Official Quant thread for CAT 2013

MBA CAT 2022
1021
@maddy2807 said:
Consider the following equation;x^2 + y^2 + z^2 = (x – y)(y – z)(z – x)Which of the following statement is definitely true? 1) The above equation has no integer solutions for x, y, z. 2) The above equation has finitely many distinct integer solutions for x, y, z. 3) The above equation has 2 distinct integer solutions for x, y, z. 4) The above has infinitely many integer solution for x, y, z.
In demand Q

solving...............
1022
@realslimshady said:
@bullseyes i understand the concept you're using here but in the case of 18 wouldnt i still have to find the 13th factor, which itself is difficult. am i right or am i missing something?
for that you can directly go to middle factor/s, 15/16 here in case...and can move backword..
1023
@maddy2807 said:
Consider the following equation;x^2 + y^2 + z^2 = (x – y)(y – z)(z – x)Which of the following statement is definitely true? 1) The above equation has no integer solutions for x, y, z. 2) The above equation has finitely many distinct integer solutions for x, y, z. 3) The above equation has 2 distinct integer solutions for x, y, z. 4) The above has infinitely many integer solution for x, y, z.
2?
1024
@maddy2807 i tried a lot but i found no solution is its answere no solution ?
1025

try bit more. i will post ans in mrng. n will tag one who ans.

gud nitpuys
1026

when we solve lhs we get

x^2(z-y)+z^2(y-x)+y^2(x-z)
now we place this eaual to x^2+y^2+z^2
now using corresponding ters
z-y=1
y-x=1
x-z=1
which is npt possible nytime so answere is a
what i get
1027
@maddy2807 i gave my method of doing it tell the answere
1028
@sauravd2001 said:
when we solve lhs we getx^2(z-y)+z^2(y-x)+y^2(x-z)now we place this eaual to x^2+y^2+z^2now using corresponding ters z-y=1y-x=1x-z=1which is npt possible nytime so answere is awhat i get
I got the same..stuck here..
@maddy2807 tag me with OA
1029
@abhi_14 said:
A man invests in Cipro an amount of र60000 in र100 shares sold at a premium of 200%. Cipro offers an annual dividend of 50%. After collecting the dividend at the end of a year, he sells 25% of his shares since their market price had appreciated by 331/3%. After another year, he collects his dividend (again 50%) and sells his remaining shares, the price of which again appreciated by 25%. What is his profit (including the total dividend) from these transactions?र1,12,500र52,500र43,750र82,500
P.s - apology for late reply

total investement - 60000

face value of share = 100
market value 200% of 100 = 300
no of shares = 60000/300 = 200
dividend = 50% ( always on face value) = 50
total dividend recieved= 200*50 = 10000 ( no of shares * dividend)
25% shares sold on 33 1/3% = 25% of 200 * 300(1 + 33 1/3) = 50 * 400 = 20000
dividend on remaining shares = 50
so total dividend recieved = 150 * 50 = 7500
noe rest of the shares sold at 25% more price inc = 150 * 500 = 75000

total inflow = 10000 + 20000 + 7500 + 75000 = 112500
profit = 112500 - 60000 = 52500/-
1030
@maddy2807 said:
Consider the following equation;x^2 + y^2 + z^2 = (x – y)(y – z)(z – x)Which of the following statement is definitely true? 1) The above equation has no integer solutions for x, y, z. 2) The above equation has finitely many distinct integer solutions for x, y, z. 3) The above equation has 2 distinct integer solutions for x, y, z. 4) The above has infinitely many integer solution for x, y, z.
option 2 and 4 me se ....

1031
@realslimshady said:
@bullseyes i understand the concept you're using here but in the case of 18 wouldnt i still have to find the 13th factor, which itself is difficult. am i right or am i missing something?
here u can look for he middle factor. which will be square root of the number
1032
@maddy2807 said:
Consider the following equation;x^2 + y^2 + z^2 = (x – y)(y – z)(z – x)Which of the following statement is definitely true? 1) The above equation has no integer solutions for x, y, z. 2) The above equation has finitely many distinct integer solutions for x, y, z. 3) The above equation has 2 distinct integer solutions for x, y, z. 4) The above has infinitely many integer solution for x, y, z.
it should be 4.


1033
@maddy2807 said:
Consider the following equation;x^2 + y^2 + z^2 = (x – y)(y – z)(z – x)Which of the following statement is definitely true? 1) The above equation has no integer solutions for x, y, z. 2) The above equation has finitely many distinct integer solutions for x, y, z. 3) The above equation has 2 distinct integer solutions for x, y, z. 4) The above has infinitely many integer solution for x, y, z.
getting the answer as option a using the same method as used by @sauravd2001
1034
In a right angled triangle ABC, c represents the hypotenuse satisfying c > 2 units. Then find the range in which the following value lies "log(a + b) c + logc (a + b)"?

Edited : (a+b) & c is in base

Options :
(1.5,2.1)
(3.1, 3.5)
(2.2,2.7)
(1.9,2.1)
1035
Find the remainder when 432104321043210. . . . . . (upto 3000 digits) is divided by 9999.?
1036
@bullseyes said:
Find the remainder when 432104321043210. . . . . . (upto 3000 digits) is divided by 9999.?
For divisibility by 9999: group into 4 digit numbers and add them and the sum should be divisible by 9999.

Group the given number into 4 digits and add
R[(4321 + 0432 + 1043 + 2104 + 3210) * 150]/9999
=> R[(11110) * 150]/9999
=> R[1111 * 150]/9999
=> R[166650]/9999
=> 6666 (Answer)
1037
@maddy2807 said:
Consider the following equation;x^2 + y^2 + z^2 = (x – y)(y – z)(z – x)Which of the following statement is definitely true? 1) The above equation has no integer solutions for x, y, z. 2) The above equation has finitely many distinct integer solutions for x, y, z. 3) The above equation has 2 distinct integer solutions for x, y, z. 4) The above has infinitely many integer solution for x, y, z.
0, 0, 0=1 solution
0, 1, -1=3 solutions
=> a total number of 4 Integer Solutions.
=> option (b)
1038
@bullseyes said:
In a right angled triangle ABC, c represents the hypotenuse satisfying c > 2 units. Then find the range in which the following value lies "log(a + b) c + logc (a + b)"?
log(a + b) c + logc (a + b)
= [log {(a+b) }^2+ {log c ^2}]/{log(a+b) * log c}

please provide options
1039
@bullseyes said:
Find the remainder when 432104321043210. . . . . . (upto 3000 digits) is divided by 9999.?
since 9999= 10^4-1
add no.s in group of 4 [4321+0432+1043+2104+3210+ 4321...................... 750 no.s ]
so, sum = 150*(11110)
Remainder = 150*(11110) % 9999
= 1111 * [1500/9]
= 1111*3* [500 mod 3]
= 6666
1040
Q> While adding all the page numbers of a book, I found the sum to be 1000. But then I realized that two page numbers (not necessarily consecutive) have not been counted. How many different pairs of two page numbers can be there?