Question Pack 1 = If X is an integer greater than 1, is X eq

This topic has expert replies
User avatar
Legendary Member
Posts: 698
Joined: Tue Jul 21, 2015 12:12 am
Location: Noida, India
Thanked: 32 times
Followed by:26 members
GMAT Score:740
If X is an integer greater than 1, is X equal to the 12th power of an integer?

1) X is equal to the 3rd power of an integer
2) X is equal to the 4th power of an integer
R I C H A,
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Dec 07, 2016 6:49 pm
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Dec 08, 2016 9:20 pm
Try some small numbers to show that each statement alone is insufficient. (If x = 1, the answer is YES, if x = 2, the answer is NO.)

From there, we've got C or E.

If we know that x = m³ and and that x = n�, we can say that m³ = n�. That means that whatever x is, each of its prime factors can be broken up into THREES (one for each cube root) and into FOURS (one for each fourth root).

Since x's # of each prime factor is a multiple of 3 and of 4, it must be a multiple of the LCM of 3 and 4, or a multiple of 12. So x has 12 of each of its prime factors, and MUST be a twelfth power.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Thu Dec 08, 2016 10:48 pm
richachampion wrote:If X is an integer greater than 1, is X equal to the 12th power of an integer?

1) X is equal to the 3rd power of an integer
2) X is equal to the 4th power of an integer
It is clear that each statement is insufficient.

Now combine the two.

S1: Say, X = K^(1/3) => X^3 = K; K is an integer;

S2: Say, X = M^(1/4) => X^4 = M; M is an integer;

=> X^3 * X^4 = K*M = N; N is an integer (Product of two integers, K and M is integer)

=> K^12 = N

=> X = N^(1/12)

Hope this helps!

-Jay

_________________
Manhattan Review GMAT Prep

Locations: New York | Mumbai | Ho Chi Minh City | Budapest | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Legendary Member
Posts: 712
Joined: Fri Sep 25, 2015 4:39 am
Thanked: 14 times
Followed by:5 members

by Mo2men » Sat Dec 10, 2016 12:57 am
Jay@ManhattanReview wrote:
richachampion wrote:If X is an integer greater than 1, is X equal to the 12th power of an integer?

1) X is equal to the 3rd power of an integer
2) X is equal to the 4th power of an integer
It is clear that each statement is insufficient.

Now combine the two.

S1: Say, X = K^(1/3) => X^3 = K; K is an integer;

S2: Say, X = M^(1/4) => X^4 = M; M is an integer;

=> X^3 * X^4 = K*M = N; N is an integer (Product of two integers, K and M is integer)

=> K^12 = N

=> X = N^(1/12)

You have interpreted each statement as 3rd root and 4th root, while it is should be power.

x = K^3

x= M^4

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Dec 10, 2016 3:09 am
richachampion wrote:If X is an integer greater than 1, is X equal to the 12th power of an integer?

1) X is equal to the 3rd power of an integer
2) X is equal to the 4th power of an integer
Test an EASY CASE.
Test POWERS OF 2.

Statement 1:
x = 2³, 2�, 2�, 2¹²...
If x = 2³, then x is NOT equal to the 12th power of an integer.
If x = 2¹², then x IS equal to the 12th power of an integer.
INSUFFICIENT.

Statement 2:
x = 2�, 2�, 2¹²...
If x = 2�, then x is NOT equal to the 12th power of an integer.
If x = 2¹², then x IS equal to the 12th power of an integer.
INSUFFICIENT.

Statements combined:
The smallest value common to both the red list and the blue list is 2¹², which is the 12th power of an integer.
If we extend the two lists, we get:
x = 2¹�, 2¹�, 2²¹, 2²�...
x = 2¹�, 2²�, 2²�...
The next value common to both lists is 2²� = 4¹², which is the 12th power of an integer.
Implication:
To satisfy both statements, x must be the 12th power of an integer.
SUFFICIENT.

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7223
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Sat Dec 10, 2016 4:35 am
richachampion wrote:If X is an integer greater than 1, is X equal to the 12th power of an integer?

1) X is equal to the 3rd power of an integer
2) X is equal to the 4th power of an integer
We are given that X is an integer greater than 1 and must determine whether X is equal to the 12th power of an integer.

Statement One Alone:

X is equal to the 3rd power of an integer.

Using the information in statement one, we cannot determine whether X is equal to the 12th power of an integer. For example, if X = 8 = 2^3, then it's not equal to the 12th power of an integer. However, if X = (2^4)^3 = 2^12, then it is equal to the 12th power of an integer. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

X is equal to the 4th power of an integer

Using the information in statement two, we cannot determine whether X is equal to the 12th power of an integer. For example, if X = 16 = 2^4, then it's not equal to the 12th power of an integer. However, if X = (2^3)^4 = 2^12, then it is equal to the 12th power of an integer. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, we know that X is equal to the 3rd power of an integer and that X is also equal to the 4th power of some other integer. Let's represent X as a^3 where a is an integer > 1. Since a^3 is also a fourth power, the fourth root of a^3 is an integer. The only way this could happen is if a is also the fourth power of an integer; in other words, a by itself is a fourth power, say a = b^4 where b is an integer > 1.

Thus, X = a^3 = (b^4)^3 = b^12. Therefore, X is equal to the 12th power of an integer.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Sun Dec 11, 2016 9:32 pm
Mo2men wrote:
Jay@ManhattanReview wrote:
richachampion wrote:If X is an integer greater than 1, is X equal to the 12th power of an integer?

1) X is equal to the 3rd power of an integer
2) X is equal to the 4th power of an integer
It is clear that each statement is insufficient.

Now combine the two.

S1: Say, X = K^(1/3) => X^3 = K; K is an integer;

S2: Say, X = M^(1/4) => X^4 = M; M is an integer;

=> X^3 * X^4 = K*M = N; N is an integer (Product of two integers, K and M is integer)

=> K^12 = N

=> X = N^(1/12)

You have interpreted each statement as 3rd root and 4th root, while it is should be power.

x = K^3

x= M^4
You rightly pointed out. Pl. read '^(1/3)' as '^3', '^(1/4)' as '^4', and '^(1/12)' as '^12', then the explanation is good to go. I liked Mitch's simplistic approach. It's better.