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

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Math Expert
Joined: 02 Sep 2009
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If k is a positive integer, what is the value of k? [#permalink]

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03 Apr 2018, 21:58
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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.

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Joined: 16 Sep 2016
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Re: If k is a positive integer, what is the value of k? [#permalink]

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03 Apr 2018, 22:18
Bunuel wrote:
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.

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,
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Joined: 26 Feb 2016
Posts: 2933
Location: India
GPA: 3.12
Re: If k is a positive integer, what is the value of k? [#permalink]

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03 Apr 2018, 23:32
Bunuel wrote:
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.

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,

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)
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Re: If k is a positive integer, what is the value of k? [#permalink]

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04 Apr 2018, 00:42
pushpitkc wrote:
Bunuel wrote:
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.

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,

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)

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

1+1=2 so even, k can be 2 and 3
insufficient E
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Re: If k is a positive integer, what is the value of k? [#permalink]

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04 Apr 2018, 00:48
kunalcvrce wrote:

Hi even k=2,
factors are f=1,and2

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

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!
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Manager
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Location: India
Concentration: General Management, Marketing
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If k is a positive integer, what is the value of k? [#permalink]

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Updated on: 04 Apr 2018, 01:39
pushpitkc wrote:
kunalcvrce wrote:

Hi even k=2,
factors are f=1,and2

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

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!

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.

Originally posted by kunalcvrce on 04 Apr 2018, 01:02.
Last edited by kunalcvrce on 04 Apr 2018, 01:39, edited 2 times in total.
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If k is a positive integer, what is the value of k? [#permalink]

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04 Apr 2018, 01:03
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)
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Re: If k is a positive integer, what is the value of k? [#permalink]

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05 Apr 2018, 23:05
kunalcvrce wrote:
pushpitkc wrote:
kunalcvrce wrote:

Hi even k=2,
factors are f=1,and2

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

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!

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.

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.
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Joined: 27 Jul 2017
Posts: 52
Re: If k is a positive integer, what is the value of k? [#permalink]

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06 Apr 2018, 23:22
Bunuel wrote:
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.

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.

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Re: If k is a positive integer, what is the value of k?   [#permalink] 06 Apr 2018, 23:22
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