Quant by Arun Sharma

MBA CAT 2024
4663
50 mod 11 leaves remainder 5 isn't it? What is euler's number?
may be these are very basic question but plz help.

eluer numbers :-

a^1002 remainder by 40

prime factors of 40 = 5 and 2

=> eluer number of 40 = 40*(1-1/5)*(1-1/2) = 16

now , a^16 leaves remainder 1 when divided by 40

=> we can write 1002 = 16*62 + 10

a^(16*62) leaves remainder 1 on dividing by 40

so , at the end you just need to find remainder on dividing a^10 by 40

NOTE :- 'a' and 40 should be co-prime to each other
4664

Q1. 7^6n - 6^6n , where n is an integer>0 , is divisible by

a) 13 b) 127 c)559 d)None of these


Q2. The integers 34041 and 32506, when divided by a three digit integer n, leave the same remainder, what is the value of n?

a) 289 b)367 c) 453 d)307

Pls tell me the logic behind the above two problems...

ANSWERS:
1. b
2. d


:) thanx in advance 😃

4665
Q1. 7^6n - 6^6n , where n is an integer>0 , is divisible by

a) 13 b) 127 c)559 d)None of these


Q2. The integers 34041 and 32506, when divided by a three digit integer n, leave the same remainder, what is the value of n?

a) 289 b)367 c) 453 d)307

Pls tell me the logic behind the above two problems...

ANSWERS:
1. b
2. d


:) thanx in advance :)


1) E(127) = 126.
126 is of the form 6n. so remainder of 7^6n - 6^6n by 127 wld be 0.

2) Let the common remainder be k.
=> (34041 x) and (32506 x) is completely divisible by n.
So (34041 x 32506 + x) = 1535 will also be divisible by n.
From options -> 1535 = 307*5.
4667

On a certain pasture the grass grows at an even rate. It is known that 40 cows can graze on it for 40 days before the grass is exhausted, but 30 cows can graze there as long as 60 days. How many days would the pasture last if 20 cows were to graze on it?


A drawer contains a number of red and blue socks.If I pull two out at random, then their chance of being a red pair is one half and their chance of being a blue pair is one twelfth. How many socks are in the drawer?How many of each color?
pls explain the proceedings

4668
questions from LOD 1 inequalities
Find the range of x

q1. x-6>|x^2 - 5x + 9
(a) x3
(c) 1(e) none of these

q2. (x-1|-3)(x+2-5)(a) -7(b) x4
(c) x3
(d) any of these
(e) None of these


1) Option C.
2) Option E.
4670

Quote:
Originally Posted by zoomin
After 3 equal percentage rise in the salary the sum of 100 rupees turned into140 rupees and 49 paisa.
Find the Percentage rise in the salary?
a. 12% b.22% c.66% d.82%
My take is 12%

Yar this question actually needs no calc.
100 in first 12% increase becomes 112.
in the next lets take 10% instead of 12, this wld make the sum arnd 123+ say 125.xx
in the next also 125.xx ka 10% will yield something aroung 150. which is very close to our result. hence 12%.

Waise even this is not required. when we look at the options the second least is 22%, in the first term the sum becomes 122. toh 3 times mein it wld go way over 150. Hence sidha 12% mark kardo.

Ps - Dont apply this method in very close options.

And if u want to go with a method then;
((100+x)/100)^3=140.49.

my take
this can be solved with the help of options...12% satisfies the condition.12 % is the answer. through method it should be ((100+x)^3)/(100)^2 =140.49

4671
questions from LOD 1 inequalities
Find the range of x

q1. x-6>|x^2 - 5x + 9
(a) x3
(c) 1(e) none of these

q2. (x-1|-3)(x+2-5)(a) -7(b) x4
(c) x3
(d) any of these
(e) None of these


for 1st question :it should be (c) 1 for second quest: option a
4672
@enceladus.

OA (as per arun sharma ) is 1)c
2)a

Could u please explain how you arrived at c for the first question


Haan yaar it would be option a for 2nd ques. I misread the options. Srry.
I just did it by substituting values frm the options.
4674
Utsav, (6^51)^52 is not same as 6^(51^52).
Pls check.

For verification, look at this.


I know there is a difference and I solved it as, (50^51)^52 Mod 11, since there was no clarity in the question, (which generally would be there), I didnt quote your method as a wrong one.
4675
hey maybe i am wrong here..but i am kinda confused..
let,
cp = X rs
sp = 24 rs
Profit = (24-X)rs
Profit% = {/X}*100

since its a profitable deal, therefore X
now when cp and sp are interchanged, and its a loss situation,
Loss% = {/24}*100
since XProfit%
but it is given profit% = Q%
and loss% = 62.5Q%
i am confused here....

here you make a mistake...
in case of loss...
loss=x-24/24 *100
but you make it as..
loss=24-x/24 *100..
this would be..create flawd answer!!
4676
On a certain pasture the grass grows at an even rate. It is known that 40 cows can graze on it for 40 days before the grass is exhausted, but 30 cows can graze there as long as 60 days. How many days would the pasture last if 20 cows were to graze on it?


