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# How many factors does positive integer n have?

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Intern
Joined: 13 Nov 2010
Posts: 21
How many factors does positive integer n have?  [#permalink]

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25 Nov 2010, 18:39
1
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Difficulty:

55% (hard)

Question Stats:

67% (01:34) correct 33% (01:23) wrong based on 72 sessions

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How many factors does positive integer n have?

(1) The difference between the largest and the smallest factors of n is 21

(2) n + 1 has 2 factors

M24-36

How many divisors does positive integer have?

1.The difference between the largest and the smallest divisor of is 21
2. has 2 divisors

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
S1 is sufficient. The difference between the largest and the smallest divisor of . Thus, .

S2 is not sufficient. Consider and .

The correct answer is A. Does not make sense to me at all. In order for A to be true, it looks like we have to assume all the factors are 22 consecutive integers.
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Re: How many factors does positive integer n have?  [#permalink]

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25 Nov 2010, 20:01
1
yufenshi wrote:
How many divisors does positive integer have?

1.The difference between the largest and the smallest divisor of is 21
2. has 2 divisors

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
S1 is sufficient. The difference between the largest and the smallest divisor of . Thus, .

S2 is not sufficient. Consider and .

The correct answer is A. Does not make sense to me at all. In order for A to be true, it looks like we have to assume all the factors are 22 consecutive integers.

ANS: A
I am not sure if my approach is correct, but lets c...
(A) - the smallest divisor of a number is 1 and the largest divisor of the number is the number itself. Now, as per statement A, the number seems to be 22. Hence, we can find outhow many divisors 22 has. Sufficient
(B) - As you pointed out, its not sufficient.

hence, ANS:(A)

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Joined: 13 Nov 2010
Posts: 1
Re: How many factors does positive integer n have?  [#permalink]

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27 Nov 2010, 07:16
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?
Math Expert
Joined: 02 Sep 2009
Posts: 50627
How many factors does positive integer n have?  [#permalink]

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27 Nov 2010, 07:39
1
2
vvs8787 wrote:
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?

That's because yufenshi didn't post the whole question. Original question is:

How many factors does positive integer n have?

(1) The difference between the largest and the smallest factors of $$n$$ is 21. The largest factor of an integer is that integer itself and the smallest factor is 1. So, we are given that $$n-1=21$$ or $$n=22$$. 22 has 4 factors: 1, 2, 11, and 22. Sufficient.

(2) $$n+1$$ has 2 factors. This statement just says that $$n+1$$ is a prime number, so $$n$$ can be for example 2 ($$2+1=3$$) and have 2 factors or 6 ($$6+1=7$$) and have 4 factors. Not sufficient.

Hope it's clear.
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Re: How many factors does positive integer n have?  [#permalink]

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29 Nov 2010, 06:15
Bunuel wrote:
vvs8787 wrote:
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?

That's because yufenshi didn't post the whole question. Original question is:

How many positive divisors does positive integer N has got

(1) The difference between the largest and the smallest divisor of N is 21 --> the largest divisor of an integer is this integer itself and the smallest divisor is 1, so N-1=21 --> N=22 --> 22 has 4 factors. Sufficient.

(2) N+1 has 2 divisors --> just say that N+1 is a prime number, so N can be for example 2 (2+1=3) and have 2 factors or 6 (6+1=7) and have 4 factors. Not sufficient.

Hope it's clear.

from the statement 2 it is N has 2 divisors but you took N+1 has 2 divisors
pls explain this

Math Expert
Joined: 02 Sep 2009
Posts: 50627
Re: How many factors does positive integer n have?  [#permalink]

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29 Nov 2010, 06:23
anilnandyala wrote:
Bunuel wrote:
vvs8787 wrote:
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?

That's because yufenshi didn't post the whole question. Original question is:

How many positive divisors does positive integer N has got

(1) The difference between the largest and the smallest divisor of N is 21 --> the largest divisor of an integer is this integer itself and the smallest divisor is 1, so N-1=21 --> N=22 --> 22 has 4 factors. Sufficient.

(2) N+1 has 2 divisors --> just say that N+1 is a prime number, so N can be for example 2 (2+1=3) and have 2 factors or 6 (6+1=7) and have 4 factors. Not sufficient.

Hope it's clear.

from the statement 2 it is N has 2 divisors but you took N+1 has 2 divisors
pls explain this

I'm not sure understood your question.

Question is: what is the number of factors of N?

N+1 has 2 divisors means that N+1=prime;

Now, if N=2 then it has 2 factors (N+1=3=prime has two factors);
But if N=6 then it has 4 factors (N+1=7=prime has two factors).
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Re: How many factors does positive integer n have?  [#permalink]

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14 Nov 2017, 11:03
Bunuel wrote:
vvs8787 wrote:
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?

That's because yufenshi didn't post the whole question. Original question is:

How many positive divisors does positive integer N has got

(1) The difference between the largest and the smallest divisor of N is 21 --> the largest divisor of an integer is this integer itself and the smallest divisor is 1, so N-1=21 --> N=22 --> 22 has 4 factors. Sufficient.

(2) N+1 has 2 divisors --> just say that N+1 is a prime number, so N can be for example 2 (2+1=3) and have 2 factors or 6 (6+1=7) and have 4 factors. Not sufficient.

Hope it's clear.

Hi Bunuel, I have a question, when considering the divisors, do we have to consider negative divisors as well.
So accordingly the least divisor will be negative of the given value and the biggest divisor will be the number itself, then statement 1 becomes $$- x + 21 = x => x = 10.5$$ but x is an integer.

Thanks
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Re: How many factors does positive integer n have?  [#permalink]

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14 Nov 2017, 21:52
hellosanthosh2k2 wrote:
Bunuel wrote:
vvs8787 wrote:
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?

That's because yufenshi didn't post the whole question. Original question is:

How many positive divisors does positive integer N has got

(1) The difference between the largest and the smallest divisor of N is 21 --> the largest divisor of an integer is this integer itself and the smallest divisor is 1, so N-1=21 --> N=22 --> 22 has 4 factors. Sufficient.

(2) N+1 has 2 divisors --> just say that N+1 is a prime number, so N can be for example 2 (2+1=3) and have 2 factors or 6 (6+1=7) and have 4 factors. Not sufficient.

Hope it's clear.

Hi Bunuel, I have a question, when considering the divisors, do we have to consider negative divisors as well.
So accordingly the least divisor will be negative of the given value and the biggest divisor will be the number itself, then statement 1 becomes $$- x + 21 = x => x = 10.5$$ but x is an integer.

Thanks

Hi Santhoshk

As far as I know, divisors in GMAT refers ONLY to positive divisors. So for example integer '6' has only 4 divisors - which are 1, 2, 3, 6.
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Re: How many factors does positive integer n have?  [#permalink]

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14 Nov 2017, 22:03
please correct the question, option 2 shall be "N+1 has 2 divisors" instead of "has 2 divisors"
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Joined: 02 Sep 2009
Posts: 50627
Re: How many factors does positive integer n have?  [#permalink]

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14 Nov 2017, 22:16
asthagupta wrote:
please correct the question, option 2 shall be "N+1 has 2 divisors" instead of "has 2 divisors"

Edited the question. Now, it's correct.
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Re: How many factors does positive integer n have? &nbs [#permalink] 14 Nov 2017, 22:16
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