Official Quant thread for CAT 2013

pankaj1988 · February 4, 2013, 12:47pm

If the hands of clock coincide every 80 min and hands of another clock coincide every 65 min, what is approximate time difference between two clocks in exactly 24 hours time interval as shown by correct clock ?

a)272 min

b)145 min

c)220 min

d)200 min

ani6 · February 4, 2013, 12:48pm

Anshu gave Bobby and Chandana s many pens as each one of them already had.The Chandana gave Anshu and Bobby as many pens as each already had.Now each had an equal number of pens.The total number of pens is 72.

(a) How many pens did Bobby have initially

(b) How many pens did Chandana have initially

(c) How many pens did Anshu have initially pls expain in detail with steps

chandrakant.k · February 4, 2013, 12:55pm

@Kvothe. said:
Need help in solving this question...

Q - Find the 44th digit from the left

(1111....... 72 times)^2

Please provide explanation

is it 8?? sorry typo last time and not able to edit in office 😞

@ani4588 said:

you are forgetting the case when the no starts with a 0

number cannot start with 0

@vbhvgupta said:

OA is 294840

@vbhvgupta said:
how many 6-digit numbers contain exactly 4 different digits?

ok here you go

let abcd be the four different digit

now we need to select 4 numbers from 10

so 10C4 = 210

the other 2 letters can be either same or different

when same : 4

when diff = 4C2 =6

in case of same arrangment would be 6!/3! = 120

in case of diff 6!/2!2! = 180

so total arrangemetns = 210*(4*120+6*180) = 210*(480+1080) = 210*1560=327600

now let us subtract the cases with starting 0

1/10 of the numbers of would be starting with 0 = 32760

so 327600-32760 = 294840

ani4588 · February 4, 2013, 12:56pm

@ani6 said:
Anshu gave Bobby and Chandana s many pens as each one of them already had.The Chandana gave Anshu and Bobby as many pens as each already had.Now each had an equal number of pens.The total number of pens is 72.(a) How many pens did Bobby have initially(b) How many pens did Chandana have initially(c) How many pens did Anshu have initially pls expain in detail with steps

a)6

b)24

c)42 ??

ani4588 · February 4, 2013, 12:57pm

@chandrakant.k thats what i was referring to... u forgot to deduct the case where no starts with a zero

pankaj1988 · February 4, 2013, 1:05pm

@chandrakant.k said:
is it 8?? sorry typo last time and not able to edit in office

Bhai yeh kaise kiya aapne ?

chandrakant.k · February 4, 2013, 1:08pm

@pankaj1988 said:

Bhai yeh kaise kiya aapne ?

if the answer is right then i will post the approach 😃 😃 was

from afternoon. finally got. hope it is correct. I will add the method at that time. 😃 😃

@ani4588 said:

@chandrakant.k thats what i was referring to... u forgot to deduct the case where no starts with a zero

oh i mistook it 😃 thanks

ani4588 · February 4, 2013, 1:10pm

@chandrakant.k
(1111....... 72 times)^2
according to wolframaplha it should be 9. kya approach use kiya??

ishu1991 · February 4, 2013, 1:20pm

@pankaj1988 said:
If the hands of clock coincide every 80 min and hands of another clock coincide every 65 min, what is approximate time difference between two clocks in exactly 24 hours time interval as shown by correct clock ?a)272 minb)145 minc)220 min d)200 min

14 +6/11 mins are lost in 80mins
--------------------------in 24.60mins

we get 2880/11 mins lost

5/11 mins are gained in 65 mins
------------------------in 24.60mins

we get 2880/26 mins gained

so difference is 262 ~=272 mins pl. confirm

chandrakant.k · February 4, 2013, 1:23pm

@ani4588 said:
@chandrakant.k
(1111....... 72 times)^2
according to wolframaplha it should be 9. kya approach use kiya??

