Factors, number properties

[hitmis]

Source : grockit.

If k is an integer > 1, does k=2?

(1) if a and b are any 2 positive factors of k, and a <> b (not equal to), then a-b is odd.

(2) k has only 2 positive factors

I thought C is the right answer but it is A

Don't agree with the explanation given. Can anyone help explain this better.

For (1),
If k=2, then 1 and 2 are its factors, 2-1 is 1 which is odd
If k=odd number say 5, then 5 and 1 are factors, 5-1=4 is even
If k=10, then 5 and 2 are factors, 5-2=3 is odd.

So K can be 2 or 10 , therefore gives no single "yes" or "no".

[kvcpk]

Don't agree with the explanation given. Can anyone help explain this better.

For (1),
If k=2, then 1 and 2 are its factors, 2-1 is 1 which is odd
If k=odd number say 5, then 5 and 1 are factors, 5-1=4 is even
If k=10, then 5 and 2 are factors, 5-2=3 is odd.

So K can be 2 or 10 , therefore gives no single "yes" or "no".

The statements provided must always satisfy your plugin values.
the example you took of k=10 doesnt satisfy the stmt1.

K=10 has factors: 1,2,5,10
difference between 5 and 2 is ODD. But difference between 5 and 1 is even.
Difference should be ODD for ANY 2 positive factors.
So this fails as a plugin.

Infact, the factors should nto contain more than one odd number or more than one even number.
one odd number is always 1.
one even number is always 2. Because, if we choose another even number, then the diff between that and 2 will become even again.

Hope this helps!!

[Viktri]

Data given:

K > 1
K is an integer

K = 2 ?

I)
a - b = odd
THEREFORE, 1 of the factors is odd and one is even
you know that there are 2 factors and one factor is even; therefore the number must be divisible by 2
the only even prime number is 2

suff

II)
K = 3 x 1
K = 5 x 1
K = 7 x 1

insuff

answer: a

Source : grockit.

If k is an integer > 1, does k=2?

(1) if a and b are any 2 positive factors of k, and a <> b (not equal to), then a-b is odd.

(2) k has only 2 positive factors

I thought C is the right answer but it is A

Don't agree with the explanation given. Can anyone help explain this better.

For (1),
If k=2, then 1 and 2 are its factors, 2-1 is 1 which is odd
If k=odd number say 5, then 5 and 1 are factors, 5-1=4 is even
If k=10, then 5 and 2 are factors, 5-2=3 is odd.

So K can be 2 or 10 , therefore gives no single "yes" or "no".

[Testluv]

Source : grockit.

If k is an integer > 1, does k=2?

(1) if a and b are any 2 positive factors of k, and a <> b (not equal to), then a-b is odd.

(2) k has only 2 positive factors

I thought C is the right answer but it is A

Don't agree with the explanation given. Can anyone help explain this better.

For (1),
If k=2, then 1 and 2 are its factors, 2-1 is 1 which is odd
If k=odd number say 5, then 5 and 1 are factors, 5-1=4 is even
If k=10, then 5 and 2 are factors, 5-2=3 is odd.

So K can be 2 or 10 , therefore gives no single "yes" or "no".

As kvcpk points out the key is the word ANY in (1). K can't be 10 because although 5-2 is odd, 10-2 is even. Thus, we can't say of the number 10 that the difference between ANY two of its factors is odd. No odd number will satisfy the statement as odd - 1 is even. And no even number other than 2 will satisfy the statement as even - 2 is even.