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15 May 2017, 19:52
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Question is
Is positive integer n divisible by 4 ?
1)n^2 is divisible by 8
2) sqrt n is an even integer.
Now answer states both options alone are enough to answer the question but my question is for second option
you have sqrt 16 = 4 (divisible by 4 and also even integer) but then you got sqrt 100 = 10 (even integer but not divisible by 4)
What do you guys think ?
Is positive integer n divisible by 4 ?
1)n^2 is divisible by 8
2) sqrt n is an even integer.
Now answer states both options alone are enough to answer the question but my question is for second option
you have sqrt 16 = 4 (divisible by 4 and also even integer) but then you got sqrt 100 = 10 (even integer but not divisible by 4)
What do you guys think ?
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stonecold
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15 May 2017, 20:50
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Hi mbsingh
The answer is absolutely correct.
We need to see if n is divisible by 4 or not.
Statment 1 ->
n^2=8k(for some integer k)=> 2^3*k
As n is an integer => n^2 must be a perfect square => All powers of its primes must be even.
Hence n^2=2^4*some integer.
Hence n must be divisible by 4.
Sufficient
Statment 2 ==>
√n=even=2m (say)
Squaring on both sides
n=even*even => 4m^2
Hence n must be divisible by 4.
Sufficient.
Hence D.
Smash that D.
The answer is absolutely correct.
We need to see if n is divisible by 4 or not.
Statment 1 ->
n^2=8k(for some integer k)=> 2^3*k
As n is an integer => n^2 must be a perfect square => All powers of its primes must be even.
Hence n^2=2^4*some integer.
Hence n must be divisible by 4.
Sufficient
Statment 2 ==>
√n=even=2m (say)
Squaring on both sides
n=even*even => 4m^2
Hence n must be divisible by 4.
Sufficient.
Hence D.
Smash that D.
15 May 2017, 22:33
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stonecold
Hi mbsingh
The answer is absolutely correct.
We need to see if n is divisible by 4 or not.
Statment 1 ->
n^2=8k(for some integer k)=> 2^3*k
As n is an integer => n^2 must be a perfect square => All powers of its primes must be even.
Hence n^2=2^4*some integer.
Hence n must be divisible by 4.
Sufficient
Statment 2 ==>
√n=even=2m (say)
Squaring on both sides
n=even*even => 4m^2
Hence n must be divisible by 4.
Sufficient.
Hence D.
Smash that D.
The answer is absolutely correct.
We need to see if n is divisible by 4 or not.
Statment 1 ->
n^2=8k(for some integer k)=> 2^3*k
As n is an integer => n^2 must be a perfect square => All powers of its primes must be even.
Hence n^2=2^4*some integer.
Hence n must be divisible by 4.
Sufficient
Statment 2 ==>
√n=even=2m (say)
Squaring on both sides
n=even*even => 4m^2
Hence n must be divisible by 4.
Sufficient.
Hence D.
Smash that D.
How exactly is second statement sufficient ?
Square root of 100 is 10 , its even but not divisible by 4
Square root of 16 is 4, its even and divisible by 4.
Both 100 and 16 are even, so how can you surely say its sufficient ?
