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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 so280 *x= 56x^{2}, 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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