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# Official Quant Thread for CAT 2011 [Part 8]

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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 something

EDIT:- 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

a = 2 and b = 5

Length = 61

Perimeter = 2*130 = 260
Aa gaya aa gaya :)
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Smoothest seas do not make tough sailors
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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

EDIT:- 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
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chillfactor Says
Given 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

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 :)
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Smoothest seas do not make tough sailors
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chillfactor Says
Given 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.

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

P.S. : Question dimag ke upar se nikal gaya .. aisa kar bhi sakte hai ?
NMIMS MBA Core 2012-14 www.partyonthehouse.com (A digital Project)
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Given 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.
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##### Attachments
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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

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
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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 ..

similarly none of the options satisfies .. hence none ..

P.S. : Chill Saar .. kaha se aise methods late ho .. big fan .. bas yaha emoticons me "BOW" down ka option nahi hai .. :D
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NMIMS MBA Core 2012-14 www.partyonthehouse.com (A digital Project)
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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

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

So no such value exists
Smoothest seas do not make tough sailors
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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

Commenting on this post has been disabled.
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

Subtract equation 1 from equation 2
100A - A = xy.xyxyxyxyxy... - 0.xyxyxyxyxy...
99A = xy
A = xy/99
Which means ab = 99.
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Smoothest seas do not make tough sailors
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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

last option .. 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

=pi*r^2 + (10-1/2pi r)^2------ from (1)
NMIMS MBA Core 2012-14 www.partyonthehouse.com (A digital Project)
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varun.tyagi Says
My take is option e.) pi*r^2 + (10-pi*r/2)^2

pls explain the working
The eternal seeker.....
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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

18278??

1 letter - 26
2 letter - 26^2
3 letter - 26^3

total 18278
NMIMS MBA Core 2012-14 www.partyonthehouse.com (A digital Project)
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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

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 = 18278
Smoothest seas do not make tough sailors
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