Quant by Arun Sharma

MBA CAT 2022
510
Yes u can square and proceed but b4 that u need to c d domain. for example here (x-2)/(1-2x) >=0 other wise lhs will be undefined. And this gives 1/2(x-2)>(1-2x) =>3x>3 =>x>1 . So our solution will be 1


Thanks for the pointers. To add to it and as far as I know for such equations we should proceed by bringing all the terms to one side. For eg. in this case 1 should be brought to LHS. That way we get a different answer
511

Hi Friends,

Please tell me method to find the remainder when 50^51^52 is divided by 11?

512

Is the answer 6 to this one??? If it is, I can tell you the method.....

513
avinav2712 Says
Is the answer 6 to this one??? If it is, I can tell you the method.....


yeah..the ans is 6..
514
pallaviagrawal Says
yeah..the ans is 6..

Ok so if it's the correct answer, here's my method:

For 50^(51^52) mod 11, we first find out 51^52 mod 10..... i.e the top part mod (11 - 1)

Quite clearly, 51^52 mod 10 = 1

Thus, effectively our expression is reduced to 50^1 mod 11, which gives the answer as 6
515

hi friends,

while going through the modern maths section of arun sharma, m really not able to find wat level of difficulty shud i go fior.
in context of the chapters as function which is quite big chaplter.
plz gimmme a clear picture!

516
Ok so if it's the correct answer, here's my method:

For 50^(51^52) mod 11, we first find out 51^52 mod 10..... i.e the top part mod (11 - 1)

Quite clearly, 51^52 mod 10 = 1

Thus, effectively our expression is reduced to 50^1 mod 11, which gives the answer as 6


Ya buddy the answer is correct but, can you please tell me why u did 51^52 mod 10 ??
517
jiteshbhimani Says
Ya buddy the answer is correct but, can you please tell me why u did 51^52 mod 10 ??

Well I don't really remember the reason (reason: no practice since jan) but this is the method followed for such problems when the divisor is a prime number. It's probably something to do with Fermit's theorem. You could probably check it out
518
jiteshbhimani Says
Ya buddy the answer is correct but, can you please tell me why u did 51^52 mod 10 ??


hi jitesh...avinav is spot on....d reason to take 51^52 mod 10 is because cyclicity of remainders when powers of 50 is divided by 11 is 10.

consider it in dis way...
50^1 mod 11 =6
50^2 mod 11 = 3
50^3 mod 11 =7
50^4 mod 11 = 9
50^5 mod 11 = 10
50^6 mod 11 = 5
50^7 mod 11 = 8
50^8 mod 11 = 4
50^9 mod 11 = 2
50^10 mod 11= 1
50^11 mod 11 = 6

n d cycle repeats. i.e we need to express power of 50 in terms of 10n+k
hence we take mod 10 of power of 50..
hope this helps..
519

somebody pls help:

Q1

3 Runners A,B,C run a race,with runner A finishing 24 m ahead of runner B and 36 m ahead of runner C .Each runner travels the entire distance at a constant speed.What was the length of race?
a)72m b)96m c)120m d)144m

520
somebody pls help:

Q1

3 Runners A,B,C run a race,with runner A finishing 24 m ahead of runner B and 36 m ahead of runner C .Each runner travels the entire distance at a constant speed.What was the length of race?
a)72m b)96m c)120m d)144m



i guess the qus is incomplete..
521
somebody pls help:

Q1

3 Runners A,B,C run a race,with runner A finishing 24 m ahead of runner B and 36 m ahead of runner C .Each runner travels the entire distance at a constant speed.What was the length of race?
a)72m b)96m c)120m d)144m

Surely some information is missing in this question.... Going by this, every option seems to hold true 😃
522
im having some probs in solving the inequalities chap of the book
can u give a detailed solution for Q.13 in tat chap for LOD1.

can u quote the question here only.so that ppl shud not go thru book while browsing..........as i m in office...nd cant knw which question is been talked abt.........................



