Quant by Arun Sharma

MBA CAT 2022
342
flanker Says
ques: In a race of 600 metres,Ajay beats vijay by 60 meters and in a race of 500 meters Vijay beats Anjay by 25 meters.By how many margins will Ajay beat Anjay in 400 meters race? a. 48m b. 52m c. 56m d. 58m picked frm pg 278 ques 74


Race - 600,
ajay -600
vijay - 540
Race - 100
ajay - 100
vijay - 90

Race - 400
vijay - 500
anjay - 475

Race - 90
vijay - 90
anjay - 85.5

So when ajay runs 100 -> anjay runs 85.5
So in case of when ajay runs 400 -> anjay runs 342

So Answer ----- 58
343
16 = 2^4.

Hence, we need to chk the last four digits of the above no. which are 4950.

Hence, it becomes: 4950 mod 16 = 6

Hope this helps. :)


Same formula is applicable for the numbers 2,3 and 5
344

hey just nw came across dis thread.....m glad...to find it....
evn i follow arunsharma.....guess..nw i will get all ma doubtz clarified...

keep rockin ......

345

Puys, I have some questions from TSD.

LOD 1:

Q24:

A car driver driving in a fog passes a pedestrian who was walking at the rate of 2km/hr in the same direction. The pedestrian could see the car for six minutes and it was visible for a distance of .6km. What was the speed of the car?

346
The sole purpose of this Thread is to bring together the CAT aspirants who are solving the Quant book by Arun Sharma. This will be a common place to discuss any doubts while solving the questions. As there are many questions in the book where either the Hint/Solution is missing or the answer itself is wrong. It will be very nice of you all to help people clear their doubts and also they could learn various methods of problem solving. This thread is not for advertising and should be taken in the right spirit.
:grab:
hi...i am using arun sharma for quants...want to know if DI and verbal from him are good...
347
Puys, I have some questions from TSD.

LOD 1:

Q24:

A car driver driving in a fog passes a pedestrian who was walking at the rate of 2km/hr in the same direction. The pedestrian could see the car for six minutes and it was visible for a distance of .6km. What was the speed of the car?

let the speed of car=x
relative speed wrt to pedestrian=x-2
6minutes=0.1 hr
(x-2)*0.1=0.6
x-2=6
x=8km/hr

plz. confirm the answer
348

Hi...
Help Me to solve these questions.

Number System LOD 2 Ques.No: 61.

Define a number K such that it is the sum of the squares of the first M natural numbers (i.e K= 1^2+2^2+...M^2) where M
a) 10 b) 11 c) 12 d)none of these

Number System LOD 2 Ques.No: 64.

Find the 28383rd term of the series 123456789101112....
a) 3 b)4 c)9 d)7

Please explain the answers...


Thanks in advance.

349
Hi...
Help Me to solve these questions.

Number System LOD 2 Ques.No: 61.

Define a number K such that it is the sum of the squares of the first M natural numbers (i.e K= 1^2+2^2+...M^2) where M
a) 10 b) 11 c) 12 d)none of these

Number System LOD 2 Ques.No: 64.

Find the 28383rd term of the series 123456789101112....
a) 3 b)4 c)9 d)7

Please explain the answers...


thanks in advance.

1.sum of squares=m(m+1)(2m+1)/6=4k
m(m+1)(2m+1)=24K=8*3*K
now, 2m+1 is odd
out of m & m+1 one is odd other will be even
when m will be even it will divisible by 8
so. m= 8,16,24,32,40,48
so, when m+1 will even then
m=7,15,23,31,39,47
so, toatl values=6+6=12
plz. confirm
350

Dear puys,

Good Stuff!

Seems there are whole a lotta Qs and amazing answers.

I'll start my preps in a day or two.

Count me as one of yours!

Cheers,
Prabu

351
1.sum of squares=m(m+1)(2m+1)/6=4k
m(m+1)(2m+1)=24K=8*3*K
now, 2m+1 is odd
out of m & m+1 one is odd other will be even
when m will be even it will divisible by 8
so. m= 8,16,24,32,40,48
so, when m+1 will even then
m=7,15,23,31,39,47
so, toatl values=6+6=12
plz. confirm



The answer is 12. Thanks for your explanation gaurishankar.
352
Hi...

Number System LOD 2 Ques.No: 64.

Find the 28383rd term of the series 123456789101112....
a) 3 b)4 c)9 d)7

Please explain the answers...


Thanks in advance.


Nos with 1 digit = 9
Nos with two digit = 99 - 9 = 90
Nos with three digit = 999 - 99 = 900

So total digits upto 999 = 2700 + 180 + 9 = 2889

Remaining = 28383 - 2889 = 25494

So the numbers with four digit until the 28383rd term = 25494/4 = 6373 Remainder 2

So 999 + 6373 = 7372

So 2nd term of nest number 7373 = 3

Answer ---- 3
Hope this is correct
353
let the speed of car=x
relative speed wrt to pedestrian=x-2
6minutes=0.1 hr
(x-2)*0.1=0.6
x-2=6
x=8km/hr

plz. confirm the answer



Thanks! Thats the right answer. I'm having a lot of problems in LOD I itself. Is it possible to discuss TSD logic, probably on mail or chat or something?
This is another problem. I have tried solving it but can't follow the logic:

H and V move towards Hossur from IIMB at 40km/hr and 60km/hr respectively. If V reaches 200minutes before H, what is the distance between IIMB and Hossur?
354
Thanks! Thats the right answer. I'm having a lot of problems in LOD I itself. Is it possible to discuss TSD logic, probably on mail or chat or something?
This is another problem. I have tried solving it but can't follow the logic:

H and V move towards Hossur from IIMB at 40km/hr and 60km/hr respectively. If V reaches 200minutes before H, what is the distance between IIMB and Hossur?

40(t+10/3)=60t.
t=20/3
so distance=20*40/3=800/3 kms.
355
40(t+10/3)=60t.
t=20/3
so distance=20*40/3=800/3 kms.



hey, the answer is 400km. guess this is wrong.
356
Nos with 1 digit = 9
Nos with two digit = 99 - 9 = 90
Nos with three digit = 999 - 99 = 900

So total digits upto 999 = 2700 + 180 + 9 = 2889

Remaining = 28383 - 2889 = 25494

So the numbers with four digit until the 28383rd term = 25494/4 = 6373 Remainder 2

So 999 + 6373 = 7372

So 2nd term of nest number 7373 = 3

Answer ---- 3
Hope this is correct



I got the explanation... but in arun sharma the answer is given as c)9. are we goin wrong somwwhere....
357
puresunshine Says
hey, the answer is 400km. guess this is wrong.

oops yah the distance=20*60/3=400
by mistake i had interchanged the time taken by both
358
oops yah the distance=20*60/3=400
by mistake i had interchanged the time taken by both



Couldn't get it. From where did the 10/3 come?
359
puresunshine Says
Couldn't get it. From where did the 10/3 come?


200 Minutes = 3 hrs 20 mins = 3.33 hrs = 3 whole 1/3 hrs = 10/3 hrs
360
puresunshine Says
Couldn't get it. From where did the 10/3 come?


200 Minutes = 3 hrs 20 mins = 3 whole 1/3 hrs = 10/3 hrs (Since the speeds are in Km/Hr)
361
vidhyasagar Says
I got the explanation... but in arun sharma the answer is given as c)9. are we goin wrong somwwhere....


Too good!

Is the remainder of any significance here?

Cheers,
Prabu