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kvcpk wrote:(16+1)^23 = 16^23 +1^23 +16*(.......)sanju09 wrote:What is the remainder when 17^23 is divided by 16?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
When divided by 16 it leaves 1 as reminder
B
I would prefer to follow Rule of Cyclicity over here !!kvcpk wrote:(16+1)^23 = 16^23 +1^23 +16*(.......)sanju09 wrote:What is the remainder when 17^23 is divided by 16?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
When divided by 16 it leaves 1 as reminder
B
Sanju Bhai,sanju09 wrote:kvcpk wrote:(16+1)^23 = 16^23 +1^23 +16*(.......)sanju09 wrote:What is the remainder when 17^23 is divided by 16?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
When divided by 16 it leaves 1 as reminder
B
Although it is the same logic, this method is much easier (and probably more reliable) like that:gmatmachoman wrote:I would prefer to follow Rule of Cyclicity over here !!kvcpk wrote:(16+1)^23 = 16^23 +1^23 +16*(.......)sanju09 wrote:What is the remainder when 17^23 is divided by 16?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
When divided by 16 it leaves 1 as reminder
B
17 ^1 ends with 7 in unit's digit
17 ^2 ends with 9
17^3 ends with 3
17 ^4 ends with 1
17^5 ends with 7....
So from here on it follows a cyclicty of 4. after that it follows a pattern.
Now 23 can be written as 4*5 +3
So if u find the remainder of 17 ^3 , it will be same as 17^23.
remainder of 17^ 3 when divided by 16 is 1 .
So for 17^23 also it will be 1.
Pick B
:roll:gmatmachoman wrote:I would prefer to follow Rule of Cyclicity over here !!kvcpk wrote:(16+1)^23 = 16^23 +1^23 +16*(.......)sanju09 wrote:What is the remainder when 17^23 is divided by 16?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
When divided by 16 it leaves 1 as reminder
B
17 ^1 ends with 7 in unit's digit
17 ^2 ends with 9
17^3 ends with 3
17 ^4 ends with 1
17^5 ends with 7....
So from here on it follows a cyclicty of 4. after that it follows a pattern.
Now 23 can be written as 4*5 +3
So if u find the remainder of 17 ^3 , it will be same as 17^23.
remainder of 17^ 3 when divided by 16 is 1 .
So for 17^23 also it will be 1.
Pick B
c 17^23 means 17*17*17*17*...23timesif you divide all of this by 16 every 17 will give 1 remainder i.e 1*1*1*1...23 times=1 remaindersanju09 wrote:What is the remainder when 17^23 is divided by 16?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
17^23 / 16 does not mean 17*17*17*17*...23times / 16*16*16*16..23 times...why are you dividing each 17 with 16. Ideally, only one time such a division should be made.amising6 wrote: c 17^23 means 17*17*17*17*...23timesif you divide all of this by 16 every 17 will give 1 remainder i.e 1*1*1*1...23 times=1 remainder
okie dudesumanr84 wrote:17^23 / 16 does not mean 17*17*17*17*...23times / 16*16*16*16..23 times...why are you dividing each 17 with 16. Ideally, only one time such a division should be made.amising6 wrote: c 17^23 means 17*17*17*17*...23timesif you divide all of this by 16 every 17 will give 1 remainder i.e 1*1*1*1...23 times=1 remainder
Its not, 17+17+17.....23 times / 16 , which you can split into several parts.
I see that a lot of people are trying various innovative approach here. Good for practice..
Don't try to innovate this simple problem. Any wrong strategy that does not hold for general will prove FATAL in exam.
I liked gmatmachoman conventional approach. Stick to it and you won't land up in trouble.
Thx suman bhai!! Is there any software that can type as we say..if so let me know...sumanr84 wrote:17^23 / 16 does not mean 17*17*17*17*...23times / 16*16*16*16..23 times...why are you dividing each 17 with 16. Ideally, only one time such a division should be made.amising6 wrote: c 17^23 means 17*17*17*17*...23timesif you divide all of this by 16 every 17 will give 1 remainder i.e 1*1*1*1...23 times=1 remainder
Its not, 17+17+17.....23 times / 16 , which you can split into several parts.
I see that a lot of people are trying various innovative approach here. Good for practice..
Don't try to innovate this simple problem. Any wrong strategy that does not hold for general will prove FATAL in exam.
I liked gmatmachoman conventional approach. Stick to it and you won't land up in trouble.
gmatmachoman wrote:There is one I used long time back when it was free. Just see if you can get any crack version for installation.sumanr84 wrote:
Thx suman bhai!! Is there any software that can type as we say..if so let me know...
https://www.downloadatoz.com/dragon-naturallyspeaking/
All I meant was that you could have phrased it little differently to arrive at the conclusion as to why are we multiplying 1*1*1*1*.... though there is only one 16 for division.amising6 wrote: c 17^23 means 17*17*17*17*...23timesif you divide all of this by 16 every 17 will give 1 remainder i.e 1*1*1*1...23 times=1 remainder
sumanr84 wrote:All I meant was that you could have phrased it little differently to arrive at the conclusion as to why are we multiplying 1*1*1*1*.... though there is only one 16 for division.amising6 wrote: c 17^23 means 17*17*17*17*...23timesif you divide all of this by 16 every 17 will give 1 remainder i.e 1*1*1*1...23 times=1 remainder
Even when you use this approach it may result in chaos if the problem was 17^23 / 15
You will get 2*2*2*2*..23 times(if I have correctly understood your point) ...then how will you proceed from here...??
now make a group of four 2's i.e 16 *16*16*16*16*8 divide by 15
so every 16 will give 1so u will be left with 1*8 mod 15=8
nathanalgren has put up a nice approach.
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