-Chaitz
Just Another PAGAL
Just die for once to know how to live


HI DUDE
GIVEN QUESTION
(X-3)(X-4)4
SO THE EQUATION BECOMES
(X-3)(X-4)=>X-3=>XCONTRADICTING TO OUR SSUMPTION
NOW CONSIDER X(X-3)(X-4)X-3XSO THE ANSWER IS XGIVEN WRONG ANSWER IN THE BOOK
523

I beg everybody's pardon and for sure i skipped the data ,this is the complete question: please help.This is on page 135 arun sharma preassessment test of block 3

Q1
3 Runners A,B,C run a race,with runner A finishing 24 m ahead of runner B and 36 m ahead of runner C ,while runner B finishes 16 m ahead of runner C.Each runner travels the entire distance at a constant speed.What was the length of race?
a)72m b)96m c)120m d)144m

524
I beg everybody's pardon and for sure i skipped the data ,this is the complete question: please help.This is on page 135 arun sharma preassessment test of block 3

Q1
3 Runners A,B,C run a race,with runner A finishing 24 m ahead of runner B and 36 m ahead of runner C ,while runner B finishes 16 m ahead of runner C.Each runner travels the entire distance at a constant speed.What was the length of race?
a)72m b)96m c)120m d)144m

The answer is 96 m.....

If all 3 participate so when A completes 96 m, B completes 72 and C does 60.

Now, if only B and C participate, B wins by 16 m..... Thus, B completes 96 m, which is (4/3) * 72

Also for C, (4/3) * 60 = 80, which is 16 short of B. Thus, this is the answer

Suppose you would have chosen 120, then
A = 120, B = 96 and C = 84

For B and C, multiply both by 5/4
B = 120 and C = 105
Here the difference is only 15 and is thus not correct.

These types of questions are better solved thru options
525
I beg everybody's pardon and for sure i skipped the data ,this is the complete question: please help.This is on page 135 arun sharma preassessment test of block 3

Q1
3 Runners A,B,C run a race,with runner A finishing 24 m ahead of runner B and 36 m ahead of runner C ,while runner B finishes 16 m ahead of runner C.Each runner travels the entire distance at a constant speed.What was the length of race?
a)72m b)96m c)120m d)144m


i agree with avinav...going backward from ans options is easier...

another approach..

let distance be x meters. Distance covered by A,B and C:
A=x
B=x-24
C=x-36

when B completes d race, he is 16 m ahead of C ie when B covers the remaining 24m, C covers only 20m

hence ratio of their distances is 24/20 i.e 6/5.

Hence (x-24)/(x-36)=6/5

Solving, x=96.
526
The answer is 96 m.....

If all 3 participate so when A completes 96 m, B completes 72 and C does 60.

Now, if only B and C participate, B wins by 16 m..... Thus, B completes 96 m, which is (4/3) * 72

Also for C, (4/3) * 60 = 80, which is 16 short of B. Thus, this is the answer

Suppose you would have chosen 120, then
A = 120, B = 96 and C = 84

For B and C, multiply both by 5/4
B = 120 and C = 105
Here the difference is only 15 and is thus not correct.

These types of questions are better solved thru options




Likewise, we can also proceed with by assuming the distance to be 100. That is when a covers 100 mt then the distances covered by B and C will be 76 and 64 respectively. When B covers 100 mts the distance covered by C is 84 mts. Therefore when B covers 76 mts then C covers 63.84 mts which we have as 64. Thus the total distance is approx 100
527

please help me with these questions.



Q1)
in an organisation,the daily average wages of 20 illiterate employees is decreased from Rs 25 to Rs 10.
thus the average salary of all the literate and illiterate employees is decreased by Rs 10per day.the number of educated employees working in the organisation are:-

a) 15 b) 20

c)10 d) 25



Q2)


the average age of 8 persons in a committee is inctreased by 2 years when two men aged 35yrs and 45 yrs are substituted by two women.find the average age of two women.

a) 48 b) 45
c) 51 d) 42 e) 46


Q3)

528
please help me with these questions.

Q2)


the average age of 8 persons in a committee is inctreased by 2 years when two men aged 35yrs and 45 yrs are substituted by two women.find the average age of two women.

a) 48 b) 45
c) 51 d) 42 e) 46


Q3)

The 2nd one can be easily solved....

If we take the avg of 8 persons' age as x.... the total sum of all ages would be 8x

Now, suppose the total weight of the two women added is y.

So, 35 + 45 = 80 is decreased from 8x.

Thus, 8x - 80 + y = 8 (x + 2) = 8x + 16

We get y = 96..... Thus, the total weight of both the women is 96 kg and the average would be 48 kg
529
please help me with these questions.

Q1)
in an organisation,the daily average wages of 20 illiterate employees is decreased from Rs 25 to Rs 10.
thus the average salary of all the literate and illiterate employees is decreased by Rs 10per day.the number of educated employees working in the organisation are:-

a) 15 b) 20

c)10 d) 25



15*20
------- = 10
x + 20

=> x = 10