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For how many different positive integers n is a divisor of n

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For how many different positive integers n is a divisor of n [#permalink] New post 27 Oct 2010, 20:19
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For how many different positive integers n is a divisor of n^3 + 8?

A. None
B. One
C. Two
D. Three
E. Four
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 07:58, edited 1 time in total.
Renamed the topic and edited the question.
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Re: PS - Integers and divisors [#permalink] New post 27 Oct 2010, 20:25
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For how many different positive integers n is a divisor of n^3 + 8?

A. None
B. One
C. Two
D. Three
E. Four

The question asks for how many different positive integers n, n^3+8 is divisible by n.

Well the first term n^3 is divisible by n, the second term, 8, to be divisible by n, should be a factor of 8.

8=2^3 hence it has 3+1=4 factors: 1, 2, 4, and 8. Therefore n^3+8 is divisible by n for 4 values of n: 1, 2, 4, and 8.

Answer: E.
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Re: For how many different positive integers n is a divisor of n [#permalink] New post 09 Jul 2013, 08:00
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Re: For how many different positive integers n is a divisor of n [#permalink] New post 09 Jul 2013, 19:33
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n^3 + 8 = (n+2)(n^2-2n+4)
--> 2 divisors possible, plus 1 and n
we have 4 divisors.
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Re: PS - Integers and divisors [#permalink] New post 27 Oct 2013, 08:56
Bunuel wrote:
For how many different positive integers n is a divisor of n^3 + 8?

A. None
B. One
C. Two
D. Three
E. Four

The question asks for how many different positive integers n, n^3+8 is divisible by n.

Well the first term n^3 is divisible by n, the second term, 8, to be divisible by n, should be a factor of 8.

8=2^3 hence it has 3+1=4 factors: 1, 2, 4, and 8. Therefore n^3+8 is divisible by n for 4 values of n: 1, 2, 4, and 8.

Answer: E.


Bunnel at first I got the answer 4.

Then I plugged in n=3 and got zero. PS questions are supposed to have one right answer. Why are we using only 2 here ?
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Re: PS - Integers and divisors [#permalink] New post 27 Oct 2013, 23:24
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aakrity wrote:
Bunuel wrote:
For how many different positive integers n is a divisor of n^3 + 8?

A. None
B. One
C. Two
D. Three
E. Four

The question asks for how many different positive integers n, n^3+8 is divisible by n.

Well the first term n^3 is divisible by n, the second term, 8, to be divisible by n, should be a factor of 8.

8=2^3 hence it has 3+1=4 factors: 1, 2, 4, and 8. Therefore n^3+8 is divisible by n for 4 values of n: 1, 2, 4, and 8.

Answer: E.


Bunnel at first I got the answer 4.

Then I plugged in n=3 and got zero. PS questions are supposed to have one right answer. Why are we using only 2 here ?


You cannot pick arbitrary numbers here.

The question asks "for how many different positive integers n is a divisor of n^3 + 8", so for how many different n's \frac{n^3 + 8}{n}=integer.

Now, \frac{n^3 + 8}{n}=n^2+\frac{8}{n} to be an integer n must be a factor of 8. 8 has 4 factors, thus for 4 values of n \frac{n^3 + 8}{n} will be an integer: if n is 1, 2, 4, or 8.

Hope it's clear.
_________________

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: PS - Integers and divisors   [#permalink] 27 Oct 2013, 23:24
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For how many different positive integers n is a divisor of n

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