What is the remainder when 345,606^2 is divided by 20?

Question

A. 10
B. 12
C. 14
D. 16
E. 18

Bunuel · Accepted Answer

We can solve this in 30 seconds if we get the following:

The last two digits of 345,6 06 ^2 is 36.

So, we'd have something like xxxxx36, which is xxxxx00 + 36.

xxxxx00 IS divisible by 20 (it's divisible by both 10 and 2).

36 divided by 20 yields the remainder of 16.

Answer: D.

gmatophobia · Answer

\frac{345,606^2}{ 2 * 10}

\frac{345,606 * 345,606 }{ 2 * 10}

\frac{172,803 * 345,606 }{ 10}

\frac{(172,800+3) * (345,600+6) }{ 10}

\frac{(172,800 * 345,600 + 172,800 * 6 + 345,600 * 3 + 18) }{ 10}

All the terms except the last term is divisible by 10, hence the remainder will 18.

Note  : We divided by 2 at the start, so net remainder =  \frac{18 * 2 }{ 20}  = 16

Option D

harshittahuja · Answer

What is the remainder when 345,606^2 is divided by 20?
Solution:-
5*4=20
=345606*345606/(20)
=345606*345606/(2*2*5)
=172803*172803/(5)
=here the reminder is 9/5
implies reminder is 4 
which means the 4*2*2=16

Nikitapote · Answer

To solve it in 5 sec ,

the number given has unit digit 6 , and power is 2 so using cyclicity we know 6^2 = 36 again 6 is unit digit for 345,606^2 ,

Now, 345,606^2 end with 6 and any number with unit digit 6 when divide by 10 or multiple of 20 is the number itself i.e 6 ,

Hence answer option = D) 16

What is the remainder when 345,606^2 is divided by 20?

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What is the remainder when 345,606^2 is divided by 20?

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