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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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