Last visit was: 26 Apr 2024, 15:49 It is currently 26 Apr 2024, 15:49

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Difficulty: 555-605 Levelx   Number Propertiesx                              
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619238 [34]
Given Kudos: 81609
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619238 [11]
Given Kudos: 81609
Send PM
General Discussion
User avatar
Manager
Manager
Joined: 21 Mar 2011
Status:GMATting
Posts: 96
Own Kudos [?]: 279 [2]
Given Kudos: 104
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Send PM
User avatar
Manager
Manager
Joined: 25 Oct 2013
Posts: 115
Own Kudos [?]: 166 [3]
Given Kudos: 55
Send PM
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
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.
Current Student
Joined: 04 Sep 2017
Status:Booth 1Y
Posts: 278
Own Kudos [?]: 1162 [0]
Given Kudos: 228
Location: United States (IL)
Concentration: Technology, Leadership
GMAT 1: 690 Q44 V41
GMAT 2: 730 Q50 V38
GPA: 3.62
WE:Sales (Computer Software)
Send PM
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
Bunuel wrote:
dzodzo85 wrote:
If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?

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

Could someone kindly render a more easily understood explanation than that found in the Quantitative Review 2nd Edition. It would be really appreciated.


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.

Answer: E.

Hope it helps.


For (1)+(2), how could R be positive? Isn't T automatically positive because it is T^4?

Statement 1 says RT is negative, so I assumed that R has to be negative. I'm sure this is an elementary question, but can you please show me an example of how T^4 could be negative?

Thanks in advance.
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619238 [0]
Given Kudos: 81609
Send PM
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
Expert Reply
msurls wrote:
Bunuel wrote:
dzodzo85 wrote:
If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?

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

Could someone kindly render a more easily understood explanation than that found in the Quantitative Review 2nd Edition. It would be really appreciated.


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.

Answer: E.

Hope it helps.


For (1)+(2), how could R be positive? Isn't T automatically positive because it is T^4?

Statement 1 says RT is negative, so I assumed that R has to be negative. I'm sure this is an elementary question, but can you please show me an example of how T^4 could be negative?

Thanks in advance.


t^4 cannot be negative. A number in an even power is always non-negative, so 0 or positive. Since we are told that t is nonzero, then t^4 is positive only. But t itself could be positive as well as negative. For example, t^4 = 16 = positive, t = 2 or t = -2.
Manager
Manager
Joined: 09 Jun 2019
Posts: 77
Own Kudos [?]: 46 [0]
Given Kudos: 315
GMAT 1: 570 Q42 V29
Send PM
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
HiBunuel
I understood the solution but could you expand on this a little more?
Quote:
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.


Just for improving my insight.

Thank you,
Dablu
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619238 [0]
Given Kudos: 81609
Send PM
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
Expert Reply
gurudabl wrote:
HiBunuel
I understood the solution but could you expand on this a little more?
Quote:
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.


Just for improving my insight.

Thank you,
Dablu


If we were not told that given variables are nonzero, then r and s having the opposite signs would not be enough for r^5*s^3*t^4 to be negative. In that case, we should also check whether t is not 0, because even if r and s will have the opposite signs but t = 0, then r^5*s^3*t^4 =0, so it's not negative.

Hope it's clear.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 32689
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
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.
GMAT Club Bot
Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
Moderator:
Math Expert
92948 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne