Official Quant thread for CAT 2013

MBA CAT 2024
14603
@naga25french said:
Euler number of 17 is 16 .. so number formed by writing a unit digit 16 times consecutively will be divisible by 16 ..so 22222222 ( up to 32 times will be divisible by 17 and also 22222222 ( up to 16 times will be divisible by 171 - 32 --> digit divisible and 36 - 51 divisible by 17so we are left with 22x or x22 or 2x2Its now obvious .. Just check other posts for knowing what is euler number if you are aware of it .. hope this helps

" so number formed by writing a unit digit 16 times consecutively will be divisible by 16 .." bhai can u explain ??

14604
@sundip said:
" so number formed by writing a unit digit 16 times consecutively will be divisible by 16 .." bhai can u explain ??
check this :

http://www.pagalguy.com/forums/quantitative-ability-and-di/official-quant-thread-cat-2011-part-2-t-67094/p-2761065/r-2820325
14605
@sunnychopra89 said:
A no. has exactly 32 factors out of which 4 are not composite. Product of these 4 factors(not composite) is 30. How many such nos. are possible?
30=5*3*2

so prime factors are 2,5,3

32=a1*a2*a3

where a1 a2 and a3 are atleast 2

xyz=4

114-> 3 cases
221->3 cases


Total 6??
14606
@sunnychopra89 said:
A no. has exactly 32 factors out of which 4 are not composite. Product of these 4 factors(not composite) is 30. How many such nos. are possible?
My take-6
14607
@sunnychopra89 said:
A no. has exactly 32 factors out of which 4 are not composite. Product of these 4 factors(not composite) is 30. How many such nos. are possible?
http://www.pagalguy.com/forums/quantitative-ability-and-di/official-quant-thread-c-t-88456/p-3611604/r-4434685
chk this...
14608

1st 126 natural nos. are put side by side in ascending order to form a large no. 123456......125126. What will be the remainder when it is divided by 5625?

14609
@sunnychopra89 said:
A no. has exactly 32 factors out of which 4 are not composite. Product of these 4 factors(not composite) is 30. How many such nos. are possible?
5^7*2*3 => 3 cases
5^3*2^3*3=> 3 cases

total, 6 ?
14610
@gs4890 said:
5^7*2*3 => 3 cases
5^3*2^3*3=> 3 cases

total, 6 ?
6 is Correct Sir
14611
@sunnychopra89 said:
1st 126 natural nos. are put side by side in ascending order to form a large no. 123456......125126. What will be the remainder when it is divided by 5625?
5625=75*75=625*9

123456.....126 mod 6256
5126 mod 625=126

N mod 9
till 99 sum of digits will b divisible by 9

1*27=100th digit=27 mod 9=0
tens digit=1*10+2*7=24 mod 9=6
unit digit=2(0+1+2+...+9)+0+1+2+3+4+5+6 mod 9=3

9 mod 9=0

625a+126=9b

a=0

Hence 126


14612
@sunnychopra89 said:
1st 126 natural nos. are put side by side in ascending order to form a large no. 123456......125126. What will be the remainder when it is divided by 5625?
5625 = 125*5*9

Divide numerator, u'll get following results -

125K+1
5K+1
9K

thus, 126 ?
14613

In how many ways can 12 balls be divided among 3 people such each can get a max of 6 balls . Let me know how to take care of this max condition ?

14614

70 cows can graze on a field for 24 days and 30 cows can graze on the same field for 60 days.

Some grass is there when the cows start grazing and grass grows subsequently at a fixed rate.
How many cows can graze on the field for 96 days?

14615
@bs0409 said:
In how many ways can 12 balls be divided among 3 people such each can get a max of 6 balls . Let me know how to take care of this max condition ?
a+b+c + K = 12

Total ways possible without any conditions attached => 15c3

Now, each gets max of 6 balls

a+7+b+c+ K = 12

Total ways not possible => 8c3*3

Thus, 15c3-8c3*3 ?

14616
@bs0409 said:
In how many ways can 12 balls be divided among 3 people such each can get a max of 6 balls . Let me know how to take care of this max condition ?
14C2 - 3* 7C2 ??

@gs4890 bhai kaise ho??
14617
@Abhishek9891 said:
70 cows can graze on a field for 24 days and 30 cows can graze on the same field for 60 days.Some grass is there when the cows start grazing and grass grows subsequently at a fixed rate.How many cows can graze on the field for 96 days?

70*24=A+24x
30*60=A+60x

36x=1800-1680
36x=120
x=10/3

A=1800-200=1600

A+96x=Y*96
(1600+96*10/3)/96=Y
1600/96+10/3
20=Y
14618

P and Q are 2 distinct whole nos. and P+1, P+2....P+7 are integral multiples of Q+1, Q+2....Q+7 respectivly. What is the min value of P?

14619
@sunnychopra89 said:
P and Q are 2 distinct whole nos. and P+1, P+2....P+7 are integral multiples of Q+1, Q+2....Q+7 respectivly. What is the min value of P?
can i have d options..:P
14620
@sunnychopra89 said:
P and Q are 2 distinct whole nos. and P+1, P+2....P+7 are integral multiples of Q+1, Q+2....Q+7 respectivly. What is the min value of P?
take the lcm of 1,2 ,3, 4,5,6,7 ie 420
14621
@gs4890 said:
a+b+c + K = 12Total ways possible without any conditions attached => 15c3Now, each gets max of 6 ballsa+7+b+c+ K = 12Total ways not possible => 8c3*3Thus, 15c3-8c3*3 ?
variable 'K' kyu liya?

Dummy variable to tab lete the na wen all the items may not be distributed, yaha to all 12 are getting distributed na?

ya toh mai sab bhul gaya
14622
@vikky312 said:
variable 'K' kyu liya?Dummy variable to tab lete the na wen all the items may not be distributed, yaha to all 12 are getting distributed na?ya toh mai sab bhul gaya
u r right i think. mein bhi bhul gaya sab