GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Jul 2018, 16:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Is integer x negative?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 03 Aug 2010
Posts: 101
GMAT Date: 08-08-2011

### Show Tags

27 Apr 2011, 16:05
1
3
00:00

Difficulty:

65% (hard)

Question Stats:

44% (00:45) correct 56% (00:39) wrong based on 134 sessions

### HideShow timer Statistics

Is integer x negative?

(1) $$x^2 = -5x$$
(2) $$|x| = -x$$
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1899
Re: Is integer x negative? [#permalink]

### Show Tags

27 Apr 2011, 16:59
1
Yalephd wrote:
Is integer x negative

(1) $$X^2 = -5x$$
(2) $$|X| = -X$$

Sol:

Q: Is x<0?
1. $$X^2=-5x$$. It looks like a trick to use block "X" and small "x". The expression is equivalent to $$X^2=-5z$$.
"x"(small x) may be 0 or -ve.
Not Sufficient.

2. $$|X|=-X$$
This expression will hold good for any $$X \le 0$$
X can be 0 or -ve.
Not Sufficient.

Combining both;
X can be 0 or -ve.

Not Sufficient.

Ans: "E"
_________________
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345
Re: Is integer x negative? [#permalink]

### Show Tags

27 Apr 2011, 17:16
1
1
fluke wrote:

1. $$X^2=-5x$$. It looks like a trick to use block "X" and small "x".

I'd bet that was just a typo - I'm sure the 'X' is supposed to be the same as the 'x'. The real GMAT would never mix capital and small letters in the same equation, at any rate. If that's the case, then from Statement 1 we know:

x^2 + 5x = 0
x(x + 5) = 0

and since one of our factors must equal zero, either x=0 or x=-5. So x might be negative, and might not be negative, and the statement is not sufficient. Similarly Statement 2 is true for x=0 and for any negative number, so the answer is E.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Manager
Joined: 03 Aug 2010
Posts: 101
GMAT Date: 08-08-2011
Re: Is integer x negative? [#permalink]

### Show Tags

27 Apr 2011, 17:17
Sorry about that. Didn't mean the have different cases of X. I'll revise the question:

Is integer $$X$$ negative

(1) $$X^2 = -5X$$
(2) $$|X| = -X$$

I'll leave the original as is so that your answer below makes sense for other viewers.

fluke wrote:
Yalephd wrote:
Is integer x negative

(1) $$X^2 = -5x$$
(2) $$|X| = -X$$

Sol:

Q: Is x<0?
1. $$X^2=-5x$$. It looks like a trick to use block "X" and small "x". The expression is equivalent to $$X^2=-5z$$.
"x"(small x) may be 0 or -ve.
Not Sufficient.

2. $$|X|=-X$$
This expression will hold good for any $$X \le 0$$
X can be 0 or -ve.
Not Sufficient.

Combining both;
X can be 0 or -ve.

Not Sufficient.

Ans: "E"
Manager
Joined: 09 Aug 2010
Posts: 100
Re: Is integer x negative? [#permalink]

### Show Tags

27 Apr 2011, 19:24
Yalephd wrote:
Is integer x negative

(1) $$X^2 = -5x$$
(2) $$|X| = -X$$

x<0?

(1) $$X^2 = -5x$$
$$X^2 + 5X = 0$$
$$(X)(X + 5) = 0$$
Solutions: x=0 OR x = -5
INSUFFICIENT

(2) $$|X| = -X$$
$$|X| + X = 0$$
Solutions: x=0 OR x<0
INSUFFICIENT

Therefore, E
Retired Moderator
Joined: 16 Nov 2010
Posts: 1468
Location: United States (IN)
Concentration: Strategy, Technology
Re: Is integer x negative? [#permalink]

### Show Tags

27 Apr 2011, 20:19
(1)

x^2 = -5x

so x can be 0 or -5

(2)

|X| = -X

X can be 0 or any -ve Integer

(1) and two are insufficient too,

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1134
Re: Is integer x negative? [#permalink]

### Show Tags

28 Apr 2011, 01:22
a gives x=0 or -5
b gives x-0 or <0

a+b gives essentially the same interpretation for values of x.

Hence E.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Director
Joined: 01 Feb 2011
Posts: 684
Re: Is integer x negative? [#permalink]

### Show Tags

30 Apr 2011, 12:50
i agree with fluke's explanation above

1. Not sufficient

x can be 0 or -ve

2. Not sufficient
x can be 0 or - ve

together still not sufficient as x can be 0 or <0

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2669
Re: Is integer x negative? [#permalink]

### Show Tags

12 Oct 2017, 18:15
Yalephd wrote:
Is integer x negative?

(1) $$x^2 = -5x$$
(2) $$|x| = -x$$

Statement One Alone:

x^2 = -5x

Simplifying the above equation, we have:

x^2 + 5x = 0

x(x + 5) = 0

x = 0 or x = -5

Thus, we do not know whether x is negative, since x could be 0. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

|x| = -x

The equation is true if and only if x is nonpositive. For example, if x = 0, then |0| = -0 since both sides can be simplified to be 0. If x = -1, then |-1| = -(-1) since both sides can be simplified to be 1. Since x can be either 0 or some negative number, statement two alone is not sufficient to answer the equation.

Statements One and Two Together:

From statement one, x could be 0 or -5. From statement two, x could be 0 or any negative number. Thus, we still don’t have enough information to determine if x is negative (since there is a possibility that x = 0).

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: Is integer x negative?   [#permalink] 12 Oct 2017, 18:15
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.