Number Systems ( 16 to 20 )

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16. How many natural numbers are there between 22 and 100 which are exactly divisible by 5?


A)    6

B)    12

C)    15

D)    13

E)    None of these

View Answer

 

Answer: option (C)

Explanation:

The required numbers are 25, 30, 35, 40,…., 95.

This is an A.P. in which a = 25, d = 5 and l = 95

Let the number of terms in it be n

Then, tn = 95

  • a + (n – 1)d = 95
  • 25 + (n – 1) * 5 = 95
  • (n – 1) * 5 = 70
  • (n – 1) = 14
  • n = 15

 

17. If the number 5 * 2 is divisible by 6, then * = ?

A)    9

B)    8

C)    2

D)    7

E)    None of these

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Answer: option (C)

Explanation:

6 = 3 * 2.

So, 5 * 2 is divisible by 2.

Replace * by x

Then, (5 + x + 2) must be divisible by 3.

So, x = 2.

 

18. The sum of even numbers between 1 and 31 is:

A)    6

B)    128

C)    240

D)    512

E)    None of these


View Answer

 

Answer: option (C)

Explanation:

Let Sn = (2 + 4 + 6 + ….. + 30). This is an A.P. in which a = 2, d = 2, and l = 30

Let the number of terms be n. Then,

  • a + (n – 1)d = 30
  • 2 + (n – 1) * 2 = 30
  • n = 15

∴ Sn = n/2 (a + l) = 15/2 * (2 + 30) = 15 * 16 = 240

 

19. Which one of the following cannot be the square of a natural number?

A)    32761

B)    81225

C)    32437

D)    20164

E)    None of these

View Answer

 

Answer: option (C)

Explanation:

The square of a natural number never ends in 2, 3, 7 or 8

∴ 32437 is not the square of a natural number.

 

20. Which natural number is nearest to 6485, which is completely divisible by 55?

A)    6435

B)    6500

C)    6550

D)    6525

E)    None of these

View Answer

 

Answer: option (A)

Explanation:

55

55

98

55

435

385

          50

∴ required number = 6485 – 50 = 6435

 

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