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

### Set A

1.Find that smallest number which when diminished by 11 is completely divisible by 14, 15, 21, 32 and 60.

(a)1681

(b)1679

(c)3371

(d)3349

2.The sum of two numbers is 36 and their G.C.D. is 4. How many such pairs are possible?

(a)1

(b)2

(c)3

(d)4

3.The sum of two numbers is 320 and their L.C.M. is 1584. What are those numbers?

(a)144, 176

(b)180, 140

(c)134, 186

(d)160, 140

4.The L.C.M. of two numbers greater than 29 is 4147 and their H.C.F. is 29. What is the sum of those number?

(a)966

(b)696

(c)669

(d)666

5.The H.C.F. and L.C.M. of two numbers is 13 and 455. If one of the number is between 75 and 125 then it is

(a)78

(b)104

(c)91

(d)117

6.The difference of two number whose L.C.M. and H.C.F. is same will be

(a)0

(b)1

(c)can’t be determined

(d)None of these

7.The sum of two numbers is 377. If the sum and the difference of their L.C.M. and H.C.F. are respectively 2665 and 2639 then the numbers are

(a)144, 156

(b)130, 143

(c)117, 234

(d)156, 221

8.The L.C.M of two numbers is 45 times their H.C.F. If one numbers is 125 and the sum of their L.C.M and H.C.F. is 1150 then the other number is

(a)225

(b)270

(c)315

(d)180

9.The L.C.M. of two numbers is 10 times their H.C.F. The sum of their L.C.M. and H.C.F. is 330. If one of the number is 60 then what is the other number?

(a)180

(b)150

(c)250

(d)90

10.The L.C.M. of two numbers is 56 times their H.C.F. The sum of the L.C.M. and H.C.F. of these numbers are 2565. If one of the number is 315 then what is the other number?

(a)450

(b)360

(c)450

(d)495

Answers and Solution:

1. (c)

Required number = (LCM. of 14,15,21,32 and 60) + 11

= 3360 + 11 = 3371

2. (c)

Let, numbers are 4x and 4y

so, 4x + 4y = 36

or, x + y = 9

so (x,y) = (1,8),(2,7),(4,5) so total 3 pairs are possible

3. (a)

4. (b)

Let, numbers are 29a and 29b where a and b are co-prime numbers.

From the question , 29ab = 4147, ab = 143 = 13*11

so, the sum of numbers = 29a + 29b = 29(a+b) = 29(13+11)

= 29 * 24 = 696

5. (c)

6. (a)

7. (d)

8. (a)

Let, H.C.F = x so, L.C.M = 45x

from the question x + 45x = 1150

or, x = 25 = G.C.F and 45x = 1125 = L.C.M

for two numbers, (G.C.F * L.C.M) = (product of numbers)

so 25 * 1125 = 125 * second number

so second number = 225

9. (b)

10. (b)

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

### Set B

1.In a test consisting 75 questions carrying one mark each Anil answered 75% of the first 40 questions correctly. What approximate percent of the other 35 questions does he need to answer correctly to score 80% on the entire test.

(a)90

(b)86

(c)70

(d)65

2.If the numerator of a fraction is increased by 200% and the denominator of the fraction is increased by 150%. The result fraction is 9/10. The original fraction is

(a)27/40

(b)5/7

(c)3/5

(d)3/4

3.The ratio of the number of students in schools X, Y and Z is 6 : 8 : 7 respectively. If the number of students is increased by 20%, 25% and 20% respectively, then the new ratio will be

(a)18 : 25 : 21

(b)12 : 13 : 7

(c)6 : 10 : 7

(d)None

4.The mean of the marks obtained by 100 students is 60. If the marks obtained by one of the students was incorrectly calculated as 82, whereas the actual marks obtained by him was 72. What is the correct mean.

(a)59.9

(b)61

(c)60.1

(d)None

5.A, B and C started a business. A invested Rs. 25 lakh and then 10 L after one year. B paid Rs. 35 Lakh and then after 2 years he took out. Rs. 10 lakh. C invested Rs. 30 lakh. What be their proportion of share after 3 years?

(a)19 : 19 : 18

(b)10 : 10 : 9

(c)11 : 10 : 9

(d)16 : 13 : 8

6.Eleven players of a team has average age of 23 years. Among them, the average age of 3 different group of 3 players each is 21 years, 24 years and 26 years respectively. These groups does not include captain and wicket keeper. If captain is 8 years older then wicket keeper, then age of captain is

(a)20 yrs.

(b)23 yrs.

(c)26 yrs.

(d)24 yrs.

7.A sum of money is divided among P, Q, R, S in the ratio of 3 : 7 : 9 : 13 respectively. If the share of P and R together is Rs. 16440, then what is the difference between the amounts of Q and S.

(a)Rs. 9460

(b)Rs. 8220

(c)Rs. 27400

(d)Rs. 10580

8.A shopkeeper sells 250 mere of cloth for Rs. 9000 at a profit of Rs. 6 per metre. The cost price per metre of cloth is

(a)Rs. 50

(b)Rs. 60

(c)Rs. 30

(d)Rs. 36

9.The total of the ages of a class of 75 girls is 1650 years the average age of 25 of them is 24 years and that of another 25 is 20 years. Find the average age of remaining girls.

(a)21 years

(b)22 years

(c)26 years

(d)None

10.In 2009, cost of material : labour : overheads for a car was 5 : 4 : 3, but in 2010, cost of material increased by 16%, labor increased by 10% while overheads reduced by 8%. What is increased percent in price of car?

(a)6%

(b)7%

(c)8%

(d)10%

Answers and Solution:

1.(b)

75% * 40 + x% * 35 = 80% * 75

=> x = 86

2.(d)

3.(a)

4.(a)

correct mean = 60 - (82-72)/100 = 59.9

5.(a)

A's MEI = (25*1+35*2) = 95

B's MEI = (35*2+25*1) = 95

C's MEI = (30*3) = 90

proportion of share = 95 : 95: 90 = 19 : 19 : 18

6.(d)

7.(b)

(3x+9x) = 16440

=> x = 16440/12

difference of Q and S = 13x-7x = 6x = 6*16440/12 = 8220

8.(c)

9.(b)

Let the average rest 25 girls = x, then

Total ages of 75 girls = 1650 = 25*24+25*20+25*x

x = 22

10.(c)

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