A drawer contains a number of red and blue socks.If I pull two out at random, then their chance of being a red pair is one half and their chance of being a blue pair is one twelfth. How many socks are in the drawer?How many of each color?
pls explain the proceedings



Suppose the grass grows at x unit per day, then
40 cows --> 40 days (A + 40x)
30 cows --> 60 days (A + 60x)
20 cows --> n days (A + nx)
=> 1600 cow days = A+40x
and, 1800 cd = A+60x
solving, we get x=10 and A=1200
=> 20n = 1200+10n
=> n = 120
Thus, is 120 days

the 2nd question i am unable to solve can someone help pls
4677

Hey guys please dont go for this book..if you dont have ample time for reading it 2-3 times..because its gonna mix your concepts with widely different concepts of this book..and you will get badly confused in the exam..so instead of it read simple books it will help you more...:)

:)

4678

From pg 523 ( 4rth edition)

3.In how many ways can a person send invitation cars to 6 of his friends if he has four servants to distribute the cards ?

8. How many straight lines can be formed from 8 non collinear points i the X-Y plane ?

11. In how many ways can the letters of the word PATNA be rearranged ?

12.In the above question, how many words would be there which would start with the letter P ?

27. In how many ways can Ram chose a vowel and a consonant from the word ALLAHABAD ?

34. A man has 3 shirts , 4 trousers and 6 ties . what are the no of ways in which he can dress himself ?

4679
Suppose the grass grows at x unit per day, then
40 cows --> 40 days (A + 40x)
30 cows --> 60 days (A + 60x)
20 cows --> n days (A + nx)
=> 1600 cow days = A+40x
and, 1800 cd = A+60x
solving, we get x=10 and A=1200
=> 20n = 1200+10n
=> n = 120
Thus, is 120 days

the 2nd question i am unable to solve can someone help pls


for 2nd quest. no. of red socks=85, no. of blue socks=35
total socks=120
4680
From pg 523 ( 4rth edition)

3.In how many ways can a person send invitation cars to 6 of his friends if he has four servants to distribute the cards ?


Each invitation can be received through any of the 4 servants. So, total number of ways = 4^6


8. How many straight lines can be formed from 8 non collinear points i the X-Y plane ?

Since all the points are non-collinear, one has to select any of the 2 lines to draw a line = 8C2 = 28


11. In how many ways can the letters of the word PATNA be rearranged ?

There are a total of 5 letters which can be arranged in 5! ways but since there is no difference in the two A's we have to divide the total number of arrangements by 2!
So, total number of ways = 5!/2! = 60


12.In the above question, how many words would be there which would start with the letter P ?

Lets fix the 1st letter as P then we are left with a total of 4 letters out of which there are 2 A's, so the remaining can be arranged in 4!/2! ways = 12


27. In how many ways can Ram chose a vowel and a consonant from the word ALLAHABAD ?

Ram can select only A as a vowel and for consonants he has L,H,B and D. So, a total of 4 selections are possible. Hence the total number of ways of selecting a vowel and consonant = 1*4 = 4


34. A man has 3 shirts , 4 trousers and 6 ties . what are the no of ways in which he can dress himself ?

He can select a shirt in 3 ways, a trouser in 4 ways and a tie in 6 ways. So, total number of ways = 3*4*6 = 72
On a lighter note, he can choose to wear only a shirt and a trouser and no tie, or only a shirt or only a trouser and so on. So, that would change the total number of ways :)

Just a piece of suggestion. You dont seem to be comfortable with the basics of P&C;, so, I'd suggest you to go through RD Sharma of Class 11. Solve all the exercises in there and I guarantee that you wont have any problems with P&C; in future.
4681

Page 20 , Question number 10 , part B , 2 equilateral Triangles have the sides of 35 and 85 respectively

How many such equal parts can be measured?

Answer should be : (34/17) * 3 + (85/17)*3= 21

why it is (34/17) + (85/17) ?

Regards,
Ashish

4682
hi everybody

i m little confused in arun sharmas quant question frm number system page - 20 ,ques-15

the greatest num which will divide 4003, 4126, 4249 leaving the same remainder.
ans given in book is 41

isnt it shud be the hcf of abs val of ( 4003-4126) (4126 - 4249 ) (4003 -4249 )....
which is 123.
plz help


Dude now am really confused here , question in my book is the greatest number which will divide 4003 , 4126 and 4249

and the answer given is 41 , in my opinion, it should none of above
4683

I am unable to solve dis-
Find the number of numbers that can be formed using all the digits 1,2,3,4,3,2,1 only once so that digits occupy odd places only.

4684
I am unable to solve dis-
Find the number of numbers that can be formed using all the digits 1,2,3,4,3,2,1 only once so that digits occupy odd places only.


If there are 7 digits only as given and they have to appear at only odd places, then what comes at even places?
4685
UtsavGambhir Says
If there are 7 digits only as given and they have to appear at only odd places, then what comes at even places?

this is d question in arun sharma... it means dis is a wrong question??