Aptitude - Numbers - Discussion

Discussion Forum : Numbers - General Questions (Q.No. 129)
129.
Which of the following numbers will completely divide (461 + 462 + 463 + 464) ?
3
10
11
13
Answer: Option
Explanation:

(461 + 462 + 463 + 464) = 461 x (1 + 4 + 42 + 43) = 461 x 85

     = 460 x (4 x 85)

     = (460 x 340), which is divisible by 10.

Discussion:
16 comments Page 1 of 2.

Atchaya s said:   6 years ago
Actually it will be the very easiest one.

It belongs to unit digit problem, for 4 their unit digits is only 4 and 6.

Because 4^1 = 4, 4^2 = 16 here unit digit is 6 then 4^3=64 here unit digit will be 6 this pattern follows. Here, 4 raises odd pwr it is 4 and 4have even pwr it has 6 apply it in the above que.

(4+6+4+6 = 20) it is completely divisible by 10 only then answer will be 10.
(4)

Vibhava said:   9 years ago
For x=odd means: 4 raised to odd no. ie. 4^1,4^3,4^5...will get 4,64,1024.
Here unit values are 4,4,4.

Similarly for x=even: 4 raised to even no. ie. 4^2,4^4,4^6... will get 16,256,4096...
here the unit places are 6,6,6.

So will get alternative 4 and 6 as unit places.
Hope I conveyed a little.
(1)

Jijo said:   1 decade ago
In the case of 4,the unit values are 4 and 6

The unit value:
For x=odd no:(1,3,5,..), 4 raised to x = 4
For x=even no:(2,4,6,..), 4 raised to x = 6

In here unit values are 4,6,4 and 6

So 4+6+4+6=20, The unit value is 0

So it is divisible by 10

Ashok said:   9 years ago
Please explain me about the unit place rules. I can't understand it. What is even and odd here.
I'm confusing.
(1)

Pankaj Tiwari said:   4 years ago
What is the remainder of the solution? Anyone, please explain.

Rohit Patil said:   7 years ago
This can be solved easily by using a unit digit concept.

Sonu Kumar said:   4 years ago
How 1 will be applied in 1st one? Please explain to me.
(1)

Srikant said:   9 years ago
I can't understand it, please explain me in detail.

Sayak Ojha said:   2 years ago
How (1+4+4²+4³)=85?
Anyone explain this step to me.
(2)

Souravmaya said:   8 years ago
How to take (1 + 4 + 4^2 + 4^3)?

Explain it.


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