Quant by Arun Sharma

Hey i think the answer would be 3^17 only as u have extracted the powers of 3 so x and y can not be 3 or a multiple of 3
so in that case they wont be divisible by 3
hence 3^17

I would also like to ask divyaakanksha to post the solution or answer to the above problem in case she has it other wise we can ask quant devils like implex or made_for_iims people who can confirm the asnwers but i think it is fine

lets c what others have to say


There is a possibility of 3^10*x-y being divisible by 3
'=For eg: 5-2=3 has 3 as a factor
or 101-2 =99 has 3^2 as factors
There is a possibility of 3^10*x-y being divisible by 3
'=For eg: 5-2=3 has 3 as a factor
or 101-2 =99 has 3^2 as factors

see i think chance of 3^10*x-y being divisible by 3 is zero as
(3^10*x-y) mod 3 have
(0-y mod 3) as the first term is already divisible by 3 hance until and unless the value of y is not a multiple of 3 it cannot divide the complete term.

correct me if i am wrong !!!!!
what is the highest power of 3 available in the expression 58!-38!
a) 17
b)18
c)19
d)none of these

the correct ans is 17..i dnt hav d solution ...

juz c this approch, from fact58 - fact38 lets take fact 38 common which have 3's power as17 and in remaining factor, some multiple of three -1 will be the number so ans is 17.

Q1. gives remainder and {.} denotes the fractrional part of that. The fractional part is of the form (0.bx). The value of x could be

A) 2
B) 4
C) 6
D) 8
E) None of these


Q2. denotes the greatest value just below x and {x} its fractional value. The sum of ^2 and {x} is 25.16. Value of x is

a) 5.16
b) -4.84
c) Both (a) and b)
d) 4.84
e) Cannot be determined



Q3. The mean of 1, 2, 2 ^ 2,. 2 ^ 31 lies in between

a) 2 ^ 24 to 2 ^ 25
b) 2 ^ 25 to 2 ^ 26
c) 2 ^ 26 to 2 ^ 27
d) 2 ^ 29 to 2 ^ 30
e) 2 ^ 23 to 2 ^ 24


Q4. denotes the greatest integer value just below x and {x} its fractional value. The sum of ^ 3 and {x} ^ 2 is -7.91. Find x

a) -2.03
b) -1.97
c) -2.97
d) -1.7
e) none of these


i dont get the concept in Q2 and Q4 .. plz help me out. thanks:)




Q2. denotes the greatest value just below x and {x} its fractional value. The sum of ^2 and {x} is 25.16. Value of x is

a) 5.16
b) -4.84
c) Both (a) and b)
d) 4.84
e) Cannot be determined



Q3. The mean of 1, 2, 2 ^ 2,. 2 ^ 31 lies in between

a) 2 ^ 24 to 2 ^ 25
b) 2 ^ 25 to 2 ^ 26
c) 2 ^ 26 to 2 ^ 27
d) 2 ^ 29 to 2 ^ 30
e) 2 ^ 23 to 2 ^ 24


Ya....fr Qn 2solve from options....
5.16 = 5 + 0.16
so its ^2 =25 {x} =0.16...
So 25.16


similarly r -4.84 we can write it as -5 + 0.16...
So 25.16 therefore both a and b
option c....

Q 3.
1,2,2^2,.......2^31
32 terms,....
Sum of gp

a(r^n -1)/(r-1)
1(2^32 -1)/(2-1)
= 2^32 -1

mean == (2^ 32 -1)/32
== (2^32-1)/2^5
======= (2^27)-1/32
so mean is clearly between 2^26 to 2^27

Option c


Q4. denotes the greatest integer value just below x and {x} its fractional value. The sum of ^ 3 and {x} ^ 2 is -7.91. Find x

a) -2.03
b) -1.97
c) -2.97
d) -1.7
e) none of these


i dont get the concept in Q2 and Q4 .. plz help me out. thanks:)


Hi ....seee .....
-7.91...
sum of acube and a square...
square of a number cant be negative....

So
it shd be -8 + 0.09
k.....
Nw see wich options satisfy....
clearly its -1.97
-2 + 0.03.....
option b..
Hi ....seee .....
-7.91...
sum of acube and a square...
square of a number cant be negative....

So
it shd be -8 + 0.09
k.....
Nw see wich options satisfy....
clearly its -1.97
-2 + 0.03.....
option b..

Your partially right... it shud be -8 + 0.09...giving -2 + .3 (not .03)
so answer is d) -1.7
Your partially right... it shud be -8 + 0.09...giving -2 + .3 (not .03)
so answer is d) -1.7


Haan yaar its -2+ .3 yaa...silly mistake....
gives remainder and {.} denotes the fractrional part of that. The fractional part is of the form (0.bx). The value of x could be

A) 2
B) 4
C) 6
D) 8
E) None of these


ans is 2
3^32 is of the form 4n.hence the unit's digit would b 1.on dividing 3^32 by 50 u'll get d last digit of remainder always as 1.hence wen v divide 1 by 50 takin decimal the quotient would always b 2. so whatever d value of 'b' ,' x' would always b 2.

plzz correct me if m wrong

Q1 denotes the greatest integer value just below x and {x} its fractional value.the sum of ^3 and {x}^2 is -7.91.find x?

