Official Quant thread for CAT 2013

MBA CAT 2024
22907
@saurav205 said:
Question :a,b and c are positive integers such that a+b+c = 2003Let E = (-1)^a + (-1)^b + (-1)^c. Find the number of possible values of E.2004310032
2 ? ( -3 and 1 )
22908
@saurav205 said:
Question :a,b and c are positive integers such that a+b+c = 2003Let E = (-1)^a + (-1)^b + (-1)^c. Find the number of possible values of E.2004310032
2003 is odd
combinations = odd+odd+odd
or
even +odd +odd
so when all odd
E = -3
when 1 even and 2 odds
E = -1
22909
@saurav205 said:
Question :a,b and c are positive integers such that a+b+c = 2003Let E = (-1)^a + (-1)^b + (-1)^c. Find the number of possible values of E.2004310032
Only 2 possibilities. Either a,b,c are all odds or two of them are even and one odd.

Team BV
22910
@saurav205 said:
@ScareCrow28@Subhashdec2@bodhi_vriksha and others ..Next question :The last digit of the LCM of (3^2003 - 1) and (3^2003 + 1) is :8246
4 ?

last digit of 3^2003 + 1 = 8
last digit of 3^2003 - 1 = 6
LCM(8,6) = 24
last digit = 4..
22911
@saurav205 said:
Question :a,b and c are positive integers such that a+b+c = 2003Let E = (-1)^a + (-1)^b + (-1)^c. Find the number of possible values of E.2004310032
2 ?

odd odd odd ---> E = -3
odd even even ---> E = 1
22912
@saurav205 said:
2003 is oddcombinations = odd+odd+oddor even +odd +oddso when all odd E = -3when 1 even and 2 odds E = -1


Edited my post :
1 odd + 2 evens
hence +1 and -3 are the two possibilities..

22913
@saurav205 said:
@ScareCrow28@Subhashdec2@bodhi_vriksha and others ..Next question :The last digit of the LCM of (3^2003 - 1) and (3^2003 + 1) is :8246
4 by any chance.??
22914

A question from my side now:

I write all natural numbers starting from one except the ones whose any digit is prime. First 10 numbers that I write are; 1, 4, 6, 8, 9, 10, 11, 14, 16, 18.

What will be the 100th number that I write?

Team BV

22915
@bodhi_vriksha said:
A question from my side now:I write all natural numbers starting from one except the ones whose any digit is prime. First 10 numbers that I write are; 1, 4, 6, 8, 9, 10, 11, 14, 16, 18.What will be the 100th number that I write?Team BV
488??
22916
@bodhi_vriksha : suppose : if the number is 110 ?? then will be considered or not
22917
@bodhi_vriksha said:
A question from my side now:I write all natural numbers starting from one except the ones whose any digit is prime. First 10 numbers that I write are; 1, 4, 6, 8, 9, 10, 11, 14, 16, 18.What will be the 100th number that I write?Team BV
488 ??
1s --> 5
10s --> 6
40s --> 6
60s --> 6
80s--> 6
90s --> 6
5 + 6x = 100
x = 15.xx
And so on.. Till 479 there are 95 numbers..Hence 100th number = 488 ..
22918
@Logrhythm
@bodhi_vriksha :

i am getting 64X
22919
@bodhi_vriksha said:

A question from my side now:

I write all natural numbers starting from one except the ones whose any digit is prime. First 10 numbers that I write are; 1, 4, 6, 8, 9, 10, 11, 14, 16, 18.

What will be the 100th number that I write?

Team BV

214 ??
22920
@Dexian said:
214 ??
2 is prime
22921
@ScareCrow28 said:
2 is prime
poor me...
sorry bro sab bhul gya humm main...
22922
@ziddiarmaan see, the digits in use here are 0,1,4,6,8 and 9

6 digits, so count in base 6...

100 in base 6 = 244

hence, here = 488...
22923

haan 488....

@ScareCrow28 ..

u r right sir jee

22924
@bodhi_vriksha said:
A question from my side now:I write all natural numbers starting from one except the ones whose any digit is prime. First 10 numbers that I write are; 1, 4, 6, 8, 9, 10, 11, 14, 16, 18.What will be the 100th number that I write?Team BV
0,1,4,6,8,9..
so 100 in base 6 = 244
hence 100th number = 488

courtesy @anytomdickandhary sir..
22925
@Dexian said:
haan 488....@ScareCrow28 ..u r right sir jee
How could I forget the base method! I knew it! @Logrhythm @mailtoankit
22926
@mailtoankit said:
0,1,4,6,8,9..
so 100 in base 6 = 244
hence 100th number = 488

courtesy @anytomdickandhary sir..
ye mast hai....