Is x greater than 1?
(1) 1/x > −1
(2) 1/x^5 > 1/x^3
Source: GMATclub Test
OA:B
Is x greater than 1? .......Inequality question
This topic has expert replies
- GMATGuruNY
- 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
Statement 1:Mo2men wrote:Is x greater than 1?
(1) 1/x > −1
(2) 1/x^5 > 1/x^3
It's possible that x=2 (in which case the answer to the question stem is YES) or that x=1 (in which case the answer to the question stem is NO).
INSUFFICIENT.
Statement 2:
The inequality in Statement 2 implies that x is nonzero, since division by 0 is not allowed.
Implication:
We can multiply the inequality by ANY EVEN POWER OF X, since (nonzero number)^(even power) = positive.
Multiplying each side by x�, we get:
x�/x� > x�/x³
x > x³.
When a value greater than 1 is cubed, the result is GREATER then the original value.
Thus, no value greater than 1 will satisfy x > x³, implying that x is NOT greater than 1.
SUFFICIENT.
The correct answer is B.
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
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
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi Mo2men,
This question can be solved by TESTing VALUES.
We're asked if X is greater than 1. This is a YES/NO question.
1) 1/X > -1
IF...
X = 1, then 1/1 > -1 and the answer to the question is NO
X = 2, then 1/2 > -1 and the answer to the question is YES
Fact 1 is INSUFFICIENT
2) 1/(X^5) > 1/(X^3)
With this Fact, we can use Number Property patterns to determine the values of X that are NOT possible...
IF...
X = 1, then 1/1 and 1/1 are equal - and that does NOT fit what we were told, so X CANNOT be 1
IF... X > 1, then X^5 will be bigger than X^3 (try any value of X greater than 1 and you'll see). Thus, when X > 1, 1/(X^5) will be SMALLER than 1/(X^3) - and that does NOT fit what we were told, so X CANNOT be greater than1.
Since X cannot be greater than/equal to 1, the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
This question can be solved by TESTing VALUES.
We're asked if X is greater than 1. This is a YES/NO question.
1) 1/X > -1
IF...
X = 1, then 1/1 > -1 and the answer to the question is NO
X = 2, then 1/2 > -1 and the answer to the question is YES
Fact 1 is INSUFFICIENT
2) 1/(X^5) > 1/(X^3)
With this Fact, we can use Number Property patterns to determine the values of X that are NOT possible...
IF...
X = 1, then 1/1 and 1/1 are equal - and that does NOT fit what we were told, so X CANNOT be 1
IF... X > 1, then X^5 will be bigger than X^3 (try any value of X greater than 1 and you'll see). Thus, when X > 1, 1/(X^5) will be SMALLER than 1/(X^3) - and that does NOT fit what we were told, so X CANNOT be greater than1.
Since X cannot be greater than/equal to 1, the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich