Latest elitmus Aptitude Question SOLUTION: a number has only k and k-2 factor off a number n the factor 1 and n is not consider so what is possibel.. a.n+1 is perfect square. b.n-1 is a odd or prime number. c. n+1 is a eve

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(#M40156444) ELITMUS Numerical Ability question number Keep an EYE

a number has only k and k-2 factor off a number n the factor 1 and n is not consider so what is possibel..
a.n+1 is perfect square.
b.n-1 is a odd or prime number.
c. n+1 is a even number
d. all of above

Asked In elitmus rajat (8 years ago)

Unsolved Read Solution (10)

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Read Solution (10) :

Chinmay Joshi  (7 years ago)

answer is a
k (k-2) = n
hence for option a lets add 1,
= (k^2-2k) + 1
= k^2 -2k + 1
= (k-1)^2
which is a perfect square

but for k = 28,
28*26 = 728
729 is a perfect square
but n+1=728+1=729 is not even number. Therefore, option c is false so option d can not be true.

Is this solution Helpfull? Yes (26) | No (4)  

rajat  (8 years ago)

answer is d.
consider the number n=8 only 2 factor 4 and 2 other than 1 and 8.
8+1=9 perfect square.
8-1=7 odd number.

consider 15 =5*3 and k and k-2 follow 5-3=2..
15+1 =16 perect square...
15-1=14 even number..
consider 35=5*7= other than 1 and 35.
35+1=36.
35-1=34 even number..

Is this solution Helpfull? Yes (11) | No (17)  

Dwarkesh  (7 years ago)

as we can see tha option b and c are opposite to each other, if n-1 is odd then how it is possible to n+1 is even , it must be odd cz alternete numbers, and option a is right as we can see it by adding 1 in both side
k^2 -2k +1 = n + 1
(k-1)^2 = n + 1

:)

Is this solution Helpfull? Yes (8) | No (1)  

Sanjay Mogra  (8 years ago)

n+1 is perfect square . ANS a

Is this solution Helpfull? Yes (5) | No (2)  

AKSHAY K  (7 years ago)

answer is d.
and chinmay joshi 728 has other factors
eg: 4 and 182
look the question
it is mentioned only factors k & k-2 is present oder than 1 and n

Is this solution Helpfull? Yes (2) | No   

krushnendu sundar patra  (7 years ago)

Answer is option D we have to check for all possible solution .

Is this solution Helpfull? Yes (1) | No (4)  

vinod kumar korikana  (7 years ago)

as discussed by RAJAT , ans : a
n+1 is perfect square because b & c are not always right.
you have to go with opt : a

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Anil Pokhariyal  (7 years ago)

Anser is a) because
let k=5 then 5*3=15 and 15+1=16 perfect square and 15-1=14 not odd
let k=7 then 7*5=35 and 35+1=36 perfect square and 35-1=34 not odd
let k=9 then 9*7=63 and 63+1=64 perfect square
hence this would work the similar way

Let me know If you think It's not right. I would love to learn other way as well.

Is this solution Helpfull? Yes (1) | No (1)  

priyadarshan kumar  (7 years ago)

Since it is given that only K, k-2 is the factor of n except ( 1, n)
therefore
K( K - 2 ) = n
K^2 - 2K = n

NOW WE CHECK FOR EVERY VALUE OF 'K'
K=1 n = -1 NOT POSSIBLE

K=2 n = 2 NOT POSSIBLE

K=3 n=3 NOT POSSIBLE

K=4 n=8 POSSIBLE

K=5 n=15 POSSIBLE

AND SO ON..........

FROM HERE WE SEE

n+1 = 9, 16...............PERFECT SQUARE SO OPTION FIRST SATISFY BUT OPTION 'C' IS WRONG
n-1 = 8, 14................OPTION 'B' IS ALSO WRONG

HENCE THE ANSWER IS 'A'

Is this solution Helpfull? Yes (1) | No (1)  

Vikash kumar  (7 years ago)

correct answer is a
chinmay joshi make correct

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