Jinglander wrote:

can someone show me how to answer this without having to find actual number

If N is a positive integer, is 9 a factor of N?

1. 18 is a factor of N^2

2. 27 is a factor of N^3

Algebraic approach:

Given

n=integer>0. Q: is

n=9k (where

k is a positive integer)?

(1) 18 is a factor of n^2 -->

n^2=18p, where

p is a positive integer -->

n=3\sqrt{2p} --> as

n is an integer

\sqrt{2p} must be an integer too, taking the even integer values --> so basically

n=3\sqrt{2p} would be a multiple of 3*2=6, taking the following values: 6, 12, 18, ... So

n may or may not be a multiple of 9. Not sufficient.

(2) 27 is a factor of n^3 -->

n^3=27q, where

q is a positive integer -->

n=3\sqrt[3]{q} --> as

n is an integer

\sqrt[3]{q} must be an integer too --> so basically

n=3\sqrt[3]{q} would be just a multiple of 3: 3, 6, 9, 12, ... So

n may or may not be a multiple of 9. Not sufficient.

(1)+(2) From (1)

n is a positive multiple of 6 and from (2)

n is a positive multiple of 3 -->

n is a positive multiple of 6, so

n could be 6, 12, 18, ... Thus

n may or may not be a multiple of 9. Not sufficient.

Answer: E.

Also:

_________________

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.

What are GMAT Club Tests?

25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership