It is currently 24 Feb 2018, 21:26

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43898
If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

### Show Tags

07 Jan 2014, 04:20
Expert's post
13
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

62% (01:10) correct 38% (00:58) wrong based on 586 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?

(1) rt is negative
(2) s is negative

Data Sufficiency
Question: 24
Category: Arithmetic Properties of numbers
Page: 154
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 43898
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

### Show Tags

07 Jan 2014, 04:20
1
KUDOS
Expert's post
4
This post was
BOOKMARKED
SOLUTION

If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?

Since r, s, and t are nonzero integers then in order r^5*s^3*t^4 to be negative, only one condition should hold: r and s must have the opposite signs, in this case (r^5*s^3)*t^4=(negative)*(positive)=negative. Notice that if we were not told that given variables are nonzero then there would be one more condition that t must not be zero.

(1) rt is negative --> r and t have the opposite signs. Not sufficient, since no info about s.
(2) s is negative. Clearly insufficient.

(1)+(2) If r is positive then the answer will be YES (since r^5*s^3*t^4=positive*negative*positive=negative) but if r is negative then the answer will be NO (r^5*s^3*t^4=negative*negative*positive=positive). Not sufficient.

Similar questions to practice:
is-x-2-y-5-z-0-1-xz-y-0-2-y-z-98341.html
m21-q30-96613.html
is-x-7-y-2-z-3-0-1-yz-0-2-xz-95626.html
_________________
Current Student
Joined: 06 Sep 2013
Posts: 1954
Concentration: Finance
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

### Show Tags

07 Jan 2014, 09:03
1
KUDOS
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?

(1) rt is negative
(2) s is negative

Data Sufficiency
Question: 24
Category: Arithmetic Properties of numbers
Page: 154
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Has to be E.

We need to know if rs<0

Statement 1

Doesn't help much

Statement 2

Well, ok but what about the others?

Statement 1 and 2 together well let's see

If rt<0 and s<0 then

r<0 and t>0
or r>0 and t<0

We get to different values so Insuff

E

Cheers!
J
Manager
Status: GMATting
Joined: 21 Mar 2011
Posts: 108
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

### Show Tags

07 Jan 2014, 20:49
2
KUDOS
Since r,s and t are non-zero integers, they can be either +ve or -ve.
The question asks to find whether r^5*s^3*t^4 is negative?

Here, since t has an even power, we can conclude that the value of t^4 will be positive.
Therefore, we need to find out whether r*s<0 or which of the 2(r & s) has a negative value?

Statement (1):
rt<0; Either r<0 and t>0 or r>0 and t<0; No definite value of r could be found.
Also, no information about s is given; Insufficient.

Statement (2):
s<0 or s is negative;
Also, no information about r is given; Insufficient.

Combining both statements, we still cannot get a definite value for r(r could be < or >0); Insufficient

Current Student
Joined: 03 Feb 2013
Posts: 943
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE: Engineering (Computer Software)
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

### Show Tags

08 Jan 2014, 08:09
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?

(1) rt is negative
(2) s is negative

r^5*s^3*t^4 is -ve or +ve depends on value of r and s both as only they have odd powers. power of t is even, so should be always +ve.

Statement 1) rt is negative.
if r is -ve, t is +ve
if r is +ve, t is -ve.
We don't know the value of r and nothing is said about the value of s. Not sufficient.

Statement 2) s is -ve.
we don't know about r. Not sufficient.

Combining the two statements.
Still we don't know the sign of r, hence Option E)
_________________

Thanks,
Kinjal

My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961

Math Expert
Joined: 02 Sep 2009
Posts: 43898
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

### Show Tags

11 Jan 2014, 06:23
SOLUTION

If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?

Since r, s, and t are nonzero integers then in order r^5*s^3*t^4 to be negative, only one condition should hold: r and s must have the opposite signs, in this case (r^5*s^3)*t^4=(negative)*(positive)=negative. Notice that if we were not told that given variables are nonzero then there would be one more condition that t must not be zero.

(1) rt is negative --> r and t have the opposite signs. Not sufficient, since no info about s.
(2) s is negative. Clearly insufficient.

(1)+(2) If r is positive then the answer will be YES (since r^5*s^3*t^4=positive*negative*positive=negative) but if r is negative then the answer will be NO (r^5*s^3*t^4=negative*negative*positive=positive). Not sufficient.

Similar questions to practice:
is-x-2-y-5-z-0-1-xz-y-0-2-y-z-98341.html
m21-q30-96613.html
is-x-7-y-2-z-3-0-1-yz-0-2-xz-95626.html
_________________
Manager
Joined: 25 Oct 2013
Posts: 165
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

### Show Tags

02 Feb 2014, 02:31
3
KUDOS
$$r^5s^3t^4$$ can be re-written as $$(rt)^2(rst)^2*rs$$

Now $$(rt)^2$$ and $$(rst)^2$$ are always positive. The question boils down to IS rs negative?

Stmt1: rt is negative. Either r is -ve or t is -ve. No info about s. INSUFF
Stmt2: No info about r. INSUFF
Together: still no info about r, it could be +ve or -ve. E is the solution.
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Non-Human User
Joined: 09 Sep 2013
Posts: 13760
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

### Show Tags

17 Feb 2015, 19:58
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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13760
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

### Show Tags

08 Apr 2016, 04:34
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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13760
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

### Show Tags

11 Apr 2017, 15:52
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 r, s, and t are nonzero integers, is r^5*s^3*t^4 negative   [#permalink] 11 Apr 2017, 15:52
Display posts from previous: Sort by