Official Quant thread for CAT 2013

MBA CAT 2024
8421
@soham2208 said:
No, the relation between the present day's work and the previous day's work is given. Applicable to any day starting from 2nd
Okie... I was reading that statement from a different perspective... And marked CBD... 😁 I took that relationship not as a general one....
8422
@jain4444 said:
Find the value of tanx+cotx if tanx^4+cotx^4=194
was trying this for 10 odd minutes in some other method in vain
But,binomial theorem helped !

(tanx+cotx)^4 =tanx^4+4*tanx^2+6+4cotx^2+cotx^4 =200+{[(tanx+cox)^2-2}
Taking tanx+cotx=p
p^4+200+4z^2-8
p^4-4p^2-192=0
t^2-4t-192=0 =>t=16
p=4
tanx+cotx=4


A number when divided by a certain divisor leaves a remainder of 11,whereas the square of the number when divided by the same divisor,leaves a remainder of 1 .Find how many such divisors are possible
a)2
b)4
c)8
d)16
8423
@Budokai001 said:

A number when divided by 1 certain divisor leaves 1 remainder of 11,whereas the square of the number when divided by the same divisor,leaves a remainder of 1 .Find how many such divisors are possiblea)2b)4c)8d)16
I didnt understand the statement : "divided by 1 certain divisor leaves 1 remainder of 11, ". Thoda explain karo.... :)
8424
@Budokai001 said:

A number when divided by 1 certain divisor leaves 1 remainder of 11,whereas the square of the number when divided by the same divisor,leaves a remainder of 1 .Find how many such divisors are possiblea)2b)4c)8d)16
11^2 - 1 = 120 mod x = 0

x > 11

x = factors of 120 that are greater than 11

12, 15, 20, 24, 30, 40, 60, 120

8 divisors possible


8425

For how many integral values of n is sqrt{ (4(n-3))//(n-48) } a positive integer ?

a)1
b)3
c)4
d)6

8426
@Budokai001 said:
For how many integral values of n is sqrt{ (4(n-3))//(n-48) } a positive integer ?a)1b)3c)4d)6
1??
8427
@rushikesh90 said:
1??
No buddy ...
8428
@Budokai001 said:
For how many integral values of n is sqrt{ (4(n-3))//(n-48) } a positive integer ?a)1b)3c)4d)6
4(n-3)/(n-48) = k^2 , where k is an integer

4*(n-3)/(n-48) = 4 + 180/(n-48) = A

(n-48) must divide 180 for the whole thing to be an integer, and also the final result should be a perfect square

(n-48) = +/- 1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Values for which A is a perfect square => (n-48) = 3, 4, 15, 36, -45, -60

=> 6 values ?
8429
@soham2208 said:
4(n-3)/(n-48) = k^2 , where k is an integer4*(n-3)/(n-48) = 4 + 180/(n-48) = A(n-48) must divide 180 for the whole thing to be an integer, and also the final result should be a perfect square(n-48) = +/- 1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180Values for which A is a perfect square => (n-48) = 3, 4, 15, 36, -45, -60 => 6 values ?
I also got a similar thing (longer and more painful approach)...but if we put -45 we get 0 which is not a "positive integer" as the question requires....hence getting 5 values. What am I missing?

regards
scrabbler
8430
@karl both circles will touch at same point?

8431
@soham2208 said:
4(n-3)/(n-48) = k^2 , where k is an integer4*(n-3)/(n-48) = 4 + 180/(n-48) = A(n-48) must divide 180 for the whole thing to be an integer, and also the final result should be a perfect square(n-48) = +/- 1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180Values for which A is a perfect square => (n-48) = 3, 4, 15, 36, -45, -60 => 6 values ?
yarr ye 180 kiase aaya ..explain
8432
@jaiswalicsi said:
@karl both circles will touch at same point?
Yes, that is given in the question.
8433
@karl can u elaborate how length of perpendicular is calculated becoz m getng
1/2 base *height=area so 1/2*16*p=40rt2 so p=5rt2.
?.. help plz
8434
@rushikesh90 said:
yarr ye 180 kiase aaya ..explain
This is how i did bro.. Same approach till 4 + 180/(n-48) = Perfect Square
perfect squares are 0,1,4,9,16,25,36,49,64,81,100(can stop at 100 as 100>180/2)

perfect square-4 -4,-3,0,5,12,21,32,45,60,77
i.e 180/n-48 = -4,-3,0,5,12,21,32,45,60,77

Factors of 180 are -4,-3,5,12,45,60
n can be +ve or -ve so all the above 6 values contribute to ans ..so 6

8435
@scrabbler said:
I also got a similar thing (longer and more painful approach)...but if we put -45 we get 0 which is not a "positive integer" as the question requires....hence getting 5 values. What am I missing?regardsscrabbler
Yah, didn't see the positive integer thing, so it should be 5 I guess 😃
8436

@htomar said:
2sqrt(89)/3BC = 1812 -x + 2y + 10 -x = 18x - y = 2=> BD = 10taking cosines of angle B for two triangles ABD and ABCcosB = 12^2 + 18^2 - 10^2 / 2*12*18 = 12^2 + 10^2 - AD^2/ 2*12*10 solving the equation we get AD = 2sqrt(89)/3
@jaiswalicsi Ye post dekh lo, attach bhi kiya hai @htomar sir ne. Page no 428 Reply no #8556
8437
@Budokai001 said:
was trying this for 10 odd minutes in some other method in vain But,binomial theorem helped !(tanx+cotx)^4 =tanx^4+4*tanx^2+6+4cotx^2+cotx^4 =200+{[(tanx+cox)^2-2}Taking tanx+cotx=pp^4+200+4z^2-8p^4-4p^2-192=0t^2-4t-192=0 =>t=16p=4tanx+cotx=4A number when divided by a certain divisor leaves a remainder of 11,whereas the square of the number when divided by the same divisor,leaves a remainder of 1 .Find how many such divisors are possiblea)2b)4c)8d)16
N=DK1+11; D>11--------1
N^2=D^2k1^2+22dK1+121
N^2 mod D=1=D^2k1^2+22dK1+121 mod D
121modD=1; 121=DK3+1; DK3=120, D=Factors of 120 greater than 11---from 1
D={12, 15, 20, 24, 30, 40, 60, 120} 8 values.
8438
a company manufactures a car by spending some .this car is sold to to the showroom at 20% profit.this showroom sells it to ramu,a customer by making 15% profit.after a year,ramu sells the car to a second hand dealer at 30% loss who in turn sells it to another customer shamu at 5% profit margin for rupees 1,01,430.how much does the company spend for manufacturing the car?
8439
@Brooklyn said:
a company manufactures a car by spending some .this car is sold to to the showroom at 20% profit.this showroom sells it to ramu,a customer by making 15% profit.after a year,ramu sells the car to a second hand dealer at 30% loss who in turn sells it to another customer shamu at 5% profit margin for rupees 1,01,430.how much does the company spend for manufacturing the car?
1 lakh?
100 x be manufacturing cost
120x*1.15*.7*1.05=101430
100x=100000
8440
@Brooklyn said:
a company manufactures a car by spending some .this car is sold to to the showroom at 20% profit.this showroom sells it to ramu,a customer by making 15% profit.after a year,ramu sells the car to a second hand dealer at 30% loss who in turn sells it to another customer shamu at 5% profit margin for rupees 1,01,430.how much does the company spend for manufacturing the car?
100000?