Official Quant thread for CAT 2013

MBA CAT 2024
20886
@hanushanand said:
OA = 5 ?as per Question - abc*uv = cab*vu=> [100a+10b+c] [10u+v] = [100c+10b+a] [10v+u]=> 111 [au-cv] = 10 [v(b-a) + u(c-b)] --------- (1)From (1), We have - [au-cv] must be a factor of 10 i.e 0 & 10. ----- (2)from (2)for 0,=> b = (av - cu)/(v - u) ------ (3)for 10,=> b = (111+av-cu)/(v-u) ------------- (4)Now, since b -> [0,9]=> bfor 0,=> (9-a)*v >= (9-c)*uWill Do!!for 10,=> (9-a)*v - (9-c)*u >= 111Not Feasible!! and from (2), we have - v-u > 0 => v>u ----- (5)Taking values for (3), we have -[au-cv=0]a*u - c*v, v-u, a*v-c*u, b9*5 - 5*9, 4 , 56, 149*2 - 2*9, 7, 77, 118*5 - 5*8, 3, 39, 138*2 - 2*8, 6, 60, 107*5 - 5*7, 2, 24, 127*2 - 2*7, 5, 45, 96*5 - 5*6, 1, 15, 156*2 - 2*6, 4, 32, 85*2 - 2*5, 3, 21, 74*2 - 2*4, 2, 12, 63*2 - 2*3, 1, 5, 5@koyal1990 Please verify the answer, I may be wrong as it is 4:30 in the morning!!
bhai check #21174 (my post)...i am getting 36 pairs...

@koyal1990 - u were talking abt this ques?? ye toh 36 aa rahe hai mere... 😞
20887
@Logrhythm : Could you explain the answer with more steps???
20888

@sc

@scrabbler said:
That is if x, y, z all positive. Clearly can't be the case here... But aage I have no idea what to do. Algebra regardsscrabbler
Yeh waala solve kiya????
20889

Values of a forwhich roots of eq : x^2 -6ax +2 -2a +9a^2 =0 are greater than 3


No of integral sols (x,y) for eq (x-5)*(x-23) =3^y

20890
@amresh_maverick said:
Values of a forwhich roots of eq : x^2 -6ax +2 -2a +9a^2 =0 are greater than 3No of integral sols (x,y) for eq (x-5)*(x-23) =3^y
OA :

1> a >(11/9)
2> 2 solns
20891

For what real no C does the eq |x^2 + 12x +34| =C has exactly 3 roots ?


How many integral sols exist for 8s - 5t=221 such that s*t

20892

Hi all,

Please provide the solution of below question.

The sum of three consecutive even integers

is 132. Find the difference between

3 times the least and half of the greatest.

1) 44 2) 89

3) 144 4) 103

20893
in an election , 2 candidates contested a presidential election . 15% of the voters did not vote and 41 votes were invalid. the elected contestant got 314 votes more than the other candidate. if elected candidate got 45% of the total eligible votes, the individual votes of each candidate are ?
20894
@amanaspirant said:
Hi all,Please provide the solution of below question.The sum of three consecutive even integersis 132. Find the difference between3 times the least and half of the greatest.1) 44 2) 893) 144 4) 103
(x - 2) + x + (x + 2) = 132
=> x = 44

42*3 - 23 = 103
20895

thanks jain

20896

thanks jain

20897

If the square of a number of two digits is

subtracted from the square of the number

formed by interchanging the digits, the

largest number by which the result is always

divisible is

1) 9 2) 10

3) 11 4) 99
20898
@jain4444 said:
in an election , 2 candidates contested a presidential election . 15% of the voters did not vote and 41 votes were invalid. the elected contestant got 314 votes more than the other candidate. if elected candidate got 45% of the total eligible votes, the individual votes of each candidate are ?
total votes = V
Effective votes = V-0.15V-41 = 0.85V-41
since the winner won by 314 votes => 45%V-157 will be the break-even value

=>2*(45%V-157) = 0.85V-41
=>0.9V - 314 = 0.85V-41
=>V = 5460

hence individual votes = 0.45*5460 = 2457 and 2457-314=2143

ATDH.

20899
@amanaspirant said:
If the square of a number of two digits issubtracted from the square of the numberformed by interchanging the digits, thelargest number by which the result is alwaysdivisible is1) 9 2) 103) 11 4) 99
99?
20900
@amresh_maverick said:
For what real no C does the eq |x^2 + 12x +34| =C has exactly 3 roots ?How many integral sols exist for 8s - 5t=221 such that s*t
1. C = |(-12/2)^2 + 12*(-12/2) + 34| = |36 -72 +34| = 2

2. 8s = 221+5t for t=7 we get 8s = 256 => s = 32

hence general solution s = 5k+32 and t = 8k+7 where k is an integer

we want s*t
=>(5k+ 32)(8k+7)
=> (-32/5)
hence -6,-5,-4,-3,-2,-1 are the possible values of k

hence 6 integral solutions.

ATDH.

20901
@amresh_maverick said:
sir , plz explain thissince the winner won by 314 votes => 45%V-157 will be the break-even value=>2*(45%V-157) = 0.85V-41
here is a simple example to illustrate.

say winner won by a margin of 10 votes this means that if 5 (i.e 10/2=5) people voted for loser instead of the winner then votes of winner and loser will be equal.

ATDH.

20902
@amanaspirant said:
If the square of a number of two digits issubtracted from the square of the numberformed by interchanging the digits, thelargest number by which the result is alwaysdivisible is1) 9 2) 103) 11 4) 99
99 ?
20903
@amanaspirant said:
If the square of a number of two digits issubtracted from the square of the numberformed by interchanging the digits, thelargest number by which the result is alwaysdivisible is1) 9 2) 103) 11 4) 99
2 digit willbe of the form 10a+b ..
(10a + b)^2-(10b+a)^2 = 100a^2-a^2 -100b^2 + b^2
99(a^2-b^2) ...

so it'll always be divisible by 99.
20904
@amanaspirant said:
Hi all,Please provide the solution of below question.The sum of three consecutive even integersis 132. Find the difference between3 times the least and half of the greatest.1) 44 2) 893) 144 4) 103
even integers are of the form 2n
so consecutive numbers will be... 2n , 2n+2,2n+4
2n+2n+2+2n+4=132
n=21

so, numbers are .. 42, 44,46..
42*3-46/2=103
20905
@amanaspirant said:
If the square of a number of two digits issubtracted from the square of the numberformed by interchanging the digits, thelargest number by which the result is alwaysdivisible is1) 9 2) 103) 11 4) 99
99 it is..!