If k is a positive integer, what is the value of k?

Question

(1) k is a prime number less than 5.
(2) If f is any positive factor of k, then f + 1 is even.

Gladiator59 · Answer

IMO E.

1) K is prime and less than 5. We have two possibilities 2 & 3.  Insuff

2) f is   ANY   positive factor of k, f + 1 is even.
 If f + 1 is even for all f, then f has to be always odd. There is no integer for whom all positive factors are odd as every other factor will be even! ( ex. 3*2 = 6, 3*3 = 9)
  Hence Insuff

(1) + (2) also do not give us any new information.

Hence  Option (E)  is our answer.

Please correct me if I am wrong...
 gmatbusters  ,  pushpitkc  ,  stonecold

Best,
Gladi

pushpitkc · Answer

2. If f is any positive factor of k, then f + 1 is even

If k is 3, it has two positive factors 1 and 3.
If f=1, f+1 = 2 and is even
If f=3, f+1 = 4 and is even

This is possible for all prime numbers greater than 3 also.
For example, if k=7, there are 2 positive factors 1,7
f+1 is again even for both values of f.  (Insufficient)
 
But, when we combine the information in both the statements, 
the only possibility remaining is if k=3. Hence, the combined
statement is enough to answer the question (Sufficient - Option C)

kunalcvrce · Answer

Hi even k=2,
factors are f=1,and 2

1+1=2 so even, k can be 2 and 3
insufficient E

pushpitkc · Answer

Hey  kunalcvrce

Here, f=2 is a positive integer which is a factor of k=2
But f+1 is not even. Hence, we cannot use this case when combining the two statements.

Thats the reason the answer is Option C!

kunalcvrce · Answer

hey  pushpitkc 
in question it is mentioned 
If f is  any positive factor  of k, then f + 1 is even.
any positive factor of 2 can be 1 or 2.
since factor can be even after addition of one ,so k can be 2 also.

benejo · Answer

If k is a positive integer, what is the value of k?

(1) k is a prime number less than 5.
(2) If f is any positive factor of k, then f + 1 is even.

1) 2 Primes less than 5: 2,3

2) f is ANY positive factor of k, f + 1 is even. ( --> f must be odd)
k= f * something 
k= 1 * 3 = 3
k= 3 * 3 = 9

(1) + (2) 
We know that k=2 or k=3, f is a factor of k and f is odd.
Now let f=1:
k= f * something 
3= 1 * 3 (or 3 * 1)
2= 1 * 2

Still two values left for k. Hence, (E)

teaserbae · Answer

Since it is mentioned any positive factor : 
Here any doesn't mean any one of them .
Here any means on choosing any of the positive factors of 2 . as f
 f+1 is even
Hope so your doubt is clear now.

ujjwal80 · Answer

The answer should be E.

Statement 1 - k is a prime number less than 5.  This gives us two values of k i.e. 2 and 3. Therefore not sufficient.

Statement 2 - If f is any positive factor of k, then f + 1 is even.  Let say f = 3 and k = 6. This satisfies the condition of statement 2 i.e.  \frac{6}{3}  = 2 and (3+1) is even.

Let's take another value for f and k. This time let both f and k be equal to 5. Now, this also satisfies statement 2 condition as  \frac{5}{5}  = 1 and (5+1) is even. Hence not sufficient.

BOTH statement combined  doesn't refines our value. As integer 1 is the factor of all integer so clearly it is a factor of 2 and 3. Additionally (1+1) = 2, which is even. Therefore both statements combined is also not sufficient.

Please help me correct if I am wrong.

If k is a positive integer, what is the value of k?

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If k is a positive integer, what is the value of k?

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