Official Quant thread for CAT 2013

@chillfactor said:
1000x + 100y + 10z + w = 2010x = 2,10z + w = 1, so 2 waysx = 1,100y + 10z + w = 1010y = 0, 10z + w = 1010, 8 waysy = 1, 10z + w = 910, 10 ways.y = 9, 10z + w = 110, 10 waysy = 10, 10z + w = 10, 2 waystotal = 100 waysx = 0100y + 10z + w = 2010y = 10, 11, 12, ..., 20case will be same as x = 1So, total 2 + 100 + 100 = 202 ways
y = 0, 10z + w = 1010, 8 ways

how is this 8 ways coming ?
plz explain
@Aman.Malhotra said:
How many four letter word from the word "INEFFECTIVE" ?????
1422
@joyjitpal said:
what is the mistake if we do : "2 same 2 same : 3C1* 2C1 * (4!)/{(2!) * (2!)}"
Nothing just divide by 2! so as to make sure double counting is taken care of.
eg. We have II,EEE,FF
Suppose we want to choose I and F and lets say we choose I first and F 2nd
This can be done in 3C1*2C1 ways
Now if we choose F 1st and I 2nd
again 3C1*2C1
But these r the same case hence divide by 2!
@deedeedudu thanx bhai
Answer question nos. 96 €“ 97 based on the following
information.
From a group of 545 contenders, a party has to
select a leader. Even after holding a series of meetings,
the politicians and the general body failed to reach a
consensus. It was then proposed that all 545 contenders
be given a number from 1 to 545. Then they will be
asked to stand on a podium in a circular arrangement,
and counting would start from the contender numbered
1. The counting would be done in a clockwise fashion.
The rule is that every alternate contender would be asked
to step down as the counting continued, with the circle
getting smaller and smaller, till only one person remains
standing. Therefore the first person to be eliminated
would be the contender number 2.
96. Which position should a contender choose if he
has to be the leader?
A. 3 B. 67
C. 195 D. 323
E. 451
97. One of the contending politicians, Mr. Chanaya,
was quite proficient in calculations and could
correctly figure out the exact position. He was the
last person remaining in the circle. Sensing foul
play the politicians decided to repeat the game.
However, this time, instead of removing every
alternate person, they agree on removing every
300th person from the circle. All other rules were
kept intact. Mr. Chanaya did some quick
calculations and found that for a group of 542
people the right position to become a leader would
be 437. What is the right position for the whole
group of 545 as per the modified rule?
A. 3
B. 194
C. 249
D. 437
E. 543
@joyjitpal said:
y = 0, 10z + w = 1010, 8 wayshow is this 8 ways coming ?plz explain
z,w ranges from 0 to 99 => 10z= 1010 - w

=> w max = 99 => 10z = 1010-99 => z min = 92
From 92 to 99 -> 8 ways
@joyjitpal said:
Answer question nos. 96 €“ 97 based on the followinginformation.
96. B. 67
97. C. 249
(Not Sure)
A person lent out some money for 1year at 6% per annum simple interest and after 18months he again lent out the same money at a simple interest of 24% per annum. In both cases he got Rs.4704. What was the amount that he lent out if interest is paid half yearly?
a rs 4000 b rs 4200 c rs 4400 d rs 3600
Find the number of 9-digit numbers of 9 different digits such that the product of any 5 consecutive digits is a multiple of 7.
@jain4444 said:
Find the number of 9-digit numbers of 9 different digits such that the product of any 5 consecutive digits is a multiple of 7.
17*8!?
@IIM-A2013 said:
A person lent out some money for 1year at 6% per annum simple interest and after 18months he again lent out the same money at a simple interest of 24% per annum. In both cases he got Rs.4704. What was the amount that he lent out if interest is paid half yearly?a rs 4000 b rs 4200 c rs 4400 d rs 3600
b. Rs 4200
@deedeedudu said:
96. B. 6797. C. 249 (Not Sure)
approach
@joyjitpal
96. Write 545 in binary form
1000100001
Remove the leadin digit and put it at the end
0001000011
Convert 1000011 to decimal u get the ans

97. Manually counted this one looking for a better approach
@chillfactor sir help plz
@deedeedudu said:
@joyjitpal96. Write 545 in binary form1000100001Remove the leadin digit and put it at the end0001000011Convert 1000011 to decimal u get the ans97. Manually counted this one looking for a better approach@chillfactor sir help plz

solution by chill sir

Lets say that 1st person kills the 2nd and then the 3rd persons gets the sword and he will kill 4th person and so on.

In case there are 2ⁿ persons, whoever has the sword in the starting will be the only survivor. Suppose there are 2ⁿ + 1 persons. So, first person will kill 2nd person, now we are left with exactly 2ⁿ persons and sword is with 3rd person and we know that when 2ⁿ persons are there then the person having sword will be the only survivor in the end.

Similarly, when there are 2ⁿ + k persons we just have to find the who will be having the sword once k persons are dead.

Person standing at '2k'th position is the kth person to die and "2k + 1'th person will get tge sword. So,he will be the last man standing


@jain4444 said:
Find the number of 9-digit numbers of 9 different digits such that the product of any 5 consecutive digits is a multiple of 7.
xxxx7xxxx

8*8! ?
@krum said:
xxxx7xxxx8*8! ?
What if the middle no is 0 ??
@jain4444 said:
Find the number of 9-digit numbers of 9 different digits such that the product of any 5 consecutive digits is a multiple of 7.
33 * 8! ?

Case 1 : _ _ _ _ 0 _ _ _ _ / _ _ _ _ 7 _ _ _ _

9C8*8! + (9C8*8! - 8*7!) = 17*8!

Case 2: 7_ _ _ _ 0 _ _ _ / _ 7_ _ _ _ 0 _ _ / _ _ 7 _ _ _ _ 0_ / _ _ _7 _ _ _ _0

4*8! + 3*8! + 2*8! + 8! = 10*8! (7 can change positions towards the right)

Case 3: _ 0_ _ _ _ 7 _ _ / _ _ 0 _ _ _ _ 7_ / _ _ _0 _ _ _ _7

3*8! + 2*8! + 8! = 6 * 8!

Total sum = 33* 8! ?

Solved with a headache, may be wrong :banghead:
@krum said:
then product of every 5 consecutive digits won't be multiple of 7
Wont we consider 0 as a multiple of 7?
@deedeedudu Do we ever provide SI half yearly as in this case becuse it wouldn't make any diffrence 6%=3%+3% + 4200 6 % is 252. A= 4452 "4704 " is stated as the amount not 4452
@YouMadFellow said:
33 * 8! ?Case 1 : _ _ _ _ 0 _ _ _ _ / _ _ _ _ 7 _ _ _ _9C8*8! + (9C8*8! - 8*7!) = 17*8!Case 2: 7_ _ _ _ 0 _ _ _ / _ 7_ _ _ _ 0 _ _ / _ _ 7 _ _ _ _ 0_ / _ _ _7 _ _ _ _04*8! + 3*8! + 2*8! + 8! = 10*8! (7 can change positions towards the right)Case 3: _ 0_ _ _ _ 7 _ _ / _ _ 0 _ _ _ _ 7_ / _ _ _0 _ _ _ _73*8! + 2*8! + 8! = 6 * 8!Total sum = 33* 8! ?Solved with a headache, may be wrong
Elaborate it a bit more... mujhe samajh nhi aaya ye method.. :(