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⁞ Number Systems

Aptitude ➤ Number Systems ➤ 1
Question 11
Q11.  How many terms are there in 2,4,8,16....1024 ?
 

Answer :  10


Clearly 2,4,8,16...1024 form a GP. With a = 2 and r = 4/2 = 2.

Let the number of terms be n . Then

nth term = arn-1
⇒ 2 x 2n-1 = 1024
⇒ 2n-1 = 512 = 29.
⇒ n-1 = 9
⇒ n = 10.
⚔ DISCUSS

Question 12
Q12.  2 + 22 + 23 + ... + 212 = ?
 

Answer :  8190


Given series is a G.P. with a = 2, r = 4/2 = 2 and n = 12.

Sum = a(rn - 1)/ (r-1)
= 2 x (212 - 1)/(2-1)
= 2 x (4096-1)
= 2 x 4095
= 8190
⚔ DISCUSS

Question 13
Q13.  If the number 97215*6 is completely divisible by 11, then the smallest whole number in place of * will be ?
 

Answer :  3


Given number = 97215x6
(6+5+2+9) − (x+1+7) = (14 − x), which must be divisible by 11.

Therefore, x = 3.
⚔ DISCUSS

Question 14
Q14.  On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?
 

Answer :  5


Let x be the number and y be the quotient.
Then,
x = 56 × y + 29
= (8 × 7y) + (8 × 3) + 5
= 8 × (7y + 3) + 5.

Therefore,
Required remainder = 5.
⚔ DISCUSS

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