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Number System: Level 1 Test - 3

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Question 1

1. The LCM and HCF of two numbers are 4641 and 21 respectively. If one of the numbers lies between 200 and 300, find the numbers which satisfy the condition

A

273, 357

B

273, 361

C

273, 359

D

273, 363

Question 1 Explanation:

Product of the numbers = HCF x LCM = 21 x 4641 = 21 x3x7 x13x17 = 3x7 x3x7 x13x17
The numbers can be 3x7 x13 and 3x7 x17, ie, 273 and 357.

Question 2

Members of a club have their ages are in AP, the common difference being 3 months. If the youngest member of the club is just 7 years old and the sum of the ages of all the members is 250 yr, Find the number of members in the club is

A

15

B

20

C

25

D

30

Question 2 Explanation:

Let n be the number of members in the club. Then 250 =n/2[2x7+(n-1)3/12] 250= n/2[14+1/4n-1/4] 250= 7n +n^2/8-n/8 n= 25

Question 3

6 identical machines can produce a total of 270 bottles per min by running at constant speed. At this rate, how many bottles could 10 such machines produce in 4 min?

A

1800

B

648

C

2700

D

10800

Question 3 Explanation:

Answer a) Number of machines =270x10x4/6=1800

Question 4

There are two examination rooms A and B. If 10 candidates from A are sent to B, the number of students in each room is the same. If 20 candidates from B are sent to A, the number of students in A is double the number of students in B. Find the number of students in each room.

A

(a) 100 in A and 80 in B

B

(b) 80 in A and 100 in B

C

(e) 120 in A and 100 in B

D

(d) 100 in A and 120 in B

Question 4 Explanation:

A -10 = B + 10 A - B = 20 ... 1) and A + 20 = 2 (B - 20) A - 2B = - 60 ... 2 From Eqs. (i) And (ii), A = 100, B = 80

Question 5

The LCM of two numbers is 4800 and their HCF is 160. One of the numbers is 480, Find the other number is

A

16

B

16000

C

160

D

1600

Question 5 Explanation:

Product of two numbers=LCM*HCF 4800*160=480*x x=1600

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