hmmm

see in 11*11 there are 2n-1 terms

in 111*111 = 12321 2n-1 terms

this holds good for any number of 1's. i have checked it for 14 19 and 20

so when there are 72 1's the number of terms would be 143

now w are asked to find 44th term from left that means 99th term from right(ok here iwent wrong)

now this is how the logic works

111

*111

______

12321

if you observe the 2nd digit from left involves two 1's , third uses three 1's. fourth uses two 1's

so if you take 99th term from left

it should involve 99-72 = 27 1's

which means the sum you will get = 1*27 = 27

now the term before this i.e 100th digit will contain 28 digit which means it will give you 28(so 8 will be in the final answer and 2 will be carry)(though this is not the case as again this effect will be der for 101th term

but for 27th term you can take the carry will be 2

so 27+2 = 29

9 will be the 44th digit and 2 will go as carry 😃 :)

so yes 9 should be the answer :)

hope you understood ::)

PS : you got ot be careful when you have number of 1's close to the ten multiple like 29 (here the carry would be 3) and so on :)

pankaj1988 · February 4, 2013, 1:24pm

@abhishekhenry said:
A hexagon of maximum area is inscribed in a equilateral triangle .What is the ratio of the area of hexagon to the ratio of equilateral triangle.1)1:22)1:43)1:34)none Plz post the approach

Can be deduced that maximum area occur if triangle is of side 3a and Hexagon is of side a

Ar(hexagon)/Ar(triangle)=(6* _/3 /4 * a^2)/(_/3/4 * 9 * a^2)= 2:3 none

chandrakant.k · February 4, 2013, 1:34pm

@pankaj1988 i have posted my method above please check :)

ani6 · February 4, 2013, 1:47pm

@ani4588 yes..plz provide steps

chandrakant.k · February 4, 2013, 1:55pm

@ani6 said:
Anshu gave Bobby and Chandana s many pens as each one of them already had.The Chandana gave Anshu and Bobby as many pens as each already had.Now each had an equal number of pens.The total number of pens is 72.
(a) How many pens did Bobby have initially

(b) How many pens did Chandana have initially

(c) How many pens did Anshu have initially pls expain in detail with steps

let a b and c be the initail pens they had

after all the distribution each had an equal number of pens which means

4b = 24 => b = 6

2(a-(b+c)) = 24

=> a-(b+c) = 12

=> a-c = 18 -(1)

2C-2b-(a-(b+c)} = 24

2c - 12 -(a-c - b) = 24

2c -12 = 36

2c-12=36

c = 24

put in (1)

a = 18+24 = 42

so a) 6 b)24 c)42

ani6 · February 4, 2013, 2:02pm

@chandrakant.k thanks a lot

ishu1991 · February 4, 2013, 2:05pm

@ani6 said:
Anshu gave Bobby and Chandana s many pens as each one of them already had.The Chandana gave Anshu and Bobby as many pens as each already had.Now each had an equal number of pens.The total number of pens is 72.(a) How many pens did Bobby have initially(b) How many pens did Chandana have initially(c) How many pens did Anshu have initially pls expain in detail with steps

a)6
b)24
c)42

ishu1991 · February 4, 2013, 2:24pm

How many exponents of 2 are there such that if we delete first digit, remaining number is also the power of 2.

Like 2^5 = 32 .. deleting 3, we get 2 => 2^1 = 2

a) 1
b) 2
c) 5
d) 15
e) infinite

subhashdec2 · February 4, 2013, 2:27pm

@ishu1991 said:
How many exponents of 2 are there such that if we delete first digit, remaining number is also the power of 2.

Like 2^5 = 32 .. deleting 3, we get 2 => 2^1 = 2

a) 1
b) 2
c) 5
d) 15
e) infinite

32 and 64 ??

ishu1991 · February 4, 2013, 2:28pm

@Subhashdec2 said:
32 and 64 ??

explain

subhashdec2 · February 4, 2013, 2:37pm

@ishu1991 said:

explain

till 4 digits u can verify easily

lets take a 5 digit no

abcde

now bcde can be either of 1024 2048 4096 8192

a can be anything 1 to 9

consider 1024

a1024

a*10^4+1024

10^4=5^4*2^4

2^4(5^4*a+2^6)

5^4*a+2^6 to be an exponent of 2

5^4*a+2^6=2^n

5^4*a=2^n-2^6

5^4*a=2^6(2^(n-6) -1)

a should be atleast 2^6

while a can at max be 2^3

hence no 5 digit no and beyond that can be the numbers what we require