Quiz – 1

Required units digit=units digit in (4)102+(4)103(4)102+(4)103

4242 gives unit digit 6

(4)102(4)102 gives unit digit 6

(4)103(4)103 gives unit digit of 6×4=46×4=4

Unit\'s digit in (264)^{102} +(264)^{103}=6+4=0

option c

Option A

Explanation:

The number formed by the last 2 digit in the given number 67920594 is not divisible by 4

Since the given number is divible by 5,So 0 or 5 must come in place of * .But a number ending with 5 is never divisible by 8.Therefore 0 will be in units place

The number formed by the last 4 digit is 4 *0which becomes divisible by 8, if * is replaced by 4.

divided by 5 yields a remainder equal to 3 is written as follows 

n = 5 k + 3 , where k is an integer. 

add 2 to both sides of the above equation to obtain 

n + 2 = 5 k + 5 = 5(k + 1) 

The above suggests that n + 2 divided by 5 yields a remainder equal to zero. The answer is B.

and 12 it must a multiple of the lcm of 3, 5 and 12 which is 60. 

n = 60 k 

n + 60 is also divisible by 60 since 

n + 60 = 60 k + 60 = 60(k + 1) 

The answer is D

Solution 

It is the lcm of 5, 7 and 20 which is 140. 

The answer is E

Solution 

When n is divided by 8, the remainder is 3 may be written as 

n = 8 k + 3 

multiply all terms by 6 

6 n = 6(8 k + 3) = 8(6k) + 18 

Write 18 as 16 + 2 since 16 = 8 * 2. 

= 8(6k) + 16 + 2 

Factor 8 out. 

= 8(6k + 2) + 2 

The above indicates that if 6n is divided by 8, the remainder is 2. The answer is C.

We first expand (2n + 2)² 

(2n + 2)² = 4n ² + 8 n + 4 

Factor 4 out. 

= 4(n ² + 2n + 1) 

(2n + 2)² is divisible by 4 and the remainder is equal to 0. The answer is A.