Quant by Arun Sharma

MBA CAT 2024
1896
Plz Solve the following inequality:-

(x^2)-5x+8>0


if x > -8/5 (=-1.6) then
x^2-5x-8>0
x = 5 +- sqrt(57) / 2 = 5 +- 7.5 / 2 = -1.25,6.25
Since x cant be less than -1.6, we have -1.6 6.25

if x x^2 + 5x + 8 > 0
Here D = 25-32 = -7
hence -8/5 6.25 is the answer.
1897

Please solve these qs for me:

LOD III
q 43) The remainder when 2^2 + 22^2 + 222^2 + (222...49 twos)^2 is divided by 9 is

a) 2 b) 5 c) 6 d) 7

ans=c

q 53) What is the remainder when 128^1000 is divided by 153
a) 103 b) 145 c) 118 d) 152
ans=d
my take, remainder = 1 ??

q 59) Let Sm denote the sum of the squares of the first m natural numbers . For how many values of m
a) 50 b) 25 c) 36 d) 24
ans=d
q 60) for the above ques. for how many values will the sum of cubes of the first m natural numbers be a multiple of 5 (if m
a) 20 b) 21 c) 22 d) None
ans=a

q 61) How many integer values of x & y satisfy the expression 4x+7y=3 where x
a) 284 b) 285 c) 286 d) None
ans= a

I think there are a lot of errors in the answers provided at back ....

1898
Please solve these qs for me:

LOD III
q 43) The remainder when 2^2 + 22^2 + 222^2 + (222...49 twos)^2 is divided by 9 is

a) 2 b) 5 c) 6 d) 7

ans=c

q 53) What is the remainder when 128^1000 is divided by 153
a) 103 b) 145 c) 118 d) 152
ans=d
my take, remainder = 1 ??


1) Finding remainder when divided by 9 is same as finding the DigitSum of the given number
Sum of 2^2 + 4^2 + .....98^2 = 2^2(1^1+2^2 +3^2 +.....49^2)
=2^2*49*50*99 / 6 = 4*49*25*33 = 4*4*7*6 = 7*6 = 42=6

2) E(17) =16 ; 128^8%17 = (2)^24 = (2^4)^4 =1
E(9) = 6 ;128^4% 9 = 7
N= 17K+1 = 9k+7
N=52
1899


N= 17K+1 = 9k+7
N=52

please explain the step after this

understood it, the no. will be of the form of 153a+52 ; and the eqn will be
17x+1= 9y+7
1900
please explain the step after this

understood it, the no. will be of the form of 153a+52 ; and the eqn will be
17x+1= 9y+7


You need to find the smallest number which is of the form 17x+1and 9y+7
1901

LOD II:

Find the 28383rd term of the series 123456789101112...

(a) 3
(b) 4
(c) 9
(d) 7

Thanks guys,
Rohit.

1902
LOD II:

Find the 28383rd term of the series 123456789101112...

(a) 3
(b) 4
(c) 9
(d) 7

Thanks guys,
Rohit.

1-9 -->9
10-99 ->90 *2 = 180
100- 999 - >900*3 = 2700
so total = 2889
remaining digits=28383 - 2889 = 25494
25494/4 = 6373*4 + 2
hence the digit sequence will be 737373
hence last digit shub be 3
1903
1-9 -->9
10-99 ->90 *2 = 180
100- 999 - >900*3 = 2700
so total = 2889
remaining digits=28383 - 2889 = 25494
25494/4 = 6373*4 + 2
hence the digit sequence will be 737373
hence last digit shub be 3



Thanks for the reply. The answer given in Arun Sharma is option (c), i.e, 7. Any explanation?

Thanks,
Rohit.
1904
Thanks for the reply. The answer given in Arun Sharma is option (c), i.e, 7. Any explanation?


yeah d ans gvn n arun sharma s wrong...mine ans also came as 3...i tought i made a mistake...den chckd out wth odr guys...d ans s 3...many f d ans n d buk r wrng
1905

im posing a few prblems f PNC plzz help me out with these

1. how many 4 digit nos divisible by 5 can b formed by using d digits 0,1,2,3,4,5,6, nd 6?
a.230 b.588 c. 432 d.216 e.288

2.there are 7 pairs fblack nd 5 paird f white shoes.they are put in a box and are drawn one at a time.To ensure at least one pair of black shoes are taken out,what is no f shoes reqiured to be drawn out?
a.12 b.13 c.7 d.8

3.In d above qstn,what s d minimum no f shoes 2 b drawn out 2 get atleast one pair f correct shoes(either black or white)?
a.12 b.7 c.13 d.8


4.In a building there are 12 floors and ground floor.9 ppl get into d lift on ground floor.the lift doesnot stop at 1st floor.2,3,4 ppl alight d lift on its upward journey,then in how many ways can they do so?(they alight on diff floors)
a.11C3*3P3 b.11P3*9P4*3C3 c. 10P3*9P4*5P3 d.12C3

5.the no f circles dat can be drawn out f 10 points of which 7 are collinear???
a.135 b.45 c.72 d.85 e.cannot b determind

6.the sides AB,BC, and Ca f triangle ABC hv 3,4 and 5 interior pointson them.The total no f triangls formed by taking them as vertices???
a.212 b.210 c.205 d.190
wnt d ans b 12C3????


