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⁞ Number Systems

Aptitude ➤ Number Systems ➤ 1
Question 6
Q6.  What least number must be subtracted from 2000 to get a number exactly divisible by 17 ?
 

Answer :  11


On dividing 2000 by 17, we get 11 as remainder.
∴ Required number to be subtracted = 11.
⚔ DISCUSS

Question 7
Q7.  Find the number which is nearest to 3105 and is exactly divisible by 21. ?
 

Answer :  3108


On dividing 3105 by 21, we get 18 as remainder.

∴ Number to be added to 3105 = (21 - 18) - 3.

Hence, required number = 3105 + 3 = 3108.
⚔ DISCUSS

Question 8
Q8.  Find the smallest number of 6 digits which is exactly divisible by 111 ?
 

Answer :  100011


Smallest number of 6 digits is 100000.
On dividing 100000 by 111, we get 100 as remainder.

∴ Number to be added = (111 - 100) - 11.

Hence, required number = 100011.
⚔ DISCUSS

Question 9
Q9.  Find the remainder when 231 is divided by 5.
 

Answer :  3


210 = 1024.
Unit digit of 210 x 210 x 210 is 4 [as 4 x 4 x 4 gives unit digit 4].

∴ Unit digit of 231 = Unit digit of (230 X 2 ) = 4 X 2 = 8.

Now, 8 when divided by 5, gives 3 as remainder. Hence, 231 when divided by 5, gives 3 as remainder.
⚔ DISCUSS

Question 10
Q10.  How many numbers between 11 and 90 are divisible by 7 ?
 

Answer :  11


The required numbers are 14, 21, 28, 35, .... 77, 84.
This is an A.P. with a = 14 and d = (21 - 14) = 7.

Let it contain n terms. Then, Tn = 84
⇒ a + (n - 1) d = 84
⇒ 14 + (n - 1) x 7 = 84
⇒ n = 11.

Hence, Required number of terms = 11.
⚔ DISCUSS

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