Quant by Arun Sharma

MBA CAT 2022
832
varunj1984 Says
Hi I am unable to solve Arun shrma's Geometry ->Mensuration 2 ->question 38,39,40,.....till end....any explanations...I m unable to solve it.....


please post the full question...it wud be helpful s those who dont have Arun Sharma wudnt b able to solve it widout the question...
833

1.The area of the circle circumscribing 3 circles of unit radius touching each other.
2 Find the area of the triangle inscribed in a circle circumsribed by a square made by joining the midpoints of the adjacent sides ofa square of side a.

some on profit and loss..


1. find the change in the %age profit for a fruit vendor who,after finding 20% of the fruits rotten,increased his selling price by 10% over and above 15% that he was already charging.

834

the answer for the first one

.The area of the circle circumscribing 3 circles of unit radius touching each other.


see in this case make a traingle by joining the centers of the circle
the traingle is an equlilateral one so the height of teh traingle would be

sqrt(3)/2 now the distance between the centroid of the triangle and the unit radius will be the radius of the new circle circumscribing 3 circles of unit radius

R = sqrt(3)/2*2/3 +1 that is
R= (sqrt(3)+1/sqrt(3)) so the area is pi*(sqrt(3)+1/sqrt(3))^2 square units
835
2 Find the area of the triangle inscribed in a circle circumsribed by a square made by joining the midpoints of the adjacent sides ofa square of side a.


the lenght of the outer square is 2a then the area of the traingle would be

3sqrt(3)/8 * a^2
836
1. find the change in the %age profit for a fruit vendor who,after finding 20% of the fruits rotten,increased his selling price by 10% over and above 15% that he was already charging.


the answer for this one is 43.125% ???

i tried using CP and Sp funda only but some how the language of the question is a bit confusing

can u post the answers please
837

Hi shivam ,
Thanks for ur answers ...ya i understood the first geometry question...but could not understand the send geo because language is not clear...its a bit confusing...ya and i also solved the profit loss.....

838

Hi,

I have a small doubt. This is just a part of a question.

What would be the range of x for

log0.4(x-1)


Answer : x lies in [2,infinity)

839
Hi,

I have a small doubt. This is just a part of a question.

What would be the range of x for

log0.4(x-1)


Answer : x lies in [2,infinity)

whenever base oof log is less than 1 then inequality sign changes
log0.4(x-1) can be written as
(x-1)>0.4^0

so (x-1)>1
so x>2 and hencex lies in [2,infinity)
hope i am correct
feel free to revert in case of any queries
840

That's what am not getting... (x-1)>0.4^0 .... shdnt that be x-1

841
setu_sin Says
That's what am not getting... (x-1)>0.4^0 .... shdnt that be x-1

The solution is as follows:-

log(0.4)/log(x-1)
since log(0.4) is negative so log(x-1) has to be positive or equal to zero(Equal to zero...since the whole term would bcom -infinity which is also correct....we can take this into consideration)

So we have
log(x-1) >=0
log(x-1) >=log 1
x-1 >=1
x>=2

Hence the range is [2,infinity)

Thanks
Vivek
842

Guys is there a method to solve polynomial equations ...the way we factorize for quadratic equations... like for an equation :

x^2 + 5x +6 ... we factorize 6 and get 2 and 3 ,thus expanding the eqn as
x^2 + 3x +2x +6....

how would we do it for say ... x^3 -7x^2 +21x -27 =0?

843
Guys is there a method to solve polynomial equations ...the way we factorize for quadratic equations... like for an equation :

x^2 + 5x +6 ... we factorize 6 and get 2 and 3 ,thus expanding the eqn as
x^2 + 3x +2x +6....

how would we do it for say ... x^3 -7x^2 +21x -27 =0?

