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Number System: Level 1 Test - 7

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Question 1
The sum of two numbers is 462 and the HCF of these two numbers is 22. Find the maximum number of pairs that satisfy these conditions?
A
1
B
3
C
2
D
6
Question 1 Explanation: 
Since 22 is the HCF, the two numbers are 22x and 22y (x and y are prime to each other).
Also, we know
22x+22y=462
x+ y=21
Now 21 can be written as a sum of two co-prime numbers in the following ways:
(1,20) (2,19) (4,17) (5,16) (8,13) (10,11).
Therefore option d is the right answer.
Question 2
The LCM of two numbers is 280 and their ratio is  7 : 8. Find the two numbers which satisfy this criterion
A
70, 80
B
42, 48
C
35, 40
D
28, 32
Question 2 Explanation: 
Let the number be 7 x and 8x.  HCF=x,
LCM x HCF = Product of numbers
so 280 *x = 56x2 ,
x=5  
:. Numbers are 35, 40.
Question 3
If the age of Ram is one-third the age of his father Sham now, and was one-fourth the age of his father 5 yr ago, then how old will his father Sham be 5 yr from now?
A
20
B
25
C
50
D
45
Question 3 Explanation: 
Let the present age of Ram and his father be x and y respectively.
Then x=1/3y  and (x - 5) = ¼  (y - 5)
From Eqs. (i) and (ii), y = 45 yr and x = 15 yr
Hence, required age = (y + 5) = 50 yr
Question 4
Find the number which leave remainder of 1, 2 and 3 when divided by 2, 3 and 4 respectively?
A
11
B
17
C
19
D
36
Question 4 Explanation: 
The number which leave remainder 1, 2 , 3 when divided by 2,
3 ,4 respectively  is LCM of ( 2, 3 , 4)- 1
 i.e. = 12-1= 11
Question 5
If x + y > 5 and x - y > 3, then which of the following gives all possible values of x?
A
x> 3
B
x> 4
C
x > 5
D
x < 5
Question 5 Explanation: 
x + y > 5  and x-y>3
Solving Eqs. (i) and (ii), we get  2x > 8 so  x> 4
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