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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?
1 | |
3 | |
2 | |
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.
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
70, 80 | |
42, 48 | |
35, 40 | |
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.
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?
20 | |
25 | |
50 | |
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
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?
11 | |
17 | |
19 | |
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
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?
x> 3 | |
x> 4 | |
x > 5 | |
x < 5 |
Question 5 Explanation:
x + y > 5 and x-y>3
Solving Eqs. (i) and (ii), we get 2x > 8 so x> 4
Solving Eqs. (i) and (ii), we get 2x > 8 so x> 4
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