Is x<0?
1) x^5 < 0.
2) x^5 + x + 1 = 0.
The OA is the option D.
How can I get an answer from the second statement? Please, I need a clarification here. <i class="em em-cry"></i>
Is x<0?
This topic has expert replies
-
- Legendary Member
- Posts: 2898
- Joined: Thu Sep 07, 2017 2:49 pm
- Thanked: 6 times
- Followed by:5 members
Hello Vjesus12.
Let's take a look at your question.
We have to say if x<0 or not.
First statement
Second statement
Therefore, this statement is sufficient.
In conclusion, each statement alone is sufficient. The answer is the option D.
I hope it helps you. <i class="em em-smiley"></i>
Let's take a look at your question.
We have to say if x<0 or not.
First statement
Since the power is an odd number, then it implies that x will also have the same sign, so x<0. Therefore, this statement is sufficient.1) x^5 < 0.
Second statement
This equation will lead us to $$x^5+x+1=0$$ $$x^5+x=-1$$ $$x\left(x^4+1\right)=-1 $$ $$x\left(x^4+1\right)=negative\ number .$$ Now, x^4+1 is always positive, so it implies that x must be negative, that is to say, x<0.2) x^5 + x + 1 = 0.
Therefore, this statement is sufficient.
In conclusion, each statement alone is sufficient. The answer is the option D.
I hope it helps you. <i class="em em-smiley"></i>
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: Is x<0?VJesus12 wrote:Is x<0?
1) x^5 < 0.
2) x^5 + x + 1 = 0.
Key Concept: ODD exponents preserve the sign of the base.
In other words, POSITIVE^ODD = POSITIVE and NEGATIVE^ODD = NEGATIVE
Statement 1: x^5 < 0
This is telling us that x^5 = NEGATIVE
So, it must be the case that x is NEGATIVE
So, the answer to the target question is YES, it is definitely the case that x < 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x^5 + x + 1 = 0
Subtract 1 from both sides to get: x^5 + x = -1
Applying the above concept, we know that x^5 and x share the same sign.
That is, EITHER x^5 and x are both positive, OR x^5 and x are both negative
However, in order for the equation x^5 + x = -1 to hold true, it must be the case that x^5 and x are both negative
So, the answer to the target question is YES, it is definitely the case that x < 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Hi VJesus12,VJesus12 wrote:Is x<0?
1) x^5 < 0.
2) x^5 + x + 1 = 0.
How can I get an answer from the second statement? Please, I need a clarification here. <i class="em em-cry"></i>
x is a real number, therefore the trichotomy law applies to it: x is positive, x is zero or x is negative, and only one of these 3 possibilities occurs.
Now let´s consider statement (2) :
x is not zero (because 0^5 + 0 +1 would be equal to 1, not 0)
x is not positive (otherwise x^5 + x +1 would be greater than 1, not 0) , hence...
x is negative!
The above follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
Statement One Alone:VJesus12 wrote:Is x<0?
1) x^5 < 0.
2) x^5 + x + 1 = 0.
x^5 < 0
When a negative number is raised to an odd integer exponent, the result is negative. Thus, the only way for x^5 to be less than 0 is if x is less than 0. Statement one is sufficient.
Statement Two Alone:
x^5 + x + 1 = 0
Let's re-express the given equation as x^5 + x = x(x^4 + 1) = -1. Since x^4 + 1 is nonnegative, that the only way for this to be true is if x is a negative number. Statement two is also sufficient.
Answer: D
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews