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# How many divisors does positive integer have? 1.The

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Joined: 13 Nov 2010
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How many divisors does positive integer have? 1.The [#permalink]

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25 Nov 2010, 19:39
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55% (hard)

Question Stats:

52% (00:43) correct 48% (00:36) wrong based on 29 sessions

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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.
[Reveal] Spoiler: OA

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25 Nov 2010, 21:01
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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27 Nov 2010, 08:16
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?

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27 Nov 2010, 08:39
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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.
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29 Nov 2010, 07:15
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

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29 Nov 2010, 07:23
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 divisors does positive integer have? 1.The [#permalink]

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30 Sep 2017, 08:39
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Re: How many divisors does positive integer have? 1.The   [#permalink] 30 Sep 2017, 08:39
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