Plz give d necesay reasons fr solving dese sums...dnt jst give d solns

1906
im posing a few prblems f PNC plzz help me out with these

1. how many 4 digit nos divisible by 5 can b formed by using d digits 0,1,2,3,4,5,6, nd 6?
a.230 b.588 c. 432 d.216 e.288


Since the number should be divisible by 5, last digit could either be 0 or 5. The first digit can be any digit from 1 to 6 and the 2nd and 3rd digit could be any digit from 0 to 6.

Thus, number of such 4 digit numbers (in order of digits) = 6*7*7*2 = 588


2.there are 7 pairs fblack nd 5 paird f white shoes.they are put in a box and are drawn one at a time.To ensure at least one pair of black shoes are taken out,what is no f shoes reqiured to be drawn out?
a.12 b.13 c.7 d.8


We need to take out atleast 7 shoes to be sure of a black pair, since the first five we pick, could be the white ones.


3.In d above qstn,what s d minimum no f shoes 2 b drawn out 2 get atleast one pair f correct shoes(either black or white)?
a.12 b.7 c.13 d.8


Either the options are wrong or there's something wrong with the question. As far as I understand, this question asks minimum how many shoes to pick so that we get a pair or any colour. The answer has to be 3 for this, since there are only two colours, black and white.

So suppose the first we pick is white and second is black. No matter whether the third comes out to be black or white, we will surely get a pair of either black or white shoes
1907
3.In d above qstn,what s d minimum no f shoes 2 b drawn out 2 get atleast one pair f correct shoes(either black or white)?
a.12 b.7 c.13 d.8 Either the options are wrong or there's something wrong with the question. As far as I understand, this question asks minimum how many shoes to pick so that we get a pair or any colour. The answer has to be 3 for this, since there are only two colours, black and white.

So suppose the first we pick is white and second is black. No matter whether the third comes out to be black or white, we will surely get a pair of either black or white shoes

yeah i also felt dat d ans shuld b 3...but its nt in d options...it confusd me fr d previous qstn 2...i ws taking d pairs so my ans came as 14
1908
pusparghya Says
yeah i also felt dat d ans shuld b 3...but its nt in d options...it confusd me fr d previous qstn 2...i ws taking d pairs so my ans came as 14

Arun Sharma's book has quite a few errors, so this could be one of them.
1910

thanks saru........its relieving to know the solution

1911

SHASHANK3012........dis solution u hav given for Q.70 number system.......u say traingular nos. less than 1000 is 45.........dont u think it should be 44??

1912

Can anybody tell how to find out:-

what will be the sum

a> 1/1*5 + 1/5*9 + 1/9*13 +............1/221*225

b> 1/(sqr root 2 + sqr root 1) + 1/(sqr root 2 + sqr root 3)
+.....................1/(sqr root 120 + sqr root 121)

1913
Can anybody tell how to find out:-

what will be the sum

a> 1/1*5 + 1/5*9 + 1/9*13 +............1/221*225

b> 1/(sqr root 2 + sqr root 1) + 1/(sqr root 2 + sqr root 3)
+.....................1/(sqr root 120 + sqr root 121)

1) let s= 1/1*5 + 1/5*9 + 1/9*13 +............1/221*225
s = 1/4(1-1/5) + 1/4 ( 1/5 - 1/9)+....1/4(1/221 - 1/225)
= 1/4( 1-1/225)
S = 1/4(224)/225) = 56/225

2) rationalise the denominator u'll get the ans...i'll leave it to u...have any doubts then get back to me
1914

An ant climbing up a vertical pole ascends 12 metres and slips down 5 metres in every alternate hour.If the pole is 63 metres high,how long will it take to reach the top?
a)18 hrs b)17 hrs c)16 hrs 35 mins d)16 hrs 40 mins e)none of these

1915

I guess it is 17 hrs........puys pls correct me if i am wrong..!!

1916
An ant climbing up a vertical pole ascends 12 metres and slips down 5 metres in every alternate hour.If the pole is 63 metres high,how long will it take to reach the top?
a)18 hrs b)17 hrs c)16 hrs 35 mins d)16 hrs 40 mins e)none of these


the answer is 16hr 35 min guys .