Official Quant thread for CAT 2013

@chillfactor said:
Pu + Pl = 32C + Pl = 27C + Pu = 25C + Pu + Pl = 42(C, Pu, Pl) = (10, 15, 17)ABCD is a parallelogram and P is a point on the plane such that area of triangle ABP is 10 and that of triangle CPD is 20. Find the maximum and minimum possible area of parallelogram ABCD.
Min, Max=60?
@soumitrabengeri 52?
@soumitrabengeri said:
Siddharth has only three types of toys - Cars, Puzzles and Planes. All his toys except 25 arePlanes. All except 32 are Cars. All except 27 are Puzzles. How many Cars does he have?(a) 52 (b) 15 (c) 12 (d) 10
32+27+25/2-32=10
@ani4588 said:
@soumitrabengeri 52?
Please quote the question along with the answer
@soumitrabengeri my bad...
@soumitrabengeri said:
A person drew 'x' triangles on a board such that no two of them touched or intersected each other.His friend counted the various types of triangles on the board and came up with the following data.• Exactly 20 triangles were there in which all the sides were equal.• At least 32 triangles were there in which at least two sides were equal.• Exactly 12 triangles were there in which all the sides were of different lengths.• Exactly 24 triangles were there in which one interior angle was obtuse.• Exactly 28 triangles were there in which all the interior angles were acute.What is the least possible value of 'x'?(a) 52 (b) 44 (c) 96 (d) None of these
52 ???
@chillfactor said:
Pu + Pl = 32C + Pl = 27C + Pu = 25C + Pu + Pl = 42(C, Pu, Pl) = (10, 15, 17)ABCD is a parallelogram and P is a point on the plane such that area of triangle ABP is 10 and that of triangle CPD is 20. Find the maximum and minimum possible area of parallelogram ABCD.
Min= 20
Max = 60.
@soumitrabengeri said:
A person drew 'x' triangles on a board such that no two of them touched or intersected each other.His friend counted the various types of triangles on the board and came up with the following data.• Exactly 20 triangles were there in which all the sides were equal.• At least 32 triangles were there in which at least two sides were equal.• Exactly 12 triangles were there in which all the sides were of different lengths.• Exactly 24 triangles were there in which one interior angle was obtuse.• Exactly 28 triangles were there in which all the interior angles were acute.What is the least possible value of 'x'?(a) 52 (b) 44 (c) 96 (d) None of these
52?
@chillfactor said:
Pu + Pl = 32C + Pl = 27C + Pu = 25C + Pu + Pl = 42(C, Pu, Pl) = (10, 15, 17)ABCD is a parallelogram and P is a point on the plane such that area of triangle ABP is 10 and that of triangle CPD is 20. Find the maximum and minimum possible area of parallelogram ABCD.
min 20
max= 60?
A man standing at the bottom of a staircase starts tossing a coin. Every time it shows Heads, he climbs two steps, while every time it shows Tails he climbs one step. After a while, he finds that he has climbed 8 steps. How many possible sequences of Heads and Tails could he have thrown?

1) 256
2) 28
3) 36
4) 34

Please explain with approach
@soumitrabengeri said:
A man standing at the bottom of a staircase starts tossing a coin. Every time it shows Heads, he climbs two steps, while every time it shows Tails he climbs one step. After a while, he finds that he has climbed 8 steps. How many possible sequences of Heads and Tails could he have thrown?1) 256 2) 283) 36 4) 34Please explain with approach
if 34 is the ans. i knw the approach?
please confirm
@maddy2807 said:
min 20 max= 60?
kaise hoga??
@soumitrabengeri said:
A man standing at the bottom of a staircase starts tossing a coin. Every time it shows Heads, he climbs two steps, while every time it shows Tails he climbs one step. After a while, he finds that he has climbed 8 steps. How many possible sequences of Heads and Tails could he have thrown?1) 256 2) 283) 36 4) 34Please explain with approach
34?
@soumitrabengeri said:
A man standing at the bottom of a staircase starts tossing a coin. Every time it shows Heads, he climbs two steps, while every time it shows Tails he climbs one step. After a while, he finds that he has climbed 8 steps. How many possible sequences of Heads and Tails could he have thrown?1) 256 2) 283) 36 4) 34Please explain with approach
11111111 1way
11222 10 ways
111122 15 ways
1111112 7 ways
2222 1 way
Total 34?
@Torque024 said:
Min, Max=60?
@Hypertexter said:
Min= 20Max = 60.
@maddy2807 said:
min 20 max= 60?
Yup, 20 and 60 are correct.

