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If n is an integer, then n divisible by how many positive

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If n is an integer, then n divisible by how many positive [#permalink] New post 19 Feb 2011, 09:29
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If n is an integer, then n divisible by how many positive integers?

(1) n is the product of two different prime numbers.
(2) n and 2^3 are each divisible by the same number of positive integers.
[Reveal] Spoiler: OA

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Re: Dvisible [#permalink] New post 19 Feb 2011, 09:40
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Baten80 wrote:
If n is an integer, then n divisible by how many positive integers?
(1) n is the product of two different prime numbers.
(2) n and 2^3 are each divisible by the same number of positive integers.


Finding the Number of Factors of an Integer

First make prime factorization of an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.

The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: 450=2^1*3^2*5^2

Total number of factors of 450 including 1 and 450 itself is (1+1)*(2+1)*(2+1)=2*3*3=18 factors.
For more on number properties check: math-number-theory-88376.html

BACK TO THE ORIGINAL QUESTION:

If n is an integer, then n divisible by how many positive integers?

(1) n is the product of two different prime numbers --> n=ab, where a and b are primes, so # of factors is (1+1)(1+1)=4. Sufficient.

(2) n and 2^3 are each divisible by the same number of positive integers --> 2^3 has 4 different positive factors (1, 2, 4, and 8) so n has also 4. Sufficient.

Answer: D.
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if n is an integer, then n is divisible by how many positive [#permalink] New post 29 Jan 2013, 21:52
if n is an integer, then n is divisible by how many positive integers?

1) n is the product of two different integers
2) n and 2^3 are each divisible by the same number of positive integers.


Please provide detailed explanations. Thanks!
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Re: Dvisible [#permalink] New post 30 Jan 2013, 21:33
It took me just 15 seconds to solve this..
N is a product of 2 different prime nos.......then 1,n and dose two prime nos. are divisible by n ...hence 4 nos.
agen, 2^3 = 8, has 4 nos. from which it can be divided...agen n is divisible by 4 nos.
Hence, D
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Re: If n is an integer, then n divisible by how many positive [#permalink] New post 31 Jan 2013, 12:10
@ Fozzzy
Statement 1 - n is the product of two different integers . They may be 2*3 or 3*7 or any two integers. Since they yield different products. We cannot determine the # of factors for n. Hence Statement 1 - Insufficient.
Statement 2 - n and 2^3 are each divisible by the same number of positive integers. 2^3 = 8. Having 4 factors (1,2,4,8) . Since the statement says n and 8 are divisible by the same num of integers. n=4. Hence Statement 2 - Sufficient

Answer- B. 8-)
Hope this helps!
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if n is an integer then n is divisble by how many positive i [#permalink] New post 17 Jul 2013, 00:45
if n is an integer then n is divisble by how many positive integers?

1) n is the product of two different prime numbers.
2) n and 2^ {-3} are each divisible by the same number of positive integers


[Reveal] Spoiler:
Don't have OA. Please provide explanations! Thanks

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Re: if n is an integer then n is divisble by how many positive i [#permalink] New post 17 Jul 2013, 00:50
Expert's post
fozzzy wrote:
if n is an integer then n is divisble by how many positive integers?

1) n is the product of two different prime numbers.
2) n and 2^ {-3} are each divisible by the same number of positive integers


[Reveal] Spoiler:
Don't have OA. Please provide explanations! Thanks


Merging similar topics. Please refer to the solution above and ask if anything remains unclear.

P.S. You've posted this question before: if-n-is-an-integer-then-n-divisible-by-how-many-positive-109670.html#p1175381
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: if n is an integer then n is divisble by how many positive i   [#permalink] 17 Jul 2013, 00:50
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