Official Quant thread for CAT 2013

kingsleyx · November 21, 2012, 3:38pm

@shadowwarrior said:
let the number be aX...so:(10^n)+X = 57X ==> 10^n=56X....is this even possible...?@gautam22 i am no sir dude.....calling that makes me feel old(which I am not)

It should be a(10^n)+X = 57X ==> a * 10^n=56X , so a should be divisible by 7. answer is 7125 I guess .
@insane.vodka

krum · November 21, 2012, 3:44pm

@kingsleyx said:
Sum of five real numbers is 7.: the sum of their squares is 10. Find the minimum, max possible values of any one of the numbers !!

min 1
when a=b=c=d=1.5 , e=1

sujamait · November 21, 2012, 3:48pm

Let S be a set with six elements. In how many different ways can one select two subset of S, not necessarily disjoint, so that union of these two subset is S? Assume the order of selection does not matter. For example, pair of subset {a, c} and {b, c, d, e, f} represent the same selection as pair as {b, c, d, e, f} and {a, c}.
OPTIONS

1) 365
2) 64
3) 63
4) 128

ofc

krum · November 21, 2012, 3:57pm

@sujamait said:
Let S be a set with six elements. In how many different ways can one select two subset of S, not necessarily disjoint, so that union of these two subset is S? Assume the order of selection does not matter. For example, pair of subset {a, c} and {b, c, d, e, f} represent the same selection as pair as {b, c, d, e, f} and {a, c}.OPTIONS1) 365 2) 64 3) 63 4) 128 ofc

6c1*2+6c2*2^2+6c3*2^3+6c4*2^4+6c5*2^5+6c6*2^6
=12+60+160+240+192+64
=728

728/2=364

365?

rubikmath · November 21, 2012, 4:00pm

@sujamait said:
Let S be a set with six elements. In how many different ways can one select two subset of S, not necessarily disjoint, so that union of these two subset is S? Assume the order of selection does not matter. For example, pair of subset {a, c} and {b, c, d, e, f} represent the same selection as pair as {b, c, d, e, f} and {a, c}.OPTIONS1) 365 2) 64 3) 63 4) 128 ofc

1.365 ??

angadbir · November 21, 2012, 4:02pm

@sujamait said:
Let S be a set with six elements. In how many different ways can one select two subset of S, not necessarily disjoint, so that union of these two subset is S? Assume the order of selection does not matter. For example, pair of subset {a, c} and {b, c, d, e, f} represent the same selection as pair as {b, c, d, e, f} and {a, c}.OPTIONS1) 365 2) 64 3) 63 4) 128 ofc

U still in ofc????

Hadtal kardo yaar.

Each element has 3 options
Go to 1st subset
Go to 2nd subset
Go to both subsets

So total ways = (3^6-1)/2 + 1 = 365

sujamait · November 21, 2012, 4:07pm

@krum said:
6c1*2+6c2*2^2+6c3*2^3+6c4*2^4+6c5*2^5+6c6*2^6=12+60+160+240+192+64=728728/2=364365?

@Angadbir said:
U still in ofc???? Hadtal kardo yaar.Each element has 3 optionsGo to 1st subsetGo to 2nd subsetGo to both subsetsSo total ways = (3^6-1)/2 + 1 = 365

neah not now..!!

Yup! easy one!

pavimai · November 21, 2012, 4:48pm

the digits of a 3-digit number in Base 4 get reversed when it is converted into Base 3.how many such digits exist??

rubikmath · November 21, 2012, 4:55pm

@pavimai said:
the digits of a 3-digit number in Base 4 get reversed when it is converted into Base 3.how many such digits exist??

1 ??

anivesh90 · November 21, 2012, 4:56pm

@pavimai said:
the digits of a 3-digit number in Base 4 get reversed when it is converted into Base 3.how many such digits exist??

1?

youll get the following eqn--15x+y=8z

soumitrabengeri · November 21, 2012, 4:57pm

@pavimai said:
the digits of a 3-digit number in Base 4 get reversed when it is converted into Base 3.how many such digits exist??

Should be 1 possible number
If we take the number as xyz in base 4 then

16x+4y+z=x+3y+9z
hence 8z=15x+y

Only x=1 y=1 z=2 satisfies the above equation

soham2208 · November 21, 2012, 4:58pm

@pavimai said:
the digits of a 3-digit number in Base 4 get reversed when it is converted into Base 3.how many such digits exist??

(abc)(base 4) = (cba)(base 3)

=> c + 4b + 16a = a + 3b + 9c

=> b + 15a = 8c

(a,b,c) less than 2

a = 1, b = 1, c = 2

pankaj1988 · November 21, 2012, 4:59pm

@pavimai said:
the digits of a 3-digit number in Base 4 get reversed when it is converted into Base 3.how many such digits exist??

1 no...Number is 112..

realslimshady · November 21, 2012, 5:21pm

find the remainder in the following
a.3^1001/21
b.25^91/15

sorry i dnt have options for any these. help, please 😁

maddy2807 · November 21, 2012, 5:26pm

@realslimshady said:
find the remainder in the following a.3^1001/21 b.25^91/15sorry i dnt have options for any these. help, please

12 and 10

akansh_1 · November 21, 2012, 5:37pm

@realslimshady said:
find the remainder in the following a.3^1001/21 b.25^91/15sorry i dnt have options for any these. help, please

a. 3^1001/21
= 3^1000/7

E(7) = 6
Rem(1000/6) = 4
3^1000/7 = 3^4/7 = 4
Remainder = 4*3 = 12

b. 25^91/15
= 5^181/3

E(3)=2
Rem(181/2) = 1
5^181/3 = 5/3 = 2
Remainder = 5*2 = 10

anivesh90 · November 21, 2012, 5:38pm

@realslimshady said:
find the remainder in the following a.3^1001/21 b.25^91/15sorry i dnt have options for any these. help, please

a.12

b.10

mailtoankit · November 21, 2012, 5:49pm

@realslimshady said:
find the remainder in the following a.3^1001/21 b.25^91/15sorry i dnt have options for any these. help, please

12 and 10

techsurge · November 21, 2012, 5:58pm

@realslimshady said:
find the remainder in the following
a.3^1001/21
b.25^91/15

sorry i dnt have options for any these. help, please

12 and 10

solved both by Euler but removed 3 and 5 from both

vivek_goswami · November 21, 2012, 6:13pm

yaar iska solution post karna :)
In a circle, the height of an arc is 21 cm and the
diameter is 84 cm. Find the chord of 'half of the arc'.
A. 45 cm B. 40 cm
C. 42 cm D. None of the above
Thanks in advance.