Quant by Arun Sharma

MBA CAT 2024
2398
Please help me out with this one:

Set of 15 different words is given.
In how many ways is it possible to choose a subset of not more than 5 words?

a) 4944
b) 4^15
c) 15^4
d) 4943



Ans a: 4944

we can select subsets containing 0 words, 1 word, 2 words, 3 words, 4 words and 5 words.

Hence the answer will be
1 (empty set) + C(15,1) + C(15,2) + C(15,3) + C(15,4) + C(15,5) =4944
2399

hey guys there's a question in number systems that i simply cannot get through. The question's tom long to type. Its about a mock test in AMS learning systems. Its in lod 2.
Ps: i'm typing from my phone.

2400
hi puys. . . .pls help me. . ..

1.Three Mangoes,four guavas and five watermelons cost Rs. 750. Ten watermelons, six mangoes and 9 guavas cost Rs. 1580. What is the
cost of six mangoes, ten watermelons and four guavas?
a) 1280
b) 1180
c) 1080
d) Cannot be determined
Hey here's your answer to the first one.
3m+4g+5w=750
10w+6m+9g=1580 multiply equation one by 2 and subtract from the 2nd. You'l get g=80. Substitute in either equation. You'l get
10w+6m=860. so substitue again.
2401
hi puys. . . .pls help me. . ..

1.Three Mangoes,four guavas and five watermelons cost Rs. 750. Ten watermelons, six mangoes and 9 guavas cost Rs. 1580. What is the
cost of six mangoes, ten watermelons and four guavas?
a) 1280
b) 1180
c) 1080
d) Cannot be determined

2.Iqbal dealt some cards to Mushtaq and himself from a full pack of
playing cards and laid the rest aside. Iqbal then said to Mushtaq
"If you give me a certain number of your cards, I will have four times
as many cards as you will have. If I give you the same number of
cards, I will have thrice as many cards as you will have". Of the given
choices, which could represent the number of cards with iqbal?
a)9
b)31
c)12
d)35
3. Find the general term of the GP with the third term 1 and the seventh
term 8.
a)(2^3/4)^n-3
b)(2^3/2)^n-3
c)(2^3/4)^3-n
d)(2^3/4)^2-n
e) None of these

1) 3M+4G+5W=750 ......(a)
6M+9G+10W=1580 ......(b)
multiply (a) with 6 and (b) with 3 to get G=80
Substituting the value of G in (b) we get 6M+10W= 860
And 4G=320
So above two add up to give ans as 1180.

2) Let Iqbal = I and Mustaq=M
I+x=4(M-x) ......(a)
I-x=3(M+x) ......(b)

On solving, I=(7M-x)/2 ......(c)
Substituting in (a) we get M= 9x
Substituting in (c) we get I=31x
Now we'll check solution for diff values of x
let x=1. So I=31 and M=9
It satisfies the given conditions hence ans= 31.

3) Trying options,
Substituting n=3, value should become 1
(2^3/4)^3-3 = (2^3/4)^0 = 1
And substituting n=7, value should become 8
(2^3/4)^7-3 = (2^3/4)^4 = 8
So, ans is option (a).

Hope this helps 😃
2402

This is Q. No. 8 from TSD LOD 3

Three sprinters A,B and C had to sprint from points P to Q and back again (starting in that order). The time interval between the starting time of the three sprinters was 5 seconds each. Thus C started 10 seconds after A while B started 5 seconds after A. The three sprinters passed a certain point R, which is somewhere between P and Q, simultaneously (none of them having reached point Q yet). Having reached Q and reversed the direction, The third sprinter met the second one 9m short of Q and met the first sprinter 15m short of Q. Find the speed of the first sprinter if the distance between PQ is equal to 55m.

a. 4m/s
b. 3m/s
c. 2m/s
d. 1m/s
e. None of these

2403

Rohit draw a rectangular grid of 529 cells arranged in 23 rows nd 23 columns and filled each cell with a number.the nos with which he filled each cell were such that nos of each row taken from left to right formed an arithmetic series and nos of each column taken from top to bottom also formed arithmetic series . 7 and 17 th nos of 5th row were 47 nd 63 respectively.while 7 nd 17 nos of 15 th row were 53 and 77 respectively.what is sum of all nos in grid?
a.32798 b.65596c.52900d.none of these
ans=a

please puys help me solve this

2404

Interest: LOD 3: Q 20

A sum of 8000 is borrowed at 5% compound int and paid back in 3 equal installments.
What is the amount of each installment?

a) 2937.67
b) 3000
c) 2037.67
d) 2739.76

2405

Can you please explain me the following (Remainder Theorem Page#30)

1. Find the remainder when 43^197 is divided by 7.
2. Find the remainder when 51^203 is divided by 7.

2406
Can you please explain me the following (Remainder Theorem Page#30)

1. Find the remainder when 43^197 is divided by 7.
2. Find the remainder when 51^203 is divided by 7.


1.(43*43*43*...)^197/7..Take it as individual value..43/7 which gives the reminder 1..So 1^197=1
2.Same as the first one..51/7..you'll get 2^203...Now (2^3)/7=1..so its now its now (2^5)/7 which gives a reminder 4...
2407
1.(43*43*43*...)^197/7..Take it as individual value..43/7 which gives the reminder 1..So 1^197=1
2.Same as the first one..51/7..you'll get 2^203...Now (2^3)/7=1..so its now its now (2^5)/7 which gives a reminder 4...

