# Quant Questions With Solutions- 3

21. Given a number N, 2*N has 28 factors and 3*N has 30 factors. Calculate how many factors will be there in 6*N?

It is told in question that 2*N has 28 factors.

28 = 7 * 4 or 14*2 or 7 * 2 * 2

Manav is considering the case of (7 * 4) only.

For this type of questions always start like

N = 2^p * 3^q * 5^r * ......so on(beacuse 2,3,5,7,11,13,17.. are prime factors)

since the maximum limit is not given in question so it is not possible to give a single answer...

For the question how 7*4 = 28 is coming in MANAV's Solution---

Lets for an example u need to represent 48 in prime factorization--

u will write - 48 = 2^4 * 3^1

Now if u want to know how many factors does 48 has.. we need to do [(4+1) * (1+1)]= 10 factors total

IN General N = 2^p * 3^q * 5^r * 7^s.....so on

Total no of factors are = (p+1) * (q+1) * (r+1) * (s+1)......

28 = 7 * 4 or 14*2 or 7 * 2 * 2

Manav is considering the case of (7 * 4) only.

For this type of questions always start like

N = 2^p * 3^q * 5^r * ......so on(beacuse 2,3,5,7,11,13,17.. are prime factors)

since the maximum limit is not given in question so it is not possible to give a single answer...

For the question how 7*4 = 28 is coming in MANAV's Solution---

Lets for an example u need to represent 48 in prime factorization--

u will write - 48 = 2^4 * 3^1

Now if u want to know how many factors does 48 has.. we need to do [(4+1) * (1+1)]= 10 factors total

IN General N = 2^p * 3^q * 5^r * 7^s.....so on

Total no of factors are = (p+1) * (q+1) * (r+1) * (s+1)......

22. Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while tomato juice has 90% water. How many liters of tomato puree will be obtained from 20 liters of tomato juice?

a) 2 liters

b) 2.4 liters

c) 2.5 liters

d) 6 liters

b) 2.4 liters

c) 2.5 liters

d) 6 liters

20 liters of juice contains 18 liter water and 2 liter tomato pure.

now let x liters of tomato pure be produced ,then

x- 20x/100 = 2

80x/100=2

x= 2*100/80 =2.5

now let x liters of tomato pure be produced ,then

x- 20x/100 = 2

80x/100=2

x= 2*100/80 =2.5

23. P. T. Usha and Shelly John decide to run a marathan between ramnagar and jamnagar. Both start from ramnagar at 1 pm. On the way are two towns: ramgarh and rampur seprated by a distance of 15 km .P. T. Usha reaches ramgarh in 90 minutes running at a constant speed of 40 km/hr, she takes additional 30 minutes to reach rampur. Between rampur and jamnagar she maintains at averagespeed of V km/hr. Shelly John being a professional marathon runner, maintains a constant speed of 18 km/hr.they both reach jamnagar togethar after n hours. What could be the total time taken by P. T. Usha?

a) 5 hours

b) 15 hours

c) 41 hours

d) all of the above

ramnagar-------60km------ramgrah-------15km-----rampur----(n-2)vkm----jamnagar

total distance covered by shelly =18n

total distance covered by usha =60+15+(n-2)v=75+nv-2v

18n =75+nv-2v

18n-nv= 75-2v

n(18-v) =75-2v

n =75-2v/18-v

substituting the values given in the options it is found that all the first 3 values satisfy the equation obtained.

Hence "All of the above" is the answer

total distance covered by shelly =18n

total distance covered by usha =60+15+(n-2)v=75+nv-2v

18n =75+nv-2v

18n-nv= 75-2v

n(18-v) =75-2v

n =75-2v/18-v

substituting the values given in the options it is found that all the first 3 values satisfy the equation obtained.

Hence "All of the above" is the answer

24. A fresher recruitment event of Hire All Smart People ltd(HASPL) at elitmus happens in 2 cities Bangalore and Delhi. The interview call is sent to everyone who is above 70th percentile(top 30% of the pool)70% and 80% of called people accept the interview calls in Bangalore and Delhi respectively 90% and 80% of the people who accepted the call,turned out on the day of the interview respectively in Bangalore and Delhi.The 'offer' ratio is 2 out of 3 and 3 out of 4 of the people who turned up in Bangalore and Delhi respectively. If amongst people who apply there are 1000 people above 70th percentile in each of the locations. What percentage of 70th percentile from elitmus got offered in HASPL when results of both location are taken together?

a)60%

b)50%

c)45%

d)41%

fraction of people selected from bangalore = 0.7*0.9*2/3 = 0.42 or 42%

fraction of people selected from Delhi = 0.8*0.8*3/4 =0.48 or 48%

percentage of 70th percentile from elitmus got offered in HASPL when results of both location are taken together = (42+48)/2= 45 %

fraction of people selected from Delhi = 0.8*0.8*3/4 =0.48 or 48%

percentage of 70th percentile from elitmus got offered in HASPL when results of both location are taken together = (42+48)/2= 45 %

25. Eden park is a cricket field while jubilee park is a football field in Mastnagar, all cricket fields are circular and football fields are rectangular of square. Along the boundary of all fields there are advertisement displays.in mastnagar, the length of advertisement displays has to be same across allplaying fields. Area of jubliee park is 468 sqm, the farthest distance between any two points in jubliee park football field is 10*(1.43)m. Find the approximate area of eden park?

