**Find solutions for all the questions at the end of each set:**

### Set A

1. x is a five-digit number. The digit in ten thousand’s place is 1. The number formed by its digit in unit’s and ten’s places is divisible by 4. The sum of all the digits is divisible by 3. If 5 and 7 also divide x, then x will be

(a) 14040

(b) 12060

(c) 10020

(d) 10080

2. What is the weight of a cubical block of ice 50 cm in length, if one cubic metre of ice weights 900 kilograms?

(a) 113 kg

(b) 113.5 kg

(c) 112.5 kg

(d) 114 kg

3. If A, B and C are three numbers, such that, the LCM of A and B is B and the LCM of B and C is C, then the LCM of A, B and C is

(a) A

(b) B

(c) C

(D) (A+B+C)/3

4. In a class of 64 students, 50% of the students have taken Sociology and 75% of the students have taken Political Science. All Students have chosen either one subject. How many students have taken both the subjects?

(a) 12

(b) 18

(c) 14

(d) 16

5. Six men earn as much as seven women, two women earn as much as three boys, four boys earn as much as five girls. If a girl earns Rs.16 a week, what does a man earn per week?

(a) Rs.35

(b) Rs.20

(c) Rs.40

(d) Rs.30

6. Find the mean of 8 arithmetic mean between 1 and 10.

(a) 2.5

(b) 5.5

(c) 3.5

(d) 4.5

7. In an examination, A obtain 10% less than the minimum number of marks required for passing, B obtains 11(1/9) less than A, and C obtains 41(3/17)% less than the number of marks obtained by A and B together. Does C pass or fail?

(a) Pass

(b) Fail

(c) Can’t say

(d) Data inadequate

8. The marked price of a shirt and a trouser are in the ratio 2 : 3. The shopkeeper gives 30% discount on the shirt. If the total discount is 20%. Then, the discount offered on the trouser is –

(a) 12(1/2)%

(b) 33(1/3)%

(c) 13(1/3)%

(d) 8(1/3)%

9. A, B and C are partners in a business. A, whose money has been used for 4 months, claims 1/8 of the profit. B, whose money has been used for 6 months, claims 1/3 of the profit. C had invested Rs. 1560 for 8 months. How much money did A and B contribute together?

(a) 720

(b) 1560

(c) 2000

(d) 1280

10. I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. Then my age and my son’s age are respectively:-

(a) 42 yrs, 14 yrs

(b) 45 yrs, 15 yrs

(c)36 yrs, 12 yrs

(d) 48 yrs, 16 yrs

Answers and Solution:

1- (d)

No number except 10080 is divisible by 7.

further,80 is divisible by 4.

1+0+0+8+0 = 9 is divisible by 3 and 10080 is also divisible by 5.

2- (c)

volume of the cubical block of ice = 50*50*50 cm^3

= (50*50*50)/(100*100*100) m^3 = 1/8 m^3

weight of the cube = 1/8*900 = 112.50 kg

3- (c)

LCM of A & B is B => B is a multiple of both A & B

Again,

LCM of B & C is C => C is a multiple of both B & C

so LCM of ABC = C

4- (d)

5- (a)

6 men = 7 women;

2 women = 3 boys;

4 boys = 5 girls;

Now earning of a girls per week = Rs. 16

so Earning of 1 boy = 5/4*16 = 20

Earning of 1 women = 3/2*20 = 30

Earning of 1 man = 7/6*30 = 35

6- (b)

8 arithmetic mean between 1 and 10

= 2,3,4,5,6,7,8,9

Their mean = (2+3+4+5+6+7+8+9)/8 = 5.5

7- (a)

8- (c)

9- (c)

Ratio of thier prifit= 1/8 : 1/3:(1-(1/8+1/3))

= 1/8 : 1/3 : 13/24

= 3:8:13

Now,for A & C

A*4 :c*8 = 3:13

A*4 :1560*8 = 3:13

A = (1560*8*3)/(4*13) = 720

For B & C,

B*6 :c*8 = 8:13

B*6 :1560*8 = 8:13

B = (1560*8*8)/(6*13) = 1280

Contribution by A & B together

= 720+1280= 2000

10- (b)

Let the present age of my son = x yrs.

