Official Quant thread for CAT 2013

MBA CAT 2024
16363
@somnathbhatta said:
ABCD is a trapezium with AD||BC. The diagonals of the trapezium intersect at O such that AO=3 , OC=x-3, DO= x-5, OB=3x-19 . Find the value of x.a)8,9 b)7,8c)8,10d)7,10e)none of thesePS: given answer- option a . i got the answer e . one of the value of x is 8 but the other one wasn't 9. it was 13/3.
Correct Option: a
Explaination:

BOC is similar to DOA

BO/DO = OC/OA

3x-19 / x-5 = x-3 / 3

x^2 - 17x + 72 = 0

x = 8 or x = 9

Solved.
16364
@techgeek2050 said:
73 ?
approach kya hai bhai
16365
@CSK23 said:
Q : If x^2 + y^2 + z^2 = 4 and k = xy + yz + zx then1. k>= -22. k3. k >= -44. k
(x+y+z)^2 >= 0
x^2+y^2+z^2+2(xz+xy+yz) >= 0
4+2(xz+xy+yz) >= 0
(xz+xy+yz) >= -2
option 1....
16366
@techgeek2050 said:
mahn! d explanation ws superb.. but mai short me bhi samajh jata.. what i meant to say was distaking 5^2 out we get 5^2(2^6*3^4) .... the number of factors of this form will be 35. when we take the product of these 35 factors , the power of 5 will be added and since each factor will have 2 powers of 5, the total should be 35x2 = 70.. i hope m clear dis time.
take a smaller case...

product of factors of 25 which are divisible by 5...
25 = 5^2
5(5) = 2
5^2(1) = 1
hence, total power of 5 = 3...

so here when 5^2*5*1 = 5^3

hope it is clear that it does not get twice...
16367
@CSK23 said:
odd no. till 1 to 100 = 50 ;
mutliples of 4= 25 ;
add up , got 75??
16368
@ankittripathi shouldn't the equation AO/BO = DO/OC ? from similar triangles we should get this ri8 ?
16369
@amitranjan2311 said:
How many natural number
it wld be all primes (except 2)
and 4*primes

so 24+9 = 33 such numbers...


By "uniquely" i understand only in one way...
16370
@ankittripathi said:
Correct Option: aExplaination:BOC is similar to DOABO/DO = OC/OA3x-19 / x-5 = x-3 / 3x^2 - 17x + 72 = 0x = 8 or x = 9Solved.
why not BO/OA = OC/OD ??
16371
@CSK23 said:
approach kya hai bhai
sorry bro i calculated for sum and difference both..

16372
@CSK23 said:
any number being a multiple of 2 and an odd number cannot be expressed as a difference of 2 square numbers....
like 2,6,10,.... till 98... 25 numbers... den 1 also cannot be expressed... hence 74 numbers... i am not sure if 0 is a natural number...
if u write x = a^2 - b^2 = (a + b)(a-b)...
now adding both components we get 2a..
so both factors should add to be even,,, either both are odd or both are even... hence....
16373
@dragster said:
odd no. till 1 to 100 = 50 ;mutliples of 4= 25 ;add up , got 75??
bhai kaisa??
@Logrhythm said:
it wld be all primes (except 2) and 4*primes so 24+9 = 33 such numbers...
bhai we can also represent other numbers also na?.. like 8^2 - 6^2 = 28(not prime)
16374
@Logrhythm said:
it wld be all primes (except 2) and 4*primes so 24+9 = 33 such numbers...By "uniquely" i understand only in one way...
33 is neither a prime, nor it is 4*prime number... it can be written as
33 = 11*3
a + b = 11 a - b = 3
so a = 7, b = 4
33 = 7^2 - 4^2
16375
@CSK23 :

its 74 as 2 is not included!! rest approach people already explained in above posts!!
16376
@pratskool said:
any number being a multiple of 2 and an odd number cannot be expressed as a difference of 2 square numbers....like 2,6,10,.... till 98... 25 numbers... den 1 also cannot be expressed... hence 74 numbers... i am not sure if 0 is a natural number...
bhai....i guess thoda galat likh gaye aap..

it is rather that -> all the numbers of the form 4k+2 cannot be expressed as the difference of squares of two natural numbers...

whereas all odd + multiples of 4 can be expressed as a difference of squares of two natural numbers in more than one way...

and all primes(except 2)) + 4*primes can be expressed as a difference of sqaures of natural numberss in exactly one way (uniquely) ....
16377
@Logrhythm said:
bhai....i guess thoda galat likh gaye aap..it is rather that -> all the numbers of the form 4k+2 cannot be expressed as the difference of squares of two natural numbers...whereas all odd + multiples of 4 can be expressed as a difference of squares of two natural numbers in more than one way...and all primes(except 2)) + 4*primes can be expressed as a difference of sqaures of natural numberss in exactly one way (uniquely) ....
ok. i missed uniquely. got ur point now.
16378
@CSK23 :

its 74 as 2 is not included!! rest approach people already explained in above posts!!
16379
@pratskool said:
33 is neither a prime, nor it is 4*prime number... it can be written as 33 = 11*3a + b = 11 a - b = 3so a = 7, b = 433 = 7^2 - 4^2
i meant 33 such total numbers...not 33 as one such number... 😃
16380
@CSK23

Shld be 74 i thnk..

Here, x^2 - y^2 = k..,or, (x+y)(x-y) = k..

Here, a General Observation can be made: 1, 2, 6, 10......98 cannot be expressed as a difference of 2 perfect squares..

Thus, Required Number = 100 - (1, 2, 6, 10.., 98)=> 100 - 26 = 74..

@pratskool Sir ne bahut ache se explain kiya hai isse..Do Refer his Post.. :)
16381
@CSK23 said:
bhai kaisa?? bhai we can also represent other numbers also na?.. like 8^2 - 6^2 = 28(not prime)
bhai as i said...4*prime

28 = 4*7 = 4*prime...
16382
@pratskool said:
any number being a multiple of 2 and an odd number cannot be expressed as a difference of 2 square numbers....like 2,6,10,.... till 98... 25 numbers... den 1 also cannot be expressed... hence 74 numbers... i am not sure if 0 is a natural number...if u write x = a^2 - b^2 = (a + b)(a-b)... now adding both components we get 2a..so both factors should add to be even,,, either both are odd or both are even... hence....
Exact approach...answer is 74!! 0 is not a natural no...!!!