The two cases are:-

i) P lies on a line which is parallel to AB and CD and is between these two lines
This is the case for maximum area.
Area = 2(20 + 10) = 60

ii) P lies on a line which is parallel to AB and CD and is not in between these two lines
This is the case for minimum area.
Area = 2(20 - 10) = 20
@soumitrabengeri said:
A man standing at the bottom of a staircase starts tossing a coin. Every time it shows Heads, he climbs two steps, while every time it shows Tails he climbs one step. After a while, he finds that he has climbed 8 steps. How many possible sequences of Heads and Tails could he have thrown?1) 256 2) 283) 36 4) 34Please explain with approach
f(n) is the number if ways of reaching nth stair.
If first he climbs 1 step, then rest can be climbed in f(n - 1) ways
If first he climbs 2 step, then rest can be climbed in f(n - 2) ways

So, f(n) = f(n - 1) + f(n - 2)

Now, f(1) = 1 and f(2) = 2
Using them find f(8)

f(3) = f(2) + f(1) = 3
f(4) = 5
f(5) = 8
f(6) = 13
f(7) = 21
f(8) = 34

So, 34 sequences are possible
@soumitrabengeri said:
A man standing at the bottom of a staircase starts tossing a coin. Every time it shows Heads, he climbs two steps, while every time it shows Tails he climbs one step. After a while, he finds that he has climbed 8 steps. How many possible sequences of Heads and Tails could he have thrown?1) 256 2) 283) 36 4) 34Please explain with approach
Case 1: (2222)=4C4=1
Case 2: (22211)=5C3=10
Case 3: (221111)=6C2=15
Case 4: (2111111)=7C1=7
Case 5: (11111111)=8C0=1
Total ways =34
@soumitrabengeri said:
A man standing at the bottom of a staircase starts tossing a coin. Every time it shows Heads, he climbs two steps, while every time it shows Tails he climbs one step. After a while, he finds that he has climbed 8 steps. How many possible sequences of Heads and Tails could he have thrown?

1) 256
2) 28
3) 36
4) 34

Please explain with approach
different number of times Heads n tails can occur
Heads |Tails | diff sequences possible
4 0 1
3 2 5!/(3!*2!)=10
2 4 6!(4!2!) =15
1 6 7!/6!
0 8 1
Hence in total 34 ways
@soumitrabengeri said:
A man standing at the bottom of a staircase starts tossing a coin. Every time it shows Heads, he climbs two steps, while every time it shows Tails he climbs one step. After a while, he finds that he has climbed 8 steps. How many possible sequences of Heads and Tails could he have thrown?1) 256 2) 283) 36 4) 34Please explain with approach
34?
(T,H)
(0,4)(2,3)(4,2)(6,1)(8,0)
=1+5!/2!3!+6!/4!2!+7!/6!+1
@soumitrabengeri said:
A man standing at the bottom of a staircase starts tossing a coin. Every time it shows Heads, he climbs two steps, while every time it shows Tails he climbs one step. After a while, he finds that he has climbed 8 steps. How many possible sequences of Heads and Tails could he have thrown?1) 256 2) 283) 36 4) 34Please explain with approach
34?
@soumitrabengeri said:
A man standing at the bottom of a staircase starts tossing a coin. Every time it shows Heads, he climbs two steps, while every time it shows Tails he climbs one step. After a while, he finds that he has climbed 8 steps. How many possible sequences of Heads and Tails could he have thrown?1) 256 2) 283) 36 4) 34Please explain with approach
34?

@chillfactor said:
Pu + Pl = 32C + Pl = 27C + Pu = 25C + Pu + Pl = 42(C, Pu, Pl) = (10, 15, 17)ABCD is a parallelogram and P is a point on the plane such that area of triangle ABP is 10 and that of triangle CPD is 20. Find the maximum and minimum possible area of parallelogram ABCD.
min 20 & max 60?