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12 Aug 2020, 09:32
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Difficulty:
85%
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Question Stats:
45% (01:43) correct
55%
(01:45)
wrong
based on 302
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\(K = 10^{26} + 2^{26}\), and \(K\) is a multiple of \(2^n\) but NOT a multiple of \(2^{n+1}\). If n is a positive integer, what is the value of \(n+1\)?
A) 25
B) 26
C) 27
D) 28
E) 29
A) 25
B) 26
C) 27
D) 28
E) 29
Got stumped at first glance.So a good question for sure.
Here is my try:
K is a multiple of 2^N
So we can write
K.2^N = 2^26(5^26 +1)
SO,
2^N = 2^26 AND rest is expression for K
there N=26
now question asks N+1 .So 27 is my ans.
Correcting .I missed 5+1 will contribute another 2 here and so correct ans is
2^N= 2^27
implying N+1= 27
so N=28
Here is my try:
K is a multiple of 2^N
So we can write
K.2^N = 2^26(5^26 +1)
SO,
2^N = 2^26 AND rest is expression for K
there N=26
now question asks N+1 .So 27 is my ans.
Correcting .I missed 5+1 will contribute another 2 here and so correct ans is
2^N= 2^27
implying N+1= 27
so N=28
12 Aug 2020, 10:17
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K.2^N = 2^26(5^26 +1)
now we now that 5^n nay number will end with 5 which is odd. when we add 1 to the 5 then last digit will always be 6.
which is divisible by 2 hence the whole expression is divisible by 2^27 also.
hence n+1 = 28
now we now that 5^n nay number will end with 5 which is odd. when we add 1 to the 5 then last digit will always be 6.
which is divisible by 2 hence the whole expression is divisible by 2^27 also.
hence n+1 = 28