Thanks for your reply..
i got the first one but not the second one...so its now its now (2^5)/7...how is that?
Also please help me in finding the units digit of (1273)^122!.
2408
Thanks for your reply..
i got the first one but not the second one...so its now its now (2^5)/7...how is that?
Also please help me in finding the units digit of (1273)^122!.

The question is (2^203)/7..Take 2^3,its 8/7 which gives 1 s the reminder..so (2^((3*66)*5))/7..now its (2^5)/7 which is 4...
For finding the unit digit,take 3^1,3^2,3^3,3^4,3^4 ans so on..you'll be getting the unit digit as 3,9,7,1,3,9,7,1,...So for the 122nd term its 9...:
2409
This is Q. No. 8 from TSD LOD 3

Three sprinters A,B and C had to sprint from points P to Q and back again (starting in that order). The time interval between the starting time of the three sprinters was 5 seconds each. Thus C started 10 seconds after A while B started 5 seconds after A. The three sprinters passed a certain point R, which is somewhere between P and Q, simultaneously (none of them having reached point Q yet). Having reached Q and reversed the direction, The third sprinter met the second one 9m short of Q and met the first sprinter 15m short of Q. Find the speed of the first sprinter if the distance between PQ is equal to 55m.

a. 4m/s
b. 3m/s
c. 2m/s
d. 1m/s
e. None of these


Some1 pls reply!
2410

can any 1 plz solve the TSD , LOD 3- question 1, Page#283
questionon siliguri and darjeeling...
i am nt able to understand the hint given in the book

2411

Hi guys,

This question is from Probability in Arun Sharma.Could anyone please help me out with this problem?

Out of a pack of 52 cards one is lost; from the remainder of the pack, two cards are drawn and are found to be spades. find the chance that the missing card is a spade.

a) 11/50 b) 11/49 c)10/49 d)10/50

2412
Hi guys,

This question is from Probability in Arun Sharma.Could anyone please help me out with this problem?

Out of a pack of 52 cards one is lost; from the remainder of the pack, two cards are drawn and are found to be spades. find the chance that the missing card is a spade.

a) 11/50 b) 11/49 c)10/49 d)10/50


p = (13C1/52C1)* (12C2/51C2)
-----------------------------------------------------------
{ (13C1/52C1)* (12C2/51C2) + (39C1/52C1)* (13C2/51C2) }

p = 11/50

Ans : option a)

Plz correct me if i m wrong....
2413
p = (13C1/52C1)* (12C2/51C2)
-----------------------------------------------------------
{ (13C1/52C1)* (12C2/51C2) + (39C1/52C1)* (13C2/51C2) }

p = 11/50

Ans : option a)

Plz correct me if i m wrong....

Yes that is correct!! Thanks!! 😃
2414

Heres another one:

A speaks the truth 3 times out of 4, B 7 times out of 10. They both assert that a white ball is drawn from a bag containing 6 balls, all of different colours. Find the probability of the truth of the assertion.

a)12/49 b)3/10 c)21/40 d)None of these

2415

1. Find length of longest pole that can be placed in an indoor stadium 24 m long,18 m wide,16 m high.
a.30 b.25 c.34 d.580^0.5 e.36
ans= c

2.A conical tent is to accomdate 10 persons. each person must have 6 m^2 space and 30 m^3 air to breathe. what will be height of cone?
a.37.5 b.150 c.75 d.80 e.none of these
ans=e

please help me solve this!

2416
1. Find length of longest pole that can be placed in an indoor stadium 24 m long,18 m wide,16 m high.
a.30 b.25 c.34 d.580^0.5 e.36
ans= c

2.A conical tent is to accomdate 10 persons. each person must have 6 m^2 space and 30 m^3 air to breathe. what will be height of cone?
a.37.5 b.150 c.75 d.80 e.none of these
ans=e

please help me solve this!

1.
The longest pole will be the diagonal of the cuboid (the indoor stadium). To calculate the diagonal v need to use pythagoras theorem a^2 + b^2 = c^2 where c is the diagonal of the cuboid.

a= (length^2 + breadth^2)^0.5 = (24^2 + 18^2)^0.5 = 30
b = height = 16
therefore c = (30^2 + 16^2)^0.5 = 34

Hope ur able to visualise it.
2417
1. Find length of longest pole that can be placed in an indoor stadium 24 m long,18 m wide,16 m high.
a.30 b.25 c.34 d.580^0.5 e.36
ans= c

2.A conical tent is to accomdate 10 persons. each person must have 6 m^2 space and 30 m^3 air to breathe. what will be height of cone?
a.37.5 b.150 c.75 d.80 e.none of these
ans=e

please help me solve this!

2. Im not really sure about this but here goes:

each person needs 6 m2 to sit implies for 10 people area of the base needs to be 60m2.
Therefore area of base i.e (pi*r^2) = 60 --- (1)
Now, volume of cone = (1/3)*h*pi*r^2
Volume of air for one person = 30 m3
volume needed for 10 people = 300 m3
Therefore (1/3)*h*pi*r^2 = 300

i.e (1/3) *h*60 = 300 from (1)

Therefore h = 15m
Hence answer = (e) none of the above