If Area of jubliee park is 468 sqm.the farthest distance between any two points in jubliee park football field is 10sqrt(10),

and l and b are length and breadth of rectangular park, then

l^2+b^2 = (10sqrt(10))^2= 1000

l*b = 468 sq mtrs

(l+b)^2= 1000+2*468=1936

l+b=44

perimeter of rectangle= perimeter of circular field of Eden park = 2*44=88 mtrs

radius of eden park = 88/2*pi= 44*7/22= 14 mtrs

Area of eden park = Pi*r^2 = 14*14*22/7 = 44*14 = 616 sq mtrs

and l and b are length and breadth of rectangular park, then

l^2+b^2 = (10sqrt(10))^2= 1000

l*b = 468 sq mtrs

(l+b)^2= 1000+2*468=1936

l+b=44

perimeter of rectangle= perimeter of circular field of Eden park = 2*44=88 mtrs

radius of eden park = 88/2*pi= 44*7/22= 14 mtrs

Area of eden park = Pi*r^2 = 14*14*22/7 = 44*14 = 616 sq mtrs

26. From a pack of 52 playing cards, three cards are drawn random. Find the probability of drawing a king, a queen and a jack.

A king can be drawn in 4C1 ways

Similarly, a queen and a Jack can be drawn in 4C1, 4C1.

Hence,

(4c1*4c1*4c1)/(52c3)=16/5525

Similarly, a queen and a Jack can be drawn in 4C1, 4C1.

Hence,

(4c1*4c1*4c1)/(52c3)=16/5525

27. Find the total numbers in the range 100 to 1000, where in the product of individual digits of the number gives 24 (For instance: 234 gives 2*3*4 = 24)

A product of 24 can be achieved by (1,3,8), (1,4,6), (2,2,6), (2,3,4)

Now these numbers can be arranged in 3! ways respectively

However 2,2,6 can be arranged in 3!/2! ways

Hence, the answer is 3*3! + 1*3!/2! = 18+3 = 21

Now these numbers can be arranged in 3! ways respectively

However 2,2,6 can be arranged in 3!/2! ways

Hence, the answer is 3*3! + 1*3!/2! = 18+3 = 21

28. There is cask full of milk. E litres are drawn from the cask, it is then filled with water. This process is repeated. Now the ratio of milk to water is 16:9.What is the capacity of the cask in litres?

if x is capacity of cask, then

initially

x ltr milk .. 0 ltr water

after first draw and water filling by E ltrs,

x-E ltr milk and E ltr water

after 2nd draw and water filling by E ltrs,

x- [2E-(E^2/x)] and 2E -( E^2)/x ltr water

As per condition

x- [2E-(E^2/x)] /[ 2E -( E^2)/x] = 16/9

solving, we get

x=5E

initially

x ltr milk .. 0 ltr water

after first draw and water filling by E ltrs,

x-E ltr milk and E ltr water

after 2nd draw and water filling by E ltrs,

x- [2E-(E^2/x)] and 2E -( E^2)/x ltr water

As per condition

x- [2E-(E^2/x)] /[ 2E -( E^2)/x] = 16/9

solving, we get

x=5E

29. What should come in the place of (?) in the given series?

ACE, FGH, ?, PON

A) KKK

B) JKI

C) HJH

D) IKL

A +5==>F +5==>K +5==>P

C +4==>G +4==>K +4==>O

E +3==>H +3==>K +3==>N

C +4==>G +4==>K +4==>O

E +3==>H +3==>K +3==>N

30. If (9+9^2+9^3+.......9^n) is divided by 6, remainder will be? (n is a multiples of 11)

now since n is a multiple of 11 then

3(11)=33 i.e. rem =3

again 3(22)==66 rem =0

3(33)=99 rem=3

if n is odd then remainder is 3

if n is even the remainder is 0

ans remainder is 3,0

3(11)=33 i.e. rem =3

again 3(22)==66 rem =0

3(33)=99 rem=3

if n is odd then remainder is 3

if n is even the remainder is 0

ans remainder is 3,0

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