By either hit or trial u put the values and check the remainder for x=-1,1,-2,2.. so on
when the remainder is 0 then divide the equation by that value

else u can take the roots as a,b,c
where
a+b+c=-coefficient of x^2/coefficient of X^3

ab+bc+ca = coefficient of x/coefficient of X^3

abc = constant term /coefficient of X^3

use these to solve for a,b,c
844

hi here r some questions..though u might say its basic..but still i was unable to do it..plz explain concepts...while solving,,,.Is there some tutorials or concepts section where I can find such concepts...to understand..

1.value of the expression (x^2-x+1)/(x-1) cannot lie between
a) 1,3 b) -1,-3 c) 1,-3 d) -1,3

2.
Sum of the real roots of the equation x^2+5x+6 =0 is

3.If the expression ax^2+bx+c is equal to 4 when x = 0 leaves a remainder 4 when divided by x+1 and a remainder 6 when divided by x+2,than the values of a,b and c are ?

4.
Log(9-2^x)base 2 = 10^log(3-x) solve for x

845

Hi I am total noob with CAT and Quant prep.
So my doubt comes from the first chapter i.e Numbers.
Can anyone explain to me how the remainder of 21^875 / 17 can be found? Using remainder theorom only.
Or in general any division where the Numerator is raised to a large power.

846

@billibite
/17
/17
/17
/17
/17
/17
So,-1.Hence,answer should be 16.Its better to apply remainder theorem for these sums.

847
Hi I am total noob with CAT and Quant prep.
So my doubt comes from the first chapter i.e Numbers.
Can anyone explain to me how the remainder of 21^875 / 17 can be found? Using remainder theorom only.
Or in general any division where the Numerator is raised to a large power.


Hi dude. Would ask you to go through the questions discussed on Number System thread. You will get to learn useful tools to crack these number related problems.

For your question 21^875 / 17=>4^875 / 17

Also, 4^16k = 17x+1. Hence 4^875 / 17 = 4^11/17=4*(-1)^5= 13
So, remainder is 13.
848

Can sum1 help me 2 solve da qn: The sum of series represented as:
1/1*5+ 1/5*9+ 1/9*13 +--- --+1/221*225 is:
options:
a)28/225 b)56/221
c)56/225 d)none of these
thanx in advance

849
Can sum1 help me 2 solve da qn: The sum of series represented as:
1/1*5+ 1/5*9+ 1/9*13 +--- --+1/221*225 is:
options:
a)28/225 b)56/221
c)56/225 d)none of these
thanx in advance

welcome to PG priya

my take::
see u can write the general term as 1/(n*n+4) now in this case
1/4(1/n-1/n+4) now applying values we get
1/4(1-1/5+1/5-1/9.......1/224-1/225)
all the terms will cancel out except
1/4(1-1/225) so the answer is 56/225

am i correct
850
Hi I am total noob with CAT and Quant prep.
So my doubt comes from the first chapter i.e Numbers.
Can anyone explain to me how the remainder of 21^875 / 17 can be found? Using remainder theorom only.
Or in general any division where the Numerator is raised to a large power.

answer to this is 13
21^875 mod 17
4^875 mod 17
(4^2)*odd *4
so (17-1)^odd*4 mod 17 answer is 16*4 mod 17 = 13
So, remainder is 13.

@ shashank check the bold part
@billibite
/17
/17
/17
/17
/17
/17
So,-1.Hence,answer should be 16.Its better to apply remainder theorem for these sums.
851

my take::
answers

1.value of the expression (x^2-x+1)/(x-1) cannot lie between
a) 1,3 b) -1,-3 c) 1,-3 d) -1,3

max and min value of this expression is -1 and 3 hence option 2 is out of the question

2.
Sum of the real roots of the equation x^2+5x+6 =0 is

roots are -3,-2,3,2 sum is 0

3.If the expression ax^2+bx+c is equal to 4 when x = 0 leaves a remainder 4 when divided by x+1 and a remainder 6 when divided by x+2,than the values of a,b and c are ?

a=1,b=1,c=4

4.
Log(9-2^x)base 2 = 10^log(3-x) solve for x

what is the base for other log