6 = 15 * 19

so length and breadth are 19 and 15...

P.S. : Question dimag ke upar se nikal gaya .. aisa kar bhi sakte hai ?

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Hemant Yadav
@chillfactor
46,735

- 1 Like

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Hemant Yadav
@chillfactor
46,735

if the sum of the numbers (a25)^2 and a^3 is divisible by 9, then which of the following may me be a value for a?

ans options :

1, 7, 9, 8, there is no value...

i thought the answer would be 9, but its "there is no value"...why is that??

thanks

Basically the remainder when (a25)^2 + a^3 is divided by 9 should be 0

Suppose a = 9k + r, then

a25 = 9k + 7 + r

=> (a25)^2 = (9k + 7 + r)^2

which will leave remainder r^2 + 5r + 4 when divided by 9

a^3 when divided by 9, will leave remainder r^3

=> r^3 + r^2 + 5r + 4 should be divisible by 9

=> r^3 + (r + 1)(r + 4) should be divisible by 9

If r = 3p, then not possible

If r = 3p + 1, then also not possible

If r = 3k + 2, then also not possible

So, its never possible

- 2 Likes

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if the sum of the numbers (a25)^2 and a^3 is divisible by 9, then which of the following may me be a value for a?

ans options :

1, 7, 9, 8, there is no value...

i thought the answer would be 9, but its "there is no value"...why is that??

thanks

i went through the options .. it is easy that way ..

if a=1

125^2 mod 9 = 1

and 1^3 mod 9= 1

1+1 is not divisible by 9 ..

P.S. : Chill Saar .. kaha se aise methods late ho .. big fan .. bas yaha emoticons me "BOW" down ka option nahi hai .. :D

- 1 Like

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Varun Tyagi
@varun.tyagi
14,220

if the sum of the numbers (a25)^2 and a^3 is divisible by 9, then which of the following may me be a value for a?

ans options :

1, 7, 9, 8, there is no value...

i thought the answer would be 9, but its "there is no value"...why is that??

thanks

The sum of the digits of a number is the remainder by 9

so (a25)^2 % 9 = (a+7)^2

Option 1: a=1

8^2 + 1 = 65

gives remainder 2

Option 2: a = 7

14^2 + 343 = 919

gives remainder 1

Option 3: a = 9

256 + 729 = 985

gives remainder 4

Option 4: a= 8

225 + 512 = 737

gives remainder 8

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ans options :

1, 7, 9, 8, there is no value...

i thought the answer would be 9, but its "there is no value"...why is that??

thanks

Commenting on this post has been disabled.

Varun Tyagi
@varun.tyagi
14,220

could you explain the second part of the solution...i.e.

Subtract them to get:- (subtract what??)

99A = xy

=> A = xy/99 = xy/ab

thanks...

A= 0.xyxyxyxyxy....--------->1

100A = xy.xyxyxyxy..-------->2

100A - A = xy.xyxyxyxyxy... - 0.xyxyxyxyxy...

99A = xy

A = xy/99

Which means ab = 99.

- 1 Like

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A = 0.xyxyxy...

=> 100A = xy.xyxyxy...

Subtract them to get:-

99A = xy

=> A = xy/99 = xy/ab

=> ab = 99

could you explain the second part of the solution...i.e.

Subtract them to get:- (subtract what??)

99A = xy

=> A = xy/99 = xy/ab

thanks...

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A thin wire 40 meters long is cut into two pieces.one piece is used to form a circle with radius r and the other is used to form a square.no wire is left over.which of the following represents a total area,in square meters,of the square and circular regions in tyerms of r?

Pi r^2

Pi r^2+10

Pi r^2+1/4pi^2 r^2

Pir^2+(40-2pi r)^2

Pi r^2+(10-1/2pi r)^2

let two parts be x and 40-x ..

so 2pi*r=x and 40-x=4a----- (1)

so area = pi*r^2 + a^2

=

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varun.tyagi SaysMy take is option e.) pi*r^2 + (10-pi*r/2)^2

pls explain the working

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A certain stock exchange designates each stock with one,two,three letter code,where each letter is selected from the 26 letters of the alphabet.if the letters may be repeated and if the same letters used in a different order constitute a different code,how manyt different stocks is it possible to uniquely designate with theses codes?

2951

8125

15600

16302

18278

1 letter - 26

2 letter - 26^2

3 letter - 26^3

total 18278

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Varun Tyagi
@varun.tyagi
14,220

A thin wire 40 meters long is cut into two pieces.one piece is used to form a circle with radius r and the other is used to form a square.no wire is left over.which of the following represents a total area,in square meters,of the square and circular regions in tyerms of r?

Pi r^2

Pi r^2+10

Pi r^2+1/4pi^2 r^2

Pir^2+(40-2pi r)^2

Pi r^2+(10-1/2pi r)^2

My take is option e.) pi*r^2 + (10-pi*r/2)^2

2*pi*r = x

4a = 40 - x

a = (40 - 2pi*r)/4 = (20 - pi*r)/2

Total area = pi*r^2 + 1/4*(20 - pi*r)^2

= pi*r^2 + (10 - 1/2*pi*r)^2

A certain stock exchange designates each stock with one,two,three letter code,where each letter is selected from the 26 letters of the alphabet.if the letters may be repeated and if the same letters used in a different order constitute a different code,how manyt different stocks is it possible to uniquely designate with theses codes?

2951

8125

15600

16302

18278

Single letter codes: 26

Two letter codes: 26*26 = 676

Three letter codes: 26*26*26 = 17576

Total words = 26+17676 + 676 =

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