Then,the present age of mine = 3x yrs.

(3x+5)=2(1/2)(x+5)

x = 15 yrs.

Father's age = 45 yrs.

Son's age = 15 yrs.

**Find solutions for all the questions at the end of each set:**

### Set B

1. A Juice seller has three types of juice, 403 litre of 1st kind, 434 litre of 2nd kind and 465 litre of 3rd kind. Find the least possible number of cases of equal size in which different types of juice can be filled without mixing.

(a) 46

(b) 44

(c) 42

(d) 31

2. Two numbers, both greater than 29, have HCF 29 and LCM 4147. The sum of the numbers is

(a) 996

(b) 696

(c) 669

(d) 896

3. If 4 is added to one-fifth of a number and 10 is subtracted from one-fourth of that, then both becomes equal. Then find the number.

(a) 260

(b) 280

(c) 240

(d) 270

4. In a three digit number, the digit at the hundred place is twice the digit at the unit’s place and the sum of digit is 18. If the digits are reverse then number is reduced by 396. The difference of hundred’s and ten’s place digit of the number is

(a) 1

(b) 2

(c) 3

(d) 5

5. 8 men can do a work in 12 days. After 6 days of work, 4 more men are engaged to finish the work. In how many days would the remaining work be completed?

(a) 2

(b) 3

(c) 4

(d) 5

6. The average value of property of Mittal, Ambani and Singhaniya is Rs.11111 crore. The property of Singhaniya is as less as the average property as of Mittal is greater than the average property. Then, the value of property of Ambani is

(a) 111 crore

(b) 11111 crore

(c) 3703.7 crore

(d) Can’t be determined

7. There are 10 compartments in a passenger train which carries on an average 20 passengers. If 12 passengers are sitting in each compartment and no compartment has equal number of passengers then maximum how many passenger can be accommodated in any compartment?

(a) 64

(b) 45

(c) 56

(d) None of these

8. A jar is full of honey. A person draws 20% of the honey from the jar and replaces it with sugar solution. He has repeated the same process 4 times and these there is out of 512 gm of honey left in the jar. The initial amount of honey in the jar was

(a) 1.25 kg

(b) 1 kg

(c) 1.5 kg

(d) None of these

9. Renuka got married 8 years ago. Today her age is 1(1/3) times her age at the time of marriage. Her daughter’s age is 1/8 times of her age. Her daughter’s age is

(a) 3 years

(b) 4 years

(c) 6 years

(d) 8 years

10. A and B have to write 810 and 900 pages respectively in a same time period. But A completes his work 3 hours ahead of time and B completes 6 hours ahead of time. How many pages did A write per hour if B wrote 21 pages more in each hour?

(a) 45

(b) 72

(c) 54

(d) 100

ANSWERS SOLUTIONS:

1- (c)

size of each cask must be equal to greatest capcity .Hence ,capacity of cask must be equal to the HCF of 403, 434 and 465.

capacity of a cask = required HCF i.e.31

Required no of cask = 403/31 + 434/31 + 465/31

= 13 + 14 + 15 = 42

2- (b)

Let the number be 29x and 29y respectively

where x and y are prime to each other.

so LCM of 29x and 29y = 29xy

Now,29xy = 4147

so xy = 143 = 11*13

so Numbers are

29*11 = 319 and 29*13 = 377

so Required sum = 377+319 = 696

3- (b)

Let the number be = x

so x/5 + 4 = x/4 - 10

x/4 - x/5 = 10 + 4

(5x-4x)/20 = 14

x = 20*14 = 280

4- (b)

5- (c)

W1/M1D1 = W2/M2D2

1/(8*12) = 1/2/(12*D2)

D2 = 4 days

6- (b)

Acc to ques.

(M+A+S)/3 = 11111

M+A+S = 33333

M - 11111 = 11111-S

M+S = 22222

so value of property of Ambani

= 33333-22222= 11111

7- (c)

8- (a)

9- (b)

10- (c)

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