**Q.1)** A nursery has 363,429 and 693 plants respectively of 3 distinct varieties. It is desired to place these plants in straight rows of plants of 1 variety only so that the number of rows required is the minimum. What is the size of each row and how many rows would be required?

1) 56

2) 45

3) 48

4) 42

**Q.2) **The sides of a hexagonal field are 216, 423, 1215, 1422, 2169 and 2223 meters. Find the greatest length of tape that would be able to exactly measure each of these sides without having to use fractions/parts of the tape?

1) 9

2) 54

3) 27

4) 18

**Q.3)** Find the greatest number of four digits which when divided by 10, 11, 15 and 22 leaves 3, 4, 8 and 15 as remainders respectively.

1) 9907

2) 9903

3) 9893

4) None of these

Q.4) The LCM of two numbers is 936. If their HCF is 4 and one of the numbers is 72, the other is:

(1) 42

(2) 52

(3) 62

(4) None of these

Q.5) Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds. If they first beep together at 12 noon, at what time will they beep again for the first time?

(1) 12:10 P.M.

(2) 12:12 P.M.

(3) 12:11 P.M.

(4) None of these

Q.6) 4 Bells toll together at 9:00 A.M. They toll after 7, 8, 11 and 12 seconds respectively. How many times will they toll together again in the next 3 hours?

(1) 3

(2) 4

(3) 5

(4) 6

Q.7) On Ashok Marg three consecutive traffic lights change after 36, 42 and 72 seconds respectively. If the lights are first switched on at 9:00 A.M. sharp, at what time will they change simultaneously?

(1) 9 : 08 : 04

(2) 9 : 08 : 24

(3) 9 : 08 : 44

(4) None of these

Q.8) A forester wants to plant 44 apple trees, 66 banana trees and 110 mango trees in equal rows (in terms of number of trees). Also, he wants to make distinct rows of trees (i.e. only one type of tree in one row). The number of rows (minimum) that are required are:

(1) 2

(2) 3

(3) 10

(4) 11

Q.9) Three runners running around a circular track can complete one revolution in 2, 4 and 5.5 hours respectively. When will they meet at the starting point?

(1) 22

(2) 33

(3) 11

(4) 44

Q.10) The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is divided by 2, the quotient is 33. The other number is?

(1) 66

(2) 132

(3) 198

(4) 99

Q.11) The greatest number which will divide: 4003, 4126 and 4249:

(1) 43

(2) 41

(3) 45

(4) None of these

Q.12) Which of the following represents the largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12, 14, 21, 33, and 54.

(1) 9123

(2) 9383

(3) 8727

(4) None of these

Q.13) Find the greatest number of 5 digits, that will give us a remainder of 5, when divided by 8 and 9 respectively.

(1) 99931

(2) 99941

(3) 99725

(4) None of these

Q.14) Find the HCF of (3^125−1) and (3^35−1).

1) 3^5−1

2) 3^4−1

3) 3^3−1

4) 3^6−1

Q.15) What will be the least possible number of the planks, if three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length?

(1) 7

(2) 8

(3) 22

(4) None of these

Q.16) Find the L.C.M of 2.5, 0.5 and 0.175

(1) 2.5

(2) 5

(3) 7.5

(4) 17.5

Q.17) The L.C.M of 4.5; 0.009; and 0.18 = ?

(1) 4.5

(2) 45

(3) 0.225

(4) 2.25

Q.18) The L.C.M of two numbers is 1890 and their H.C.F is 30. If one of them is 270, the other will be

(1) 210

(2) 220

(3) 310

(4) 320

Q.19) What is the smallest number which when increased by 6 is divisible by 36, 63 and 108?

(1) 750

(2) 752

(3) 754

(4) 756

Q.20) What is the greatest possible rate at which a man can walk 51 km and 85 km in an exact number of minutes?

(1) 11 km/min

(2) 13 km/min

(3) 17 km/min

(4) None of these