If x is an integer, is x^3 divisible by 9?

(1) x^2 is divisible by 9.

(2) x^4 is divisible by 9.

Hi Bunuel, is it okay to reason stmt2 as below?

\(x^4\) is divisible by 9.
then either
a. x is divisible by 9 or
b. \(x^3\) is divisible by 9.

If a is true then b is also true.
if a is not true then b has to be true. therefore for \(x^4\) to be divisible by 9, \(x^3\) MUST be divisible by 9.
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Because we are told that x is an integer, while \(\sqrt{3}\) is not. Also, what does divisibility by \(3\sqrt{3}\) has to do with the question? We need to find whether x^3 divisible by 9.

Also, note two things:
1. Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers (ALL GMAT divisibility questions are limited to positive integers only).

2. On the GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that:
(i) \(a\) is an integer;
(ii) \(b\) is an integer;
(iii) \(\frac{a}{b}=integer\).

For more check [url=http://gmatclub.com/forum/divisibility-multiples-factors-tips-and-hints-174998.html]Divisibility/Multiples/Factors: Tips and hints
[/url].

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Answer: D

from 1, x^2 = 9n
multiplying both sides by x, we get
x*x^2 = x*9n
or x^3 = 9xn
let xn = p
then x^3 = 9p
i.e. x^3 is divisible by 9

Hence 1 is sufficient

from 2,
x^4 = 9m
now, since 9m should be something to the power of 4, there are only limited values of m

ex : 9 * [3*3] = 3^4 i.e. x=3
or 9*[ -3 * -3 ] = -3*-3*-3 *-3 = -3^4 i.e. x=-3
or 9*[9*81] = 3*3 * 3*3 *9*9 = 3*3*3*3*3*3*3*3 = 3^8 = (3^2)^4 i.e x = 9

in each case is either 3, -3 or a power of either of the two. hence 2 is also sufficient

and the answer is D