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

 It is currently 18 Aug 2018, 03:53

### 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

# If xyz < 0, is x < 0 ?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47981
If xyz < 0, is x < 0 ?  [#permalink]

### Show Tags

27 Jun 2014, 10:21
2
15
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:24) correct 34% (01:14) wrong based on 415 sessions

### HideShow timer Statistics

If $$xyz < 0$$, is $$x < 0$$?

(1) $$x - y < 0$$

(2) $$x - z < 0$$

Kudos for a correct solution.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 47981
If xyz < 0, is x < 0 ?  [#permalink]

### Show Tags

27 Jun 2014, 10:22
1
5
SOLUTION

If $$xyz < 0$$, is $$x < 0$$?

$$xyz < 0$$ implies that either all three unknowns are negative or one is negative and the remaining two are positive.

(1) $$x - y < 0$$. This means that $$x < y$$. Could $$x$$ be negative? Yes, if $$x$$, $$y$$, and $$z$$ are negative. Could $$x$$ be positive? Yes, if $$x$$ and $$y$$ are positive and $$z$$ is negative. Not sufficient.

(2) $$x - z < 0$$. Basically the same here. We have that $$x < z$$. Could $$x$$ be negative? Yes, if $$x$$, $$y$$, and $$z$$ are negative. Could $$x$$ be positive? Yes, if $$x$$ and $$z$$ are positive and $$y$$ is negative. Not sufficient.

(1)+(2) We have that $$x < y$$ and $$x < z$$. Could $$x$$ be positive? No, because if $$x$$ is positive then from $$x < y$$ and $$x < z$$, both $$y$$ and $$z$$ must be positive but in this case $$xyz$$ will be positive not negative as given in the stem. Therefore $$x$$ must be negative. Sufficient.

Try NEW inequalities PS question.
_________________
##### General Discussion
Director
Joined: 25 Apr 2012
Posts: 701
Location: India
GPA: 3.21
Re: If xyz < 0, is x < 0 ?  [#permalink]

### Show Tags

27 Jun 2014, 10:43
2
If $$xyz < 0$$, is $$x < 0$$?

(1) $$x - y < 0$$

(2) $$x - z < 0$$

Attachment:

Untitled.png [ 4.29 KiB | Viewed 4363 times ]

Product of 3 nos can be negative if one of them is negative and other two nos are of the same sign or if all the nos are negative.

Case 1:x=-1,y=2,z=100
Case 2:x=1,z=2,y=-100
Case 3 x=1,y=3,z=-100
Case 4:x=-100,y=-2,z=-1

Consider St 1 says : x<y...So out of the table following cases are possible

Cases 1,3 and 4: For cases 1,4 we see that x<0 but case 3 x>0...So St 1 is insufficient

St 2 says x<z, so we have case 1,2 and 4
If it is case 1 and 4 then x<0 and answer to our question is yes but if it case 2 then answer is no

Combining we see that for both statements Case and 1 and 4 are applicable and for these cases x<0.

Ans is C
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Manager
Joined: 21 Sep 2012
Posts: 218
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Re: If xyz < 0, is x < 0 ?  [#permalink]

### Show Tags

28 Jun 2014, 01:31
1
1
Bunuel wrote:

If $$xyz < 0$$, is $$x < 0$$?

(1) $$x - y < 0$$

(2) $$x - z < 0$$

Kudos for a correct solution.

Statement one :

x-y<0
x<y

Here x can take value of a positive or a negative number. x can be a negative number and y and z can be positive number or x and y can be positive numbers and z can take a negative value. Statement is insufficient.

Statement two:
x-z<0
x<z

This statement is insufficient to determine sign of x. x,y and z all can be negative or x and z can take positive values and y can be a negative number.

Both statements combined together, x is the smallest number and product of x,y and z is a negative value. so x has to be a negative number. Either x is a negative number and y and z are positive or all the three numbers are negative. In both the cases, x is a negative number. Hence Ans=C
Intern
Joined: 22 Jun 2013
Posts: 37
Re: If xyz < 0, is x < 0 ?  [#permalink]

### Show Tags

28 Jun 2014, 05:53
2

x.y.z < 0

This is possible when :
All 3 (x,y,z) are <0
OR
One of x,y,z < 0

1.
x-y<0
-> x<y
Both x & y can be positive OR x can be negative
Cannot say anything

2.
x-z<0
-> x<z
Again, Both x & z can be positive OR x can be negative
Cannot say anything

1+2
On combining x<y & x<z
This means x is the smallest of all three
therefore it must be negative for x.y.z <0 to hold true.
Math Expert
Joined: 02 Sep 2009
Posts: 47981
Re: If xyz < 0, is x < 0 ?  [#permalink]

### Show Tags

29 Jun 2014, 12:30
SOLUTION

If $$xyz < 0$$, is $$x < 0$$?

$$xyz < 0$$ implies that either all three unknowns are negative or one is negative and the remaining two are positive.

(1) $$x - y < 0$$. This means that $$x < y$$. Could $$x$$ be negative? Yes, if $$x$$, $$y$$, and $$z$$ are negative. Could $$x$$ be positive? Yes, if $$x$$ and $$y$$ are positive and $$z$$ is negative. Not sufficient.

(2) $$x - z < 0$$. Basically the same here. We have that $$x < z$$. Could $$x$$ be negative? Yes, if $$x$$, $$y$$, and $$z$$ are negative. Could $$x$$ be positive? Yes, if $$x$$ and $$z$$ are positive and $$y$$ is negative. Not sufficient.

(1)+(2) We have that $$x < y$$ and $$x < z$$. Could $$x$$ be positive? No, because if $$x$$ is positive then from $$x < y$$ and $$x < z$$, both $$y$$ and $$z$$ must be positive but in this case $$xyz$$ will be positive not negative as given in the stem. Therefore $$x$$ must be negative. Sufficient.

Kudos points given to correct solutions above.

Try NEW inequalities PS question.
_________________
Manager
Joined: 08 Apr 2013
Posts: 211
Re: If xyz < 0, is x < 0 ?  [#permalink]

### Show Tags

13 Jul 2014, 01:32
MAKE A line number to see that the matter is easy
_________________

If anyone in this gmat forum is in England,Britain, pls, email to me, (thanghnvn@gmail.com) . I have some questions and need your advise. Thank a lot.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6028
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If xyz < 0, is x < 0 ?  [#permalink]

### Show Tags

17 Nov 2015, 10:21
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If xyz<0 , is x<0 ?

(1) x−y<0

(2) x−z<0

There are 3 variables (x,y,z) and one equation (xyz<0) in the original condition, 2 equations in the given conditions, so there is high chance (C) will be our answer.
Looking at the conditions together,
x<y and x<z.
If x>0, then yz>0, so this does not satisfy xyz<0 (out of scope). Hence x has to be x<0 . This answers the question 'yes' and is therefore sufficient, making the answer (C).

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Non-Human User
Joined: 09 Sep 2013
Posts: 7755
Re: If xyz < 0, is x < 0 ?  [#permalink]

### Show Tags

23 Jul 2018, 07:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If xyz < 0, is x < 0 ? &nbs [#permalink] 23 Jul 2018, 07:28
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®.