Number System - Questions & Discussions

MBA CAT 2022
864
Plz solve this:
if 2x+3y=10 maximise x^5y^6


4x + 6y = 20
4x/5+4x/5+4x/5+4x/5+4x/5+y+y+y+y+y+y = 20

20 >= 11(x^5y^6)1/11 * (4/5)^5/11

x^5y^6 max valve = 2^20.5^12.11^-11
865
Plz solve this:
if 2x+3y=10 maximise x^5y^6



confused about the question..is it (x^5)*(y^6) or x^((5y)^6) or x^(5(y^6))..please use brackets..also anything specified about x and y?..ie whole numbers or natural or integers or real?
866
apologies for the 10^148 thingie......also cud u explain the Euler concept....not familiar with it (commerce background : :)

also am not sure but wont x mod 19 (where x is some number) give a remainder between 0 and 18, while x mod 76 will give a remainder between 0 and 75.....how can i say then that (x/4) mod 19 = x mod 76?

mebbe what i can do is find the remainder of x mod 76 and divide by 4 to get (x/4) mod 19..... just guessing.....in this case that will give me the answer....

x being 5^150-1

x mod 76 = 44

meaning x = 76p +44
or x/4 = 19p + 11 giving a remainder of 11......



See here 5^150 -1 is divisible by 4...Hence remainder by dividing 5^150-1 by 76 will be 4 times of remainder by dividing 5^150-1 by 4 and then 19...

Lets chk with a simple example....
Let x=240 (divisible by 4)
Hence 240/4 = 60...Now 60%19=3

Now chk the other way
240%76 = 12 ( 4 times 3)
867
4x + 6y = 20
4x/5+4x/5+4x/5+4x/5+4x/5+y+y+y+y+y+y = 20

20 >= 11(x^5y^6)1/11 * (4/5)^5/11

x^5y^6 max valve = 2^20.5^12.11^-11


the answer is not correct though thanks, got the concept...

its coming out to be 2^12.5^16.11^-11
868
Plz solve this:
if 2x+3y=10 maximise x^5.y^6




yes the answer is 2^12.5^16.11^-11
869

Solve these----1) S denotes the sum to infinity and Sn denotes the sum to n terms of the series 1 + 4/5 + 16/25 + ...+ If S - Sn

870
jai_praqas Says
Solve these----1) S denotes the sum to infinity and Sn denotes the sum to n terms of the series 1 + 4/5 + 16/25 + ...+ If S - Sn

my take for this is c) 4..
is it correct??
871

Number of solutions of xy/(x+y) = 196. Where x and y are natural numbers.
I think its 13.
if ordered pair then solution is 25.
would like to confirm.

872
jai_praqas Says
Solve these----1) S denotes the sum to infinity and Sn denotes the sum to n terms of the series 1 + 4/5 + 16/25 + ...+ If S - Sn

S-Sn5-(5(1-4/5)^n)5(4/5)^n( .8 )^n<.5>4 ans
873
jai_praqas Says
Solve these----1) S denotes the sum to infinity and Sn denotes the sum to n terms of the series 1 + 4/5 + 16/25 + ...+ If S - Sn

2) is it 1250?
874
SDU221989U Says
Guys pls help me i dont understand how to approach quant section my verbal is good, di is also fine but everytime i switchover to quant,n i feel like im on a war with my small n tiny head....pls help.suggest some good way out


One and only rule of getting hands on Quants is
practice...
More u practice more u get confident...

And PG is great platform for quants practice...
puys gonna help u a lot ... by personal experience
875
Solve these----1) S denotes the sum to infinity and Sn denotes the sum to n terms of the series 1 + 4/5 + 16/25 + ...+ If S - Sn
(2)If the sum of lengths of three sides of a rectangle is 100 units, then find the maximum possible area of the rectangle ? a. 1110.9 b. 1250 c. 990 d. 1008 e. 1225PG seems to have any technical problem


Solution. 1) S=1/(1-4/5) = 5
Sn=5*
S-Sn (4/5)^n For n>=4 S-Sn Thus option c. 4

Solution. 2) Let "a" and "b" be the two side of rectangle
Thus 2a+b=100...(given)
Let "A" be the area of rectangle
Therefore A=a*b
=> A=a*(100-2a)
=> A=100a - 2a^2
To find max area take derivative of "A" w.r.t "a" and equate it to 0.
Thus we get a=25 and b=50
Thus Maximum area= 25*50 =1250 Option.B
876
Solve these----1) S denotes the sum to infinity and Sn denotes the sum to n terms of the series 1 + 4/5 + 16/25 + ...+ If S - Sn


Q1. S = 1/(1-4/5) = 5
Sn = 5
S - Sn 5 - 5 + 5(4/5)^n n = 4
877
jai_praqas Says
(2)If the sum of lengths of three sides of a rectangle is 100 units, then find the maximum possible area of the rectangle ? a. 1110.9 b. 1250 c. 990 d. 1008 e. 1225PG seems to have any technical problem


2a + b = 100
Apply AM >= GM
(2a+b)/2 >= (2ab)^1/2
50^2 >= 2ab
ab
878

oh great puys... i could not get the question yesterday... and the solution is at myhand now... thanks all.


my today's question for u all.


The number of non-negative real roots of 2^x - x - 1 = 0 equals
a) 0
b) 1
c) 2
d) 3
e) 4
i'm attaching a file containing mock that u can practise.....
happy solving.....
IT IS BETTER TO FAIL IN DOING SOMETHING THAN TO EXCEL IN DOING NOTHING.
- M. K. GANDHI

879
oh great puys... i could not get the question yesterday... and the solution is at myhand now... thanks all.


my today's question for u all.


The number of non-negative real roots of 2x x 1 = 0 equals
a) 0
b) 1
c) 2
d) 3
e) 4





i'm attaching a file containing mock that u can practise.....
happy solving.....




IT IS BETTER TO FAIL IN DOING SOMETHING THAN TO EXCEL IN DOING NOTHING.
- M. K. GANDHI

x=1...i guess u have not framed the question correctly
880
Plz solve this:
if 2x+3y=10 maximise x^5.y^6

10/11>= ^1/11
10/11 = ^1/11
hence x^5*y^6 = (10/11)^11 * 6250
881

sorry dear shasahank that was my mistake... i've corrected it now... reattempt it now


my today's question for u all.



The number of non-negative real roots of 2^x - x - 1 = 0 equals
a) 0
b) 1
c) 2
d) 3

e) 4
happy solving.....
IT IS BETTER TO FAIL IN DOING SOMETHING THAN TO EXCEL IN DOING NOTHING.
- M. K. GANDHI

882
sorry dear shasahank that was my mistake... i've corrected it now... reattempt it now


my today's question for u all.



The number of non-negative real roots of 2^x x 1 = 0 equals
a) 0
b) 1
c) 2
d) 3

e) 4
happy solving.....
IT IS BETTER TO FAIL IN DOING SOMETHING THAN TO EXCEL IN DOING NOTHING.
- M. K. GANDHI

Is it 2? x = 0,1.
883
sorry dear shasahank that was my mistake... i've corrected it now... reattempt it now


my today's question for u all.



The number of non-negative real roots of 2^x x 1 = 0 equals
 a) 0
b) 1
c) 2
d) 3
e) 4

it's 2....roots are 0 n 1