Official Quant thread for CAT 2013

@raopradeep said:
i think oa is 74 -8 =64because all the odd terms and multiples of 4 can be expressed as difference of squares odd terms excluding 1 = 49 multiples of 4 = 2549+25 =74 - ( multiples of 12 coz they repeated )74-8 =66plz tell if iam right or wrong in appproach..
no... not repeated coz odd no. doesn include odd mutiples of 4.. wrong..
n such 74 be unique only ; since u can write a no.^2 as a differnc of 2 no.^2 only in 1 way ;

reason.. a^2 will need certain b^2 to form c^2..
if u add sum x^2 to a^2 it wont yield a perfect square ; these no. r unique..

for eg ;
3 , 4 ,5
5,12,13
7,24,25
8,15,17
9,40,41.. n so on...
now we r luking for jus the 1st 2terms here, did a single one repeat?? no... 5^2= 3^2 + 4^2 , 5^2=13^2-12^2 , but in 1st case its not a differnc but a sum.. we r tokin of differnc here, not sum..
that be unque..

@IIM-A2013 said:
x = sqrt(4+ sqrt(4 -sqrt(4 + sqrt(4 - sqrt(4 ......... to infinitythan x equals to ??
@IIM-A2013 said:
x = sqrt(4+ sqrt(4 -sqrt(4 + sqrt(4 - sqrt(4 ......... to infinitythan x equals to ??
+-2
@IIM-A2013 said:
x = sqrt(4+ sqrt(4 -sqrt(4 + sqrt(4 - sqrt(4 ......... to infinity

than x equals to ??
a 3 b (13^1/2 - 1)/2 c (13^1/2 + 1)/2 d 13^1/2
@dragster a 3 b (13^1/2 -1 )/2 c (13^1/2 + 1)/2 d 13^1/2

[x] denotes the greatest integer value just below x

{x} denotes the fraction value
Sum of [x]^3 and {x}^2 = -7.91; Find x ?

a.) -2.03
b.) -1.97
c.) -2.97
d.) -1.7

Please tell the approach !
@IIM-A2013 said:
x = sqrt(4+ sqrt(4 -sqrt(4 + sqrt(4 - sqrt(4 ......... to infinitythan x equals to ??

x=sqrt{4+sqrt(4-x)}
sqrng bth sides
x^2={4+sqrt (4-x)}
x^2-4=sqrt(4-x)
(x+2)(x-2)=sqrt{(2+x)(2-x)}
sqrt(x+2) * sqrt(x-2)=-1
sqrt(x+2)=-1/sqrt(x-2)
sqrng bth sides
x+2=1/x-2
x^2-4=1
x^2=5
x=+-sqrt(5)
@ananyboss said:
[x] denotes the greatest integer value just below x{x} denotes the fraction value Sum of [x]^3 and {x}^2 = -7.91; Find x ?a.) -2.03b.) -1.97c.) -2.97d.) -1.7Please tell the approach !
-2.3 ?
@dragster said:
no... not repeated coz odd no. doesn include odd mutiples of 4.. wrong..n such 74 be unique only ; since u can write a no.^2 as a differnc of 2 no.^2 only in 1 way ;reason.. a^2 will need certain b^2 to form c^2..if u add sum x^2 to a^2 it wont yield a perfect square ; these no. r unique..for eg ;3 , 4 ,5 5,12,137,24,258,15,179,40,41.. n so on...now we r luking for jus the 1st 2terms here, did a single one repeat?? no... 5^2= 3^2 + 4^2 , 5^2=13^2-12^2 , but in 1st case its not a differnc but a sum.. we r tokin of differnc here, not sum..that be unque..
i am trying to say what about numbers 12 , 24 , 36......96 ..
which got repeated

@ishu1991
a 3 b (13^1/2 - 1)/2 c (13^1/2 + 1)/2 d 13^1/2
this are options
@dragster said:
no... not repeated coz odd no. doesn include odd mutiples of 4.. wrong..n such 74 be unique only ; since u can write a no.^2 as a differnc of 2 no.^2 only in 1 way ;reason.. a^2 will need certain b^2 to form c^2..if u add sum x^2 to a^2 it wont yield a perfect square ; these no. r unique..for eg ;3 , 4 ,5 5,12,137,24,258,15,179,40,41.. n so on...now we r luking for jus the 1st 2terms here, did a single one repeat?? no... 5^2= 3^2 + 4^2 , 5^2=13^2-12^2 , but in 1st case its not a differnc but a sum.. we r tokin of differnc here, not sum..that be unque..
9^2 = 41^2 - 40^2
9^2 = 15^2 - 12^2

15^2 = 17^2 - 8^2
15^2 = 25^2 - 20^2

.... and there are more which are not unique
@ananyboss -2.03
@ananyboss -2.03
@ananyboss said:
[x] denotes the greatest integer value just below x
{x} denotes the fraction value
Sum of [x]^3 and {x}^2 = -7.91; Find x ?

a.) -2.03
b.) -1.97
c.) -2.97
d.) -1.7

Please tell the approach !
a) -2.03
@viewpt said:
Q: 12345.......3693/9, R?
if this ends in 3693...then it should be 3693*3694/2 mod 9 = 6...
@ananyboss said:
[x] denotes the greatest integer value just below x{x} denotes the fraction value Sum of [x]^3 and {x}^2 = -7.91; Find x ?a.) -2.03b.) -1.97c.) -2.97d.) -1.7Please tell the approach !
[x]^3 has to be -ve (as we are getting a -ve sum...
{x}^2 is always +ve no matter what..
also [x]^3 > 7 (as a +ve number is getting added to it and still the sum remains > 7)
so option b and d are discarded...
now, (-2)^3 = -8
-8+{x}^2 = -7.91
{x}^2 = 0.09
{x} = +/- 0.3
hence x = -2.3

are the option correct?? 2.03 ki jagaah 2.3 hona chaie (in option a)
we can backtrack too -> (-2)^3 + (.3)^2 = -7.91
so i guess it should be -2.3 only...
@techgeek2050 said:
9^2 = 41^2 - 40^29^2 = 15^2 - 12^215^2 = 17^2 - 8^215^2 = 25^2 - 20^2.... and there are more which are not unique
provide sum insight bro..

No of solutions for x+y+z = 60 if xyz are (i)natural numbers and (ii)whole numbers .post the approach in solving these kind of questions ...

@IIM-A2013 said:
@dragster a 3 b (13^1/2 -1 )/2 c (13^1/2 + 1)/2 d 13^1/2
b=>
root 13= 3.6 aprox -1 = 2.6/2=1.3
c=2.3
so must be c..
what's the OA?
@dragster said:
provide sum insight bro..
what i mean to say is that all although all odd numbers can be expressed as a difference of 2 squares, only primes can be expressed uniquely.
@techgeek2050 said:
what i mean to say is that all although all odd numbers can be expressed as a difference of 2 squares, only primes can be expressed uniquely.
seems true , but never read about "unique" concept..