Q2 find the 28383rd term of the series:123456789101112....... ???

Q3 some birds settled on the branches of a tree.first,they sat one to a branch and there was one bird too many.next they sat two to a branch and there was one branch too many.how many branches were there??

Q1 denotes the greatest integer value just below x and {x} its fractional value.the sum of ^3 and {x}^2 is -7.91.find x?

Q2 find the 28383rd term of the series:123456789101112....... ???

Q3 some birds settled on the branches of a tree.first,they sat one to a branch and there was one bird too many.next they sat two to a branch and there was one branch too many.how many branches were there??


Q1) well the answer should have been x=-1.03(which is not in the options)
-7.91 = -8 + 0.09(since we have to write it as sum of a cube & a square)
-8 = (-2)^3 and 0.09=(0.3)^2
which means x= -1.03 (since =-2 & {-1.03}=0.03)
Q3) Let Br - branches , Bi - birds
From 1st statement we get Bi - 1 = Br. ----> 1
From 2nd statement we get Br= (Bi/2) +1 ------>2

Solving 1 & 2 we get : Br=3 & Bi=4

Q2) cant figure that out!!!

I dont want to be posting questions who's solutions have already being figured out but everything here is presented in a haphazard way.
Does any body have all the chapterwise solutions & explanations in a file format?

Neways i had a doubt from Number System. M posting the question:

32^32^32 / 9 will leave a remainder

a)4 b)7 c)1 d)2

ans is option 1) rem 4

nidhisoni24 Says
ans is option 1) rem 4


can u plz explain hw did u get it? i m not able to understand the solution given in the book....

32^32^32 / 9 will leave a remainder

a)4 b)7 c)1 d)2


32/9 will give remainder as 5.
nw, 5^32^32/9 => 25^16^32/9
25/9 gives remainder as 7.
nw 7^16^32/9 => 49^8^32/9
49/7 gives remainder as 4.
4^256/9 will give final remainder as 4.
hence ans is 4.
i hope its clear..though its pretty lenghty..

arun,bikas and chetakar have a total of 80 coins among them.arun triples the number of coins with the others by giving them some coins from his own collection. next,bikas repeats the same process.after this bikas now has 20 coins.find the number of coins he had at the beginning.
a) 11
b) 10
c) 9
d) 12

Can anyone help me out with these questions fm Arun Sharma Ch 2 Progressions Lod II

Q If a times the ath term of an AP is equal to b times the bth term, find the (a+b)th term.
a) 0
b) a^2 - b^2
c) a - b
d) 1
e) a^2 + b^2




Q If the nth term of an AP is 1/n and the nth term is 1/m, then find the sum to mn terms.

(a) (mn - 1) / 4
(b) (mn + 1) /4
(c) (mn + 1) / 2
(d) (mn - 1) /2
(e) none of these


thanks for helping out:)

Can anyone help me out with these questions fm Arun Sharma Ch 2 Progressions Lod II

Q If a times the ath term of an AP is equal to b times the bth term, find the (a+b)th term.
a) 0
b) a^2 - b^2
c) a - b
d) 1
e) a^2 + b^2




Q If the nth term of an AP is 1/n and the nth term is 1/m, then find the sum to mn terms.

(a) (mn - 1) / 4
(b) (mn + 1) /4
(c) (mn + 1) / 2
(d) (mn - 1) /2
(e) none of these


thanks for helping out:)

Let the first term be f and common difference be d

a times ath term = a * [ f + (a-1)*d ] -------------(1)

b times bth term = b * [ f + (b-1)*d ] -------------(2)

we know a times ath term = b times bth term

So equating (1) and (2)

a * [ f + (a-1)*d ] = b * [ f + (b-1)*d ]

af + a(a-1) d = bf + b(b-1 )d

(af- bf ) + [ a(a-1)d - b(b-1)d] = 0

(a-b)f + [ a2 -a - b2 + b ] d = 0

(a-b)f + d[ ( a-b)(a+b) - (a-b) ] = 0

taking (a-b) common

(a-b) [ f + (a + b -1 )d ] = 0

[ f + (a + b -1 )d ] is the (a+b) the term so the (a+b) th term will be zero
arun,bikas and chetakar have a total of 80 coins among them.arun triples the number of coins with the others by giving them some coins from his own collection. next,bikas repeats the same process.after this bikas now has 20 coins.find the number of coins he had at the beginning.
a) 11
b) 10
c) 9
d) 12

Hey can you please recheck the question. See this is how I approached the problem and I am getting the answer as 20. Check out my method and point out any mistakes that you find.

Let us consider that arun(A) ,bikas(B) and chetakar(C) each have a, b, c respectively initially

after A gives the coin to B and C. B and C will each have 3 times what they had initially and A that much less.
A: a - 2b - 2c
B: 3b
C: 3c

After B gives the coins,
A: 3(a - 2b - 2c )
B: 3b - 2*(3c) - 2*(a - 2b - 2c ) -------(1)
C: 3*(3c)

equating (1) with 20
3b - 2*(3c) - 2*(a - 2b - 2c ) = 20

3b -6c - 2a + 4b +4c = 20

7b - 2a -2c -2b + 2b = 20 ( adding and subtracting 2b)

9b - 2(a+b+c) = 20

we know a+b+c= 80
9b - 2(80) = 20

9